text:
\section{Introduction}
In the past two decades, psychological science has experienced an unprecedented replicability
crisis \citep{ioannidis2005most, pashler2012editors, opensciencecollaborationEstimatingReproducibilityPsychological2015a} which uncovered a number of problematic issues, including the adoption of Questionable Research Practices \citep{john2012measuring} and Questionable Measurement Practices \citep{flake2019measurement}, the reliance on excessively small samples \citep{button2013a}, the misuse of statistical techniques \citep{pastore2019potenza}, and the consequent misleading interpretation and communication of research findings \citep{wasserstein2019moving}.

Whereas some important reasons for the crisis are intrinsically related to psychology as a science \citep{chambers2019seven}, which lead to a renewed recommendation to rely on strong and well-formalized theories when planning a study, the use of statistical inference undoubtedly plays a key role. Specifically, the inferential approach most widely used in psychological research, namely Null Hypothesis Significance Testing (NHST), has been strongly criticized \citep{gigerenzer2004null, gelman2018failure, mcshane2019abandon}. As a consequence, several alternative approaches have received increasing attention, such as the use of Bayes Factors for hypotesing testing, and the use of both Frequentist and Bayesian methods to estimate the magnitude of the effect of interest with uncertainty (see \citeauthor{kruschke2018bayesian}, \citeyear{kruschke2018bayesian}, for a comprehensive historical review).

In the current paper we focus on an upstream, but still neglected issue that is unrelated to the approach chosen by the researcher, namely the need for statistical
reasoning, i.e., ``to reason about data, variation and chance'' \citep[p. 1253]{moore1998statistics}, during all phases of an empirical study. Our work was inspired by the famous statistician Ronald Fisher (1890 -1962), who stated that ``To consult the statistician after an experiment is finished is often merely to ask him to conduct a post mortem examination. He can perhaps say what the experiment died of'' \citep[p. 17]{fish}. Indeed, we argue that too often statistical inference is seen as an isolated procedure, which is limited to the analysis of data that have already been collected. In particular, we emphasize the non-trivial importance of making statistical considerations at the onset of a research project. Furthermore, we stress that although Fisher has ironically defined them a "post mortem examination", appropriate evaluations of published results can provide a relevant contribution to the progress of (psychological) science. The ultimate goal of this paper is to increase researchers' awareness by promoting active engagement when designing their research.

To achieve this goal, we build on and further develop an idea proposed by \citeauthor{gelmanPowerCalculationsAssessing2014a} (\citeyear{gelmanPowerCalculationsAssessing2014a}) called ``prospective and retrospective design analysis'', which is virtually absent in current
research practice. Specifically, to illustrate the benefits of design analysis to the widest possible audience, we use a familiar example in psychology  where the researcher is interested in analyzing the differences between two independent groups considering Cohen's $d$ \citep{cohenStatisticalPowerAnalysis1988} as an effect size measure.

In brief, the term \textit{design analysis} has been proposed by \citeauthor{gelmanPowerCalculationsAssessing2014a} (\citeyear{gelmanPowerCalculationsAssessing2014a}) as a broader definition of power analysis,  a concept that in the statistical literature traditionally indicates the determination of an appropriate sample size given prespecified levels of Type I and Type II errors and a "plausible effects size" \citep{gigerenzer2004null}. Indeed, a comprehensive design analysis should  also explicitly consider other inferential risks, including the exaggeration ratio (Type $M$ error, i.e., the predictable average overestimation of an effect that emerges as statistically significant) and the sign error (Type $S$ error, i.e., the risk that a statistically significant effect is estimated in the wrong direction). Notably, the estimation of these errors will require an effort from psychologists to introduce their expert knowledge and hypothesize what could be considered a ``plausible effect size''. As we will see later, a key aspect of design analysis is that it can be usefully carried out both in the planning phase of a study (i.e., prospective design analysis) and for the evaluation of studies that have already been conducted (i.e., retrospective design analysis).

Although the idea of design analysis could be developed within different inferential statistical approaches (e.g., Frequentist and Bayesian), in this paper we will rely on the Neyman-Pearson (N-P) approach \citep{pearson1928use} as opposed to the widely used NHST.
The rationale for this choice is that, in addition to other strengths, the N-P approach includes formalization of the \textit{Null Hypothesis} (i.e., the absence of an effect) like NHST, but also an explicit formalization of the \textit{Alternative Hypothesis} (i.e., the magnitude of the expected effect). For a more comprehensive description of the difference between N-P and NHST approaches, we refer the reader to Gigerenzer and colleagues (\citeyear{gigerenzer2004null}).

The remainder of this paper is structured as follows. In the next paragraphs, we will briefly review the main consequences of underpowered studies, discuss two relevant misconceptions concerning the interpretation of statistically significant results, and present a theoretical framework for design analysis including some clarifications regarding the concept of ``plausible effect size''. In Section \ref{pr_and}, through familiar examples within psychological research, the benefits of prospective and retrospective design analysis will be highlighted. In Section \ref{inc_unc}, we will propose a specific method that, by explicitly taking uncertainty issues into account, could further assist researchers in evaluating scientific findings. Subsequently, in Section \ref{an_ill}, a real case study will be presented and analyzed. Finally, in Section \ref{dis_and}, we will summarize potentials, further developments, and limitations of our proposal.

To increase readability and to ensure transparency of our work, we also include two appendices:
\begin{itemize}
\item \textbf{Appendix A}. A detailed description concerning the computation and the interpretation of Cohen's $d$.
\item \textbf{Appendix B}. A brief explanation of the ad-hoc R \citep{R2018} functions used in the paper. Details on how to reproduce the presented examples and on how to use our R functions for other purposes, are also provided. Furthermore, the source code of our functions, \texttt{functions\_PRDA.R},
is freely available at the Open Science Framework (OSF) at the link \url{https://osf.io/j8gsf/files/}.
\end{itemize}

\subsection{The consequences of underpowered studies in Psychology}

In 1962, Cohen raised attention towards a problem affecting psychological research that is still very much alive today \citep{cohen1962a}. Researchers seemed to ignore the statistical power of their studies - which is not considered in NHST  \citep{gigerenzer2004null} - with severe consequences for the robustness of their research findings.
In the N-P approach, the power of a statistical test is defined as the probability that the test has to reject the Null Hypothesis ($H_0$) when the Alternative Hypothesis ($H_1$) is true. One of the problems with underpowered studies is that the probability of finding an effect, if it actually exists, is low. More importantly, if a statistically significant result (i.e., ``in general'', when the observed $p-value$ is less than .05, and consequently $H_0$ is rejected; see, \citeauthor{wasserstein2019moving}, \citeyear{wasserstein2019moving}) is obtained in an underpowered study, the effect size associated with the observed $p-value$ might be ``too big to be true'' \citep{button2013a,gelmanPowerCalculationsAssessing2014a}.

This inflation of effect sizes can be seen when examining results of replication projects, which are usually planned to have higher power than the original studies. For example, the \citet[pp. 4-5]{opensciencecollaborationEstimatingReproducibilityPsychological2015a} reported that ``Overall, original study effect sizes ($M = 0.403$, $SD = 0.188$) were reliably larger than replication effect sizes ($M= 0.197$, $SD = 0.257$)'', and in the Social Science Replication Project \citep[p. 637]{camerer2018a}, ``the effect size of the replication was on average about 50\% of the original effect size''. These considerations contributed to the introduction in the literature of the term ``decline effect'', defined as ``the notion that science routinely observes effect sizes decrease over repeated replications for reasons that are still not well understood'' \citep[p. 579]{schooler2014a}.

Given that underpowered studies are widespread in psychology \citep{cohen1962a,sedlmeier1989a,maxwellPersistenceUnderpoweredStudies2004}, the shrinkage of effect-sizes in replications could be partially explained by the fallacy of ``what does not kill statistical significance makes it stronger'' \citep{loken2017a} and by the trap of the ``winner's curse'' \citep{button2013a}.

\subsection{The ``What Does Not Kill Statistical Significance Makes It Stronger'' fallacy and the ``Winner's Curse'' trap}

When a statistically significant result is obtained in an underpowered study (e.g., power = 40\%), in spite of the low probability of this event to happen, the result might be seen as even more remarkable. In fact, the researcher might think: ``If obtaining a statistically significant result is such a rare event, and in my experiment I obtained a statistically significant result, it must be a strong one''. This is called the ``what does not kill statistical significance makes it stronger'' fallacy \citep{loken2017a}. The reason why this is a fallacy lies in the fact that it is possible to obtain statistical significance because of many other factors different from the presence of a real effect. Researchers' degrees of freedom, large measurement errors, and small sample sizes all contribute to create noise in the data, therefore inflating the perhaps true, but small underlying effect. Then, if the procedure used to analyze those data is only focused on a threshold (like in NHST, with the conventional significance level of .05), the noise in the data allows to pass this threshold.

In these situations, the apparent win in terms of obtaining a statistically significant result is actually a loss, in that the ``the lucky'' scientist who makes a discovery is cursed by finding an inflated estimate of that effect \citep{button2013a}.
This is called the ``Winner's curse'', and Figure  \ref{fig:winners.course} shows an example. In this hypothetical situation, the researcher is interested in studying an effect that can plausibly be of small dimensions, e.g. Cohen's \textit{d} of .20 (see Appendix A, for a detailed description of the calculation and interpretation of Cohen's $d$). If s/he decides to compare two groups on the outcome variable of interest, using 33 participants per group (and performing a two-tailed test), s/he will never be able to simultaneously reject $H_0$ and find an effect close to what it is plausible in that research field (i.e., .20). In fact, in this underpowered study (i.e., based on a $d$ of .20, the actual power is only 13\%) all the effects falling in the ``rejection regions'' are higher than .49 or smaller than -.49, and .20 falls in the region where the decision rules state that you cannot reject $H_0$ under the NHST approach, or that you can accept $H_0$ under the N-P approach.

\begin{figure}[H]

{\centering \includegraphics[width=\maxwidth]{Figure1}

}

\caption[Exemplary case study]{The Winner's Curse. Hypothetical study where the plausible true effect size is small (Cohen's $d=.20$) and a two tailed independent samples t-test is performed with 33 people per group. In order to reject $H_0$, the researcher has to overestimate the underlying true effect which is indicated by the dashed vertical line. \hspace{\textwidth} Note: the rejection regions of $H_0$, given a significance level of .05, lie outside the vertical black lines} \label{fig:winners.course}

\end{figure}

\subsection{Beyond Power: The Design Analysis}

As we saw in the previous example, relying solely on the statistical significance of a result can lead to completely misleading conclusions. Indeed, researchers should take into account other relevant information, such as the hypothesized ``plausible effect size'' and the consequent power of the study. Furthermore, to assist researchers with evaluating the results of a study in a more comprehensive way, \citet{gelmanPowerCalculationsAssessing2014a} suggested to consider other two relevant types of errors in addition to the traditional Type I and Type II errors, namely Type $M$ and Type $S$ error (see also, \citealp{gelman2000type,lu2019note}). Specifically, Type $M$ [magnitude] error or \textit{exageration ratio} can be viewed as the the expected average overestimation of an effect that emerges as statistically significant, whereas Type $S$ [sign] error can be viewed as the probability of obtaining a statistically significant result in the opposite direction with respect to the sign of the hypothesized plausible effect size.

Based on this consideration, \citet{gelmanPowerCalculationsAssessing2014a} proposed the term \textit{"design analysis"} to broadly identify the analysis of studies' properties, such as their statistical power, Type $M$ and Type $S$ error. Moreover, as we shall see in the next paragraph, in design analysis particular emphasis is given on the elicitation and formalization of what can be considered a \textit{plausible effect size} (see also paragraph \ref{wha_doe}) for the study of interest. In this regard, it is important to make a clarification. Although \citet{gelmanPowerCalculationsAssessing2014a} developed design analysis relying on an unstandarized effect size measure (i.e., the difference between two means), in this paper we have adapted their method to deal with Cohen's $d$, a standardized measure of effect size that is more commonly used in psychology (see Appendix A for more details on the reasons that motivated this choice).

Given these premises, the steps to perform design analysis using Cohen's $d$ as a measure of effect size can be summarized in three steps:
\begin{enumerate}
\item A plausible effect size for the study of interest needs to be identified. Rather than focusing on data at hand or on noisy estimates of a single pilot study, the formalization of a plausibile effect size should be based on an extensive theoretical literature review and/or on meta-analyses. Moreover, specific tools (see for example \citealp{o2019expert, zando2019, zondervan2017application}) that allow to incorporate expert knowledge can also be considered to increase the validity of the plausible effect size elicitation process.\footnote{To obtain a more comprehensive picture of the inferential risks associated with their study, we suggest researchers to inspect different scenarios according to different plausible effect sizes and thus to perform more than one design analysis (see for example our application to a real case study in Section \ref{an_ill}).}
\item Based on the experimental design of the study of interest (in our case, a comparison between two independent groups), a large number of simulations (i.e., 100,000) will be performed according to the identified plausible effect size. This procedure serves to provide information about what to expect if the experiment was replicated an infinite number of times assuming the pre-identified plausible effect as true.
\item Given a fixed level of Type I error (e.g., .05), power, type $M$ and type $S$ error will be calculated. Specifically, power will be estimated as the ratio between the number of obtained significant results and the number of replicates (i.e., the higher the power, the higher the probability to detect the plausible effect). Type $M$ error will be estimated as the ratio between the mean of the absoulute values of the statistically significant replicated effect sizes and the plausible effect size. In this case, larger values indicate an expected large overestimation of the plausible effect size. Type $S$ error will be the ratio between the number of significant results with opposite sign with regard to the plausible effect size and the the total number of significant results. Put in other terms, type $S$ error estimates the probability of obtaining a significant result in the wrong direction.
\end{enumerate}

Although the procedure may seem complex to implement, at the link \url{https://osf.io/j8gsf/files/} (see also Appendix B) we made available some easy-to-use R functions that allow to perform different types of design analysis for less experienced users. The same functions will also be used in the examples and application presented in this paper.

To get a first idea of the benefits of design analysis, let us re-analyze the hypothetical study presented in Figure \ref{fig:winners.course}. Specifically, given a plausible effect size equal to $d=.20$ and a sample size of 33 participants per group, a design analysis will highlight the following information: power $= 13$\%, Type $M$ error $= 3.11$, and Type $S$ error $=2$\%.
Despite the low power, which shows that the study has only a 13\% probability to detect the plausible effect size, type $M$ error explicitly indicates that the expected overestimate of a result that will emerge as statistically significant is around 3 times the plausible effect. Furthermore, given a Type $S$ error of 2\%, there is also a non negligible probability of obtaining a significant result in the wrong direction. Overall, the results of design analysis clearly tell the researcher that the study of interest could provide very poor support to both the existence and non-existence of a plausible effect size.

Another advantage of design analysis, which will be better explored in the following sections, is that it can be effectively used in the planning phase of a study, i.e., \textit{prospective design analysis}, as well as in the evaluation of already obtained study results, i.e., \textit{retrospective design analysis}.
For example, in prospective design analysis, considerations concerning power, Type $M$, and Type $S$ error could assist researchers to decide the appropriate sample size for detecting the effect of interest (if it actually exists). In a retrospective design analysis, power, Type $M$ and Type $S$ error (always calculated using the theoretically plausible effect size) can be used to obtain information about the extent to which the results of the study could be exaggerated and/or in the wrong direction. Most importantly, we believe that, engaging in a retrospective design analysis helps researchers to recognize the role of
uncertainty and to make more reasonable statistical claims, especially in those cases at risk of falling in the aformentioned  ``Winner's Curse'' trap.

In conclusion, it is important to note that whatever the type of design analysis chosen (prospective or retrospective), the relationships between power, type $M$ error, and type $S$ error are the same. For illustrative purposes, these relationships are graphically displayed  as a function of sample size in Figure \ref{fig:pmsn}. A medium-to-small effect of $d=.35$ (i.e., a reasonable average effect size for a psychological study in the absence of other relevant information, see also Section \ref{an_ill}) was considered as a plausible effect size, and Type I error was set at .05.

As expected, power increases as sample size increases. Moreover, type $M$ and type $S$ error decrease as the size of the sample increases, with the latter showing a much steeper decrease.

From an applied perspective, issues with type $M$ and $S$ errors emerge with underpowered studies which are very common in psychological research. Indeed, as can be seen in Figure \ref{fig:pmsn}, for a power of 40\% (obtained with 48 participants per group), type $M$ error reaches the worrisome value of 1.58; for a power around 10\% (i.e., with 10 participants per group), even type $S$ error becomes relevant (around 3\%).

\begin{figure}[H]
    {\centering \includegraphics[width=\maxwidth]{Figure2}}

    \caption[Exemplary case study]{Relationship between sample size and Power, Type $M$ and Type $S$ for a Cohen's $d$ of .35 in an independent samples t-test. Type I error is set at .05.}\label{fig:pmsn}
\end{figure}

\subsection{What does ``Plausible Effect Size'' mean?} \label{wha_doe}
 \begin{quotation}
 \begin{flushright}
\textit{``Thinking hard about effect sizes is important for any school of statistical inference\\ {[i.e., Frequentist or Bayesian]}, but sadly a process often neglected.'' \\ \citet[p. 92]{dienesUnderstandingPsychologyScience2008}}
 \end{flushright}
 \end{quotation}

The main and most difficult point rests on deciding what could be considered a ``plausible effect size''. Although this might seem complex, usually studies are not developed in a void. Hypotheses are derived from theories that, if appropriately formalized in statistical terms, will increase the validity of the inferential process. Furthermore, researchers are commonly interested in knowing the size and direction of effects; as shown above, this corresponds to control for Type $M$ [magnitude] error and type $S$ [sign] error.

From an epistemological perspective, \citet{kruschke2013a} suggests an interesting distinction between \textit{strong theories} and \textit{weak theories}. Strong theories are those that try to make precise predictions and could be, in principle, more easily disconfirmed. For example, a strong theory could hypothesize a medium-sized positive correlation between two variables. In contrast, weak theories make broader predictions, such as the hypothesis that two variables are correlated without specifying the strength and direction of the correlation \citep{dienesUnderstandingPsychologyScience2008}. The former type allows many more research findings to disconfirm the hypothesis, whereas the latter type allows only the result of no correlation to disconfirm it. Specifically, following Karl Popper (1902–1994), it could be argued that theories explaining virtually everything and being hard to disconfirm risk to be out of the realm of science. Thus, scientific theories should provide at least a hint on the effect that is expected to be observed.

A challenging point is to establish the dimension of this effect. It might seem paradoxical that the researcher has to provide an estimate of the effect size before running the experiment, given that s/he will conduct the study exactly with the aim of finding what that estimate is. However, strong theories should allow to make such predictions, and the way in which science accumulates should provide increasing precision to these predictions.

In practice, it might be undesirable to simply take the estimate found in a pilot study or from a single previous study published in the literature as a ``plausible effect size''. In fact, the plausible effect size refers to what could be approximately the true value of the parameter in the population, whereas the results of pilots or single studies (especially if underpowered) are noisy estimates of that parameter.

In line with \citet{gelmanPowerCalculationsAssessing2014a}, we suggest to use information outside the data at hand, such as literature reviews and/or meta-analyses taking into account issues concernig publication bias \citep{borensteinIntroductionMetaanalysis2009}. Moreover, as stated in the previous paragraph, promising procedures to elicit and formalize expert knowledge should also be considered. It is important to note that, whatever the procedures, all assumptions that will lead to the identification of a plausible effect size must be communicated in a transparent manner, thus increasing the information provided by a study and ensuring more reasonable statistical claims related to the obtained results, whether they are significant or not.

As we have seen, the identification of a plausible effect size (or a series of plausible effect sizes to explore different scenarios) requires a big effort from the researcher. Indeed, we believe that this kind of reasoning can make a substantial contribution to the planning of robust and replicable studies, as well as to the efficent evaluation of obtained research findings.

To conclude, we leave the reader with the following question: ``All other conditions being equal, if you had to evaluate two studies of the same phenomenon, the first based on a formalization of the expected plausible effect sizes of interest that is as accurate as possible, and the second one in which the size of the effects of interest was not taken into account, the findings of which study would you believe the most?'' \citep{v2019}.

\section{Prospective and retrospective design analysis}\label{pr_and}

To highlight the benefits of design analysis, and to familiarize with the concepts of Type $M$ and Type $S$ errors, we will start from a simple example that is well known in psychological research, i.e., the comparison between the means of two independent groups\footnote{We remind the reader that Appendix B provides a brief explanation of the ad-hoc R functions used in the paper, details on how to reproduce the presented examples and on how to use our R functions for other purposes. The source code of our functions, \texttt{functions\_PRDA.R}, is available at the link \url{https://osf.io/j8gsf/files/}}.

In particular, the goal of our hypothetical case study is to evaluate the differences between two treatments that aim to improve a cognitive ability called $Y$. Both treatments have the same cost, but the first is innovative, whereas the second is traditional. To this end, the researchers recruit a sample of participants who are homogeneous with respect to prespecified relevant study variables (i.e., age, IQ \dots). Next, they randomly assign each participant to one of the two conditions (i.e., innovative vs traditional treatment). After the treatment phase is completed, the means of the two groups are compared.

\subsection{Prospective Design Analysis}

Before collecting data, the researchers decide to plan the appropriate sample size to test their hypotheses, namely that there is a difference between the means of $G1$ (the group to which the innovative treatment is administered) and $G2$ (the group to which the traditional treatment is administered) \textit{vs} there is no difference.

After an extensive literature review concerning studies theoretically comparable to their own, the researchers decide that a first reasonable effect size for the difference between the innovative and the traditional treatment could be considered equal to a Cohen's $d$ of .30 (see Appendix A for a detailed description of the calculation and interpretation of Cohen's $d$).  Due to the possible presence of publication bias \citep{borensteinIntroductionMetaanalysis2009}, which could lead to an overestimation of the effects of published studies, the researchers decide to be more conservative about the estimate of their plausible effect size. Thus, they decide to consider a Cohen's $d$ of .25. Eventually, all researchers agree that a Cohen's $d$ of .25 could also represent a clinically relevant effect in order to support the greater efficacy of the innovative treatment.

Based on the above considerations, the researchers start to plan the sample size for their study. First, they fix the Type I error at .05 and - based on commonly accepted suggestions from the psychological literature - fix the power at .80. Furthermore, to explicitly evaluate the inferential risks connected to their choices they calculate the associated Type $M$ and Type $S$ errors.

Using our \texttt{R} function \texttt{design\_analysis}, they obtain the following results:
\begin{knitrout}
\definecolor{shadecolor}{rgb}{1, 1, 1}\color{fgcolor}\begin{kframe}
\begin{verbatim}
> design_analysis( d=.25 , power=.80 )
     d  power      n  typeS  typeM
  0.25   0.80 252.00   0.00   1.13
\end{verbatim}
\end{kframe}
\end{knitrout}

Based on the results, to achieve a power of .80, a sample size of 252 for each group is needed (i.e., total sample size = 504). With this sample size, the risk of obtaining a statistically significant result in the wrong direction (Type $S$ error) is practically 0 and the expected exaggeration ratio (Type $M$ error) is  1.13. In other words, the expected overestimation related to effects that will emerge as statistically significant will be around 13\% of the hypothesized plausible effect size.

Although satisfied in terms of expected  type $S$ and type $M$ risks, the researchers are concerned about the economic feasibility of recruiting such a ``large'' number of subjects. After a long discussion, they decide to explore which inferential risks would result for a lower level of power, namely 60\%\footnote{Specifically,  we agree with \citet{gelman2019don} that an 80\% level of power should not be used as an automatic routine, and that requirements of 80\% power could encourage
researchers to exaggerate their effect sizes when planning sample size.}.

Using the function \texttt{design\_analysis}
\begin{knitrout}
\definecolor{shadecolor}{rgb}{1, 1, 1}\color{fgcolor}\begin{kframe}
\begin{verbatim}
> design_analysis( d=.25 , power=.60 )
     d  power      n  typeS  typeM
  0.25   0.60 158.00   0.00   1.30
\end{verbatim}
\end{kframe}
\end{knitrout}
they discover that: 1) the overall required sample size is considerably smaller (from 504 to 316 = 158 $\times$ 2), thus increasing economic feasability of the study; 2) the Type $S$ error remains negligible (0\%) ; 3) the exaggeration ratio considerably increases (from 1.13 to 1.30); thus, an effect that will emerge as statistically significant will be on average 130\% of the hypothesized plausible effect size.

The researchers now need to make a decision. Even though, from a merely statistical point of view, the optimal choice would be to consider a power of 80\%, other relevant aspects must be evaluated, such as the possibility to obtain additional funding, the practical implications of an expected overestimation of the plausible effect size, and the phase of the study (i.e., preliminary/exploratory, intermediate or final/confirmatory).

Whatever the decision, the researchers have to be aware of the inferential risks related to their choice. Moreover, when presenting the results, they have to be transparent and clear in communicating such risks, thus highlighting the uncertainty associated with their conclusions.

\subsection{Retrospective Design Analysis}

To illustrate the usefulness of retrospective design analysis, we refer to the example presented in the previous paragraph. However, we introduce three new scenarios which can be considered as representative of what commonly occurs during the research process:
\begin{itemize}
\item \textbf{Scenario 1 (S1): Evaluating sample size based on a single published study.}\footnote{Even though in this paper we strongly recommend not to plan sample size based on a single study, we propose this example to further emphasize the inferential risks associated with the information provided by a single underpowered study.}\\
Imagine that the researchers decide to plan their sample size based on a single published study in the phase of formalizing a plausible effect size, either because the published study presents relevant similarities with their own study, or because there are no other published studies available.\\
\textit{Question}: What type of inferential risks can be associated with this decision?\\
\textit{Issues}: Using a single study as a reference point without considering other sources (e.g., theoretical framework, experts' opinion, or a meta-analysis), especially when the study has a low sample size and/or the effect of interest is small, can lead to use an excessively optimistic estimate of the effect size to plan an appropriate sample size \citep{gelmanPowerCalculationsAssessing2014a}.
\item \textbf{Scenario 2 (S2): Difficulty in recruiting the planned number of research participants.}\\
Imagine that, due to unforeseen difficulties (e.g., insufficient funding), the researchers are not able to recruit the pre-planned number of participants as defined based on prospective design analysis.\\
\textit{Question}: How to evaluate the inferential risks associated with the new reduced sample size? How to communicate the obtained results?\\
\textit{Issues}:  Researchers are often tempted to evaluate the results of their study based on the observed effect size. This procedure, known as ``post-hoc power analysis'', has been strongly criticized and many statistical papers explicity advise against its use (see for example, \citealp{gelman2019don, goodman1994use}). Indeed, to evaluate the information provided by the obtained results, researchers should use the a piori plausible effect size, i.e., the one formalized before collecting their data.
\item \textbf{Scenario 3 (S3): No prospective design analysis because the number of participants is constrained.}\\
Imagine the number of participants involved in the study have specific characteristics which make it impossible to yield a large sample size, or that the type of treatment is particularly expensive and therefore it cannot be tested on a large sample. In this case, the only possibility is to recruit the largest possible number of participants.\\
\textit{Question}: What level of scientific quality can be provided by the results?\\
\textit{Issues}:  Although study's results can provide a useful contribution to the field, there are several associated inferential risks that the researchers need to communicate in a transparent and constructive way.
\end{itemize}

As we will see below, retrospective design analysis can be a useful tool to deal with the questions and the issues raised across all three scenarios.

For the sake of simplicity and without loss of generalizability, suppose that in each of the three scenarios the researchers obtained the same results (see Table \ref{tab:mean_comp}). \\

\begin{table}[h]
\centering
\caption{Comparison of the cognitive skill $Y$ between the two groups}
\label{tab:mean_comp}
\begin{tabular}{llccccc}
\hline
Group & $n$ & $M$ & $SD$ & $t(df)$ & $p$ & Cohen's $d$ ($95\% \, CI$) \\ \hline
Innovative treatment  & 31 & 114 & 16 & 3.496 (60) & 0.001 & .90 (0.38-1.43) \\
Traditional treatment & 31 & 100 & 15 &  &  & \\ \hline
\end{tabular}
\end{table}

At a first glance, the results indicate a statistically significant difference in favor of the innovative treatment (see Table \ref{tab:mean_comp}), with a large effect size (i.e., $d=0.90$). However, the 95\% confidence interval for Cohen's $d$ is extremely wide, suggesting that both medium-small (i.e., $d=0.38$) and very large (i.e., $d=1.43$) effects are consistent with the observed data.

A closer look indicates that the estimated effect size seems too large when compared with the initial guess of the researchers (i.e. $d=.25$). Furthermore,
an estimated $d$ of 0.90 seems, in general, implausibly large for a difference between two cognitive treatments (see also Appendix A). The latter interpretation seems to be also supported by the fact that the hypothesized plausible effect size is not even included in the estimated confidence interval.
Overall, in order to prevent the aforementioned ``Winner's Curse'' and ``What Does Not Kill Statistical Significance Makes It Stronger'' heuristics, results must be evaluated and eventually communicated with caution and skepticism.

To obtain a clearer picture of the inferential risks associated with the observed results, we can perform retrospective design analysis using $d=.25$ as plausible effect size and 31 participants per group as sample size:
\begin{knitrout}
\definecolor{shadecolor}{rgb}{1, 1, 1}\color{fgcolor}\begin{kframe}
\begin{verbatim}
> design_analysis( n=31, d=.25 )
power typeS typeM
 0.16  0.01  2.59
\end{verbatim}
\end{kframe}
\end{knitrout}

As can be seen, the power is markedly low (i.e, only 16\%) and the Type $M$ error even suggests an expected overestimation around two and a half times the plausible effect size. Lastly, the Type $S$ error, although small, indicates a 1\% risk of obtaining a significant result in the wrong direction (i.e., the traditional treatment is better than the innovative treatment). Let's see how this information could be helpful to deal with the three presented scenarios.

In S1, the researchers took a single noisy estimate as the plausible effect size from a study that found a ``big'' effect size (e.g., 0.90). The retrospective design analysis shows what happens if the plausible effect size is, in reality, much smaller (i.e., 0.25). Specifically, given the low power and the high level of Type $M$ error, researchers should definitely abandon the idea of planning their sample size based on a single published study. Furthermore, issues regarding the presence of Questionable Research Practices \citep{arrison2014responsible, john2012measuring}  and Questionable Measurement Practices \citep{flake2019measurement} in the considered published study must be at least explored. From an applied perspective, researchers should continue with a more comprehensive literature review  and/or consider the opportunity to use an effect size elicitation procedure based on experts' knowledge \citep{o2019expert, zondervan2017application}.\\

In S2, to check the robustness of their results, researchers might initially be tempted to conduct a power analysis based on their observed effect size ($d=0.90$). Acting in this way, they would obtain a completely misleading post-hoc power of 94\%. In contrast, the results of retrospective design analysis based on the a-priori plausible effect size ($d=.25$) highlight the high level of inferential risks related to the observed results. From an applicative perspective, researchers should be very skeptical about their observed results. A first option could be to replicate the study on an independent sample, perhaps asking for help from other colleagues in the field. In this case, the effort to recruit a larger sample could be well-justified based on the retrospective design analysis.

In S3, given the low power and the high level of Type $M$ error, results should be presented as merely descriptive by clearly explaining the uncertainty that characterizes them. Researchers should first reflect on the possibility of introducing improvements to the study protocol (i.e., improving the reliability of the study variables). As a last option, if improvements are not considered feasible, the researchers might consider not continuing their study.

Despite its advantages, we need to emphasize that design analysis should not be used as an \textit{automatic problem solver machine}: ``Let's pull out an effect size \dots let me see the correct sample size for my experiment''. In other words, to obtain reliable scientific conclusions there is no ``free lunch''. Rather, psychologists and statisticians have to work together, case by case, to obtain a reasonable effect size formalization and to evaluate the associated inferential risks. Furthermore, researchers are encouraged to explore different scenarios via sensitivity analysis (see, Section \ref{an_ill}) to better justify and optimize their choices.

\section{Incorporating uncertainty concerning effect size formalization in retrospective design analysis}\label{inc_unc}

As shown in the previous examples, a key point both in planning (i.e., prospective design analysis) and in evaluating (i.e., retrospective design analysis) a study is the formalization of a plausible effect size. Using a single value to summarize all external information and previous knowledge with respect to the study of interest can be considered an excessive simplification. Indeed, all uncertainty concerning the magnitude of the plausible effect size is not explicitly taken into consideration. In particular, the level of heterogeneity emerging from the examination of published results and/or from different opinions of the consulted experts is poorly formalized. The aim of this paragraph is to propose a method that can assist researchers to deal with these relevant issues. Specifically, we will focus on the evaluation of the results of a study (i.e., retroprospective design analysis).

Our method could be summarized in the following three steps: 1) defining a lower and an upper bound within which the plausible effect size can reasonably vary; 2) formalizing an appropriate probability distribution that reflects how the effect size is expected to vary; 3) conducting the associated analysis of Power, Type $M$ and Type $S$ error.

To illustrate the procedure, we take the study presented in Table \ref{tab:mean_comp} as reference. Let us now hypothesize that after a thorough evaluation of external sources, the researchers conclude that a plausible effect size could reasonably vary between .20 and .60 (instead of specifying a too simplistic single point value). It should be noted that, from a methodological perspective, the specification of a ``plausible interval'' can be considered an efficient and informative starting point to elicit the researchers' beliefs \citep{o2019expert}.

At this point, a first option could be to assume that, within the specified interval, all effect size values have the same probability of being true. This assumption can be easily formalized using a Uniform distribution as the one shown in Figure \ref{fig:dintervals} (left panel).

\begin{figure}[H]
    {\centering \includegraphics[width=\maxwidth]{Figure3}}

    \caption[Exemplary case study]{Different ways to formalize a plausible interval for the effect size $d$. In the left panel, a Uniform distribution with lower bound = .20 and upper bound = .60 is used. In the right panel, a doubly truncated Normal distribution with lower bound = .20, upper bound = .60, mean = .40 and standard deviation equal to $\frac{1}{6}$  the lenght of the interval (i.e., $\frac{.60-.20}{6}=.067$) is used.} \label{fig:dintervals}

\end{figure}

However, from an applied point of view  it is rare for the researcher to expect that all values within the specified interval have the same plausibility. Indeed, in general conditions, it is more reasonable to believe that values around the center of the interval (i.e., .40 in our case) are more plausible, and that their plausibility gradually decreases as they move away from the center. This expectation can be directly formalized in statistical terms  using the so-called ``doubly truncated Normal distribution''. On an intuitive level (for a more complete description see \citealp*{burkardt2014truncated}), the doubly truncated Normal distribution can be seen as a Normal distribution whose values are forced to vary within a specific closed interval. In case of the formalization of the plausible effect size, we propose to use a doubly truncated Normal distribution with the following parameters: a lower and an upper bound according to the prespecified plausible interval, a mean fixed at the center of the interval, and a standard deviation that reflects the hypothesized uncertainty around the center.  A standard deviation of $\frac{1}{10}$ the length of the chosen interval will produce a substantially Normal distribution. Higher values, like $\frac{1}{6}$ the length of the interval (see right panel of Figure \ref{fig:dintervals}) will lead to normal-like distributions with increased probability on the tails, thus reflecting greater uncertainty around the center.

Coming back to our example, suppose that the researchers want to evaluate the study of interest assuming a plausible interval for Cohen's  $d$ as the one represented in Figure \ref{fig:dintervals}.
Using the ad-hoc function \texttt{design\_est}\footnote{The idea behind this function is simple. First, we sample a large number (e.g., 100,000) of effect sizes $d$ from the probability distribution associated with the plausible interval. Then, for each $d$ we calculate power, type $M$ and type $S$ error based on the sample size of the two groups involved in the comparison, and by considering the centre of the plausible interval as the most plausible effect size. In this way, a distribution for each of the three indices is finally obtained. In the output of the function, the means of the three distributions are presented as a summary value. For additional details, see Appendix B, which also shows (in section `` design\_est'') how to obtain the expected distribution of power, Type $M$ and Type $S$ errors, given the plausible interval for $d$.} they will obtain the following information \color{black}:

\begin{knitrout}\small
\definecolor{shadecolor}{rgb}{1, 1, 1}\color{fgcolor}\begin{kframe}
\begin{verbatim}
> design_est(n1=31, n2=31, target_d_limits=c(.20,.60), distribution="normal")
power typeS typeM
 0.35  0.00  1.73
\end{verbatim}
\end{kframe}
\end{knitrout}
To summarize, this information suggests that the results of the study of interest  (see, Table \ref{tab:mean_comp}) should be taken very cautiously. Indeed, the expected power is low (35\%), and the expected overestimation of the most plausible effect size (i.e., $d = .40$) is around 73\%. Furthermore, it is important to note that the observed effect size of .90 falls abundantly outside the pre-specified plausible interval of .20 - .60, thus supporting the idea that the study of interest is clearly overestimating the actual magnitude of the effect.

In general, when the observed effect size falls outside the prespecified plausible interval, we can conclude that the observed study is not coherent with our theoretical expectations. On the other hand, we could also consider that our plausible interval may be unrealistic and/or poorly formalized.
In these situations, researchers should be transparent and propose possible explanations that could be very helpful in understanding the phenomenon under study.  Although this way of reasoning requires a notable effort, the information provided will lead to a more comprehensive inference than the one deriving from a simplistic dichotomous decision  (i.e., ``reject / do not reject'') typical of the NHST approach. Indeed, in this approach the hypotheses are poorly formalized,  and power, Type $M$ and Type $S$ errors are not even considered.

\section{An illustrative application to a case study} \label{an_ill}

To illustrate how design analysis could enhance inference in psychological research, we will consider a real case study. Specifically, we will focus on Study 2 of the published paper ``A functional basis for structure-seeking: Exposure to structure promotes willingness to engage in motivated action'' \citep{kay2014functional}.

The paper presents 5 studies arising from findings showing that human beings have a natural tendency to perceive structure in the surrounding world. Various social psychology theories propose plausible explanations which share a similar assumption that had never been tested before, that is, perceiving a structured world could increase people's willingness to make efforts and sacrifices towards their own goals. In Study 2, the authors decided to test this hypothesis by randomly assigning participants to two different conditions differing in the type of text they had to read. In the ``random'' condition, the text conveyed the idea that natural phenomena are unpredictable and random, whereas in the ``structure'' condition the phenomena were described as predictable and systematic. The outcome measure was the willingness to work towards a goal that each participant chose as their ``most important''. The expected result was that participants in the  ``structure'' condition would report a higher score in the measure of goal directed behavior than those in the ``random'' condition.

\vspace{1em}

\textbullet\ \textbf{Prospective design analysis}

As we saw in the previous paragraphs, before collecting data is fundamental to plan an appropriate sample size via prospective design analysis. In this case, given the relative novelty of Study 2, is hard to identify a single plausible value for the size of the effect of interest. Rather, it seems more reasonable to explore different scenarios according to different plausible effect sizes and power levels. We will start with a minimum  $d$ of .20,  so that the study is planned to detect at least a ``small'' effect size. If the final results do not reach statistical significance, the researchers could conclude that it is unlikely that the true effect is equal to or greater than .20, and eventually decide whether it is worth replicating the study, perhaps by modifying their protocol.

As the most plausible effect size, we will consider $d=.35$, which could be considered – at least in our opinion - a typical average level to test a hypothesis in psychological research in the absence of informative external sources (see for example the results reported in \citealp{opensciencecollaborationEstimatingReproducibilityPsychological2015a})\footnote{In the \citet{opensciencecollaborationEstimatingReproducibilityPsychological2015a}, the authors conducted replications of 100 experimental and correlational studies published in three psychology journals using high powered designs and original materials when possible. They found an average effect size of $r = .197$, i.e. $d = .41$. Given the heterogeneity of the 100 studies, we propose to use a more conservative value as being representative of a typical average effect in psychology. Overall, it should be noted that all the pre-specified values of $d$, albeit plausible, are not based on a thorough theoretical revision and/or on the formalized knowledge of experts in the field. Indeed, an appropriate use of the latter two external sources would undoubtedly contribute to produce more reliable results, but discussion of these strategies is beyond the scope of this paper.}.
As extrema ratio, we will include also a d of .5, which in the words of Jacob Cohen can be referred to as ``differences that are large enough to be visible to the naked eye'' (see \citealt[p.26]{cohenStatisticalPowerAnalysis1988} and Appendix A), and that, given the experiment under investigation, could be viewed as an extremely optimistic guess. Finally, to take issues concerning the feasibility of the study into account, we will also consider two levels of power, namely 80\% and 60\%.

Overall, our ``sensitivity'' prospective design analysis (see Table \ref{tab:casestudy1}) suggests that the sample size chosen by the authors ($n=67$) is inadequate. Indeed, even in the least reasonable scenario ($d$ = .50, power = .60), a minimum of 80 participants is required. Furthermore, is should be noted, that the associated Type $M$ error is considerably high, i.e. 130\%, signaling a high risk of overstimating the plausible effect.

\begin{table}[h]
\centering
\caption{Sample size, Type M and Type S error by power and plausible effect size. Type I error is fixed at .05}
\label{tab:casestudy1}
\begin{tabular}{cccccc}
\hline
Power                & Cohen's $d$& $n$ (per sample)   & Total $n$          & Type $M$ error        & Type $S$ error    \\
\hline
\multirow{3}{*}{.80} & 0.20 & 392 & 784 &                     &                    \\
                     & 0.35 & 130 & 260 & 1.13 & 0.00\\
                     &0.50  & 64 & 128 &                     &                    \\
\hline
\multirow{3}{*}{.60} &0.20  & 244 & 488 &                     &                    \\
                     &0.35  & 82 & 164 & 1.30 & 0.00\\
                     &0.50  & 40 & 80 &                     &          \\
\hline
\end{tabular}
\end{table}
A good compromise could be to consider the second scenario ($d$ = .35, power = .80), which requires a total sample size of 260, guaranteeing optimal control of the Type $M$ error. After conducting the study with this sample size, a significant result would lead to accept the researcher's hypothesis, while a non-significant result would indicate that if an effect exists, it will presumably be less than .35. Whatever the result, the researchers could eventually present their findings in a transparent and informative way. In any case, the results could be used to improve scientific progress. As an example, other researchers could fruitfully use the observed results as a starting point for a replication study.

\textbullet\ \textbf{Retrospective design analysis}

Let us now evaluate Study 2 from a retrospective point of view. Based on their results ($M_\text{structure} = 5.26$, $SD_\text{structure}=0.88$, $M_\text{random} = 4.72$, $SD_\text{random}= 1.32$, $n_\text{total}=67$; $t(65)=2.00$, $p=.05$, $\text{Cohen's}\,d = 0.50$)\footnote{The authors reported only the total sample size ($n=67$). Since participants were randomly assigned to each of the two experimental conditions, in the following we will assume, without loss of generalizability, that 34 participants were assigned to the ``structure'' condition, and 33 to the ``random'' condition.}, the authors  concluded that ``participants in the structure condition reported higher willingness to expend effort and make sacrifices to pursue their goal compared to participants in the random condition.'' \citet[p. 487]{kay2014functional}, thus supporting their initial  hypothesis.

To evaluate the inferential risks associated with this conclusion, we now run a sensitivity retrospective design analysis on the pre-identified plausible effect sizes  (i.e., $d = .20$, $d = .35$, $d = .50$).

In line with the results emerging from prospective analysis, the retrospective design analysis indicates that the sample size used in Study 2 exposes to high inferential risks. In fact, both for a plausible effect of $d=.20$ (power = .13, type $M =$ 3.06, type $S=$ 2\%) and for a plausible effect of $d=.35$ (power = .29, type $M =$ 1.86, type $S=$ 0\%), the power is very low and the Type $M$ error reaches worrying levels. For a $d$ of .50 (chosen on the basis of plausible effects and not based on the results observed in Study 2), the Type $M$ error is 1.40, indicating an expected overestimate of 40\%. Furthermore, the power is .52, suggesting that if we replicate the study on a new sample with the same number of participants, the probability of obtaining a significant result will be around the chance level.

We also evaluate the results of Study 2 by performing a retrospective design analysis using the method presented in Section \ref{inc_unc}. Specifically, we use a doubly truncated normal distribution centered at .35 (i.e., the most plausible effect size) with a plausible interval of .25 - 45. As could be expected, the results (i.e., power = .29, type $M =$ 1.86, type $S=$ 0\%) substantially confirm what emerged from sensitivity retrospective design analysis.

In summary, our retrospective design analysis indicates that, although statistically significants the results of Study 2 are inadequate to support the authors' conclusions.

As mentioned at the beginning of this paragraph, the Study 2 of \citet{kay2014functional} was selected for illustrative purposes and in a constructive perspective. For a more comprehensive picture, we invite interested readers to consult the ``Many Labs 2 project'' \citep{klein2018many}, which showed that with a large sample size ($n=6506$) the original conclusion of Study 2 cannot be supported (i.e., $t(6498.63) = -0.94$, $p = .35$, $d = -0.02$, $95\%CI = [-0.07, 0.03]$, as well as the subsequent response of the original authors \citep{laurin2018structure}.

\section{Discussion and Conclusions}\label{dis_and}

In psychological research, statistical inference is often viewed as an isolated procedure which limits itself to the analysis of data that have already been collected. In this paper, we argue that statistical reasoning is necessary both at the planning stage and when interpreting the results of a research project. To illustrate this concept, we built on and further developed Gelman and Carlin's (2014) idea of ``prospective and retrospective design analysis''.

In line with recent recommendations \citep{cumming2014new}, design analysis involves an in-depth reasoning on what could be considered as a plausible effect size within the study of interest. Specifically, rather than focusing on a single pilot or published study, we underlined the importance of using information outside the data at hand, such as extensive literature reviews and meta-analytic studies taking issues related to publication bias into account. Furthermore, we introduced the potentials of elicitation of expert knowledge procedures (see for example \citealp{o2019expert, zondervan2017application}). Even though these procedures are still underutilized in psychology, they could provide a relevant contribution to the formalization of research hypotheses.

Moving beyond the simplistic and often misleading distinction between significant and non significant results, design analysis allows researchers to quantify, consider, and explicitly communicate two relevant risks associated with their inference, namely exaggeration ratio (Type $M$ error) and sign error (Type $S$ error). As illustrated in the paper, the evaluation of these risks is particularly relevant in studies which investigate small effect sizes in the presence of high levels of intra- and interindividual variability, with a limited sample size – a situation that is quite common in psychological research.

Another important aspect of design analysis is that it can be usefully carried out both in the planning phase of a study (i.e., prospective design analysis) and to evaluate studies that have already been conducted (i.e., retrospective design analysis), reminding researchers that the process of statistical inference should start before data collection and does not end when the results are obtained. In addition, design analysis contributes to have a more comprehensive and informative picture of the research findings through the exploration of different scenarios according to different plausible formalizations of the effect of interests.

To familiarize the reader with the concept of design analysis, we included several examples and an application to a real case study. Furthermore, in addition to the classic formalization of the effect size with a single value, we proposed an innovative method to formalize uncertainty and previous knowledge concerning the magnitude of the effect via probability distributions within a Frequentist framework. Although not directly presented in the paper, it is important to note that this method could also be efficiently used to explore different scenarios according to different plausible probability distributions.

Finally, to allow researchers to use all the illustrated methods with their own data, we also provided two easy-to-use \texttt{R} functions (see also Appendix B) which are available at the Open Science Framework (OSF) at the link \url{https://osf.io/j8gsf/files/}.

For the sake of simplicity, in this paper we limited our consideration to Cohen's $d$ as an effect size measure within a Frequentist approach. However, the concept of design analysis could be extended to more complex cases and to other statistical approaches. For example, our \texttt{R} functions could be directly adapted to other effect size measures, such as Hedges' $g$, Odds Ratio, $\eta^2$ and $R^2$. Moreover, concerning the proposed method to formalize uncertainty and prior knowledge, other probability distributions beyond those proposed in this paper (i.e., the uniform and the doubly truncated normal) could be easily added. This was one of the main reasons behind the choice to use resampling methods to estimate power, Type $M$ and Type $S$ errors instead of using an analytical approach.

Also, it is important to note that our considerations regarding design analysis could be fruitfully extended to the increasingly used Bayesian methods. Indeed, our proposed method to formalize uncertainty via probability distributions finds its natural extension in the concept of Bayesian prior.
Specifically, design analysis could be useful to evaluate the properties and highlight the inferential risks (such as type $M$ and type $S$ errors) associated with the use of Bayes Factors and parameter estimation with credible Bayesian intervals.

In sum, even though a design analysis requires big effort, we believe that it has the potential to contribute to planning more robust studies and promoting better interpretation of research findings. More generally, design analysis and its associated way of reasoning helps researchers to keep in mind the inspiring quote presented at the begininng of this paper regarding the use of statistical inference: ``Remember ATOM''.

\section*{Conflict of Interest Statement}

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

\section*{Author Contributions}

GA conceived the original idea and drafted the paper; GB, CZC and ET contributed to the development of the original idea and drafted sections of the manuscript ; MP and GA wrote the R functions; GA, MP and CZC took care of the statistical analysis and of the graphical representations. LF and AC provided critical and useful feedback. All authors contributed to manuscript revision, read and approved the submitted version.

redpajama_set_name: RedPajamaArXiv


Millboro, VA – BARC Electric Cooperative (BARC) announced Wednesday its subsidiary, BARC Connects, completed its largest commercial fiber implementation in the service area. Beginning July 1st, the Rockbridge County Public Schools (RCPS) system is live on the BARC network, which in some areas utilizes the existing RANA network infrastructure.
As BARC brings fiber-to-the-home service to local residents, it also wanted to ensure local schools have the same access, so it designed the network to connect to every school in the county. In today's world, reliable Internet access is heavily used by educators to instruct, and by students to complete coursework, homework and research.
RCPS is comprised of four elementary schools, one middle school and one high school, along with additional administrative facilities. The student body is currently made up of approximately 2,500 students.


St. Luke's Transfer Center streamlines access to our physicians and services with a single phone number. Your call can be directly linked to the physician or service you need, and, when necessary, transport can be arranged.
In a non-emergent situation, if you would prefer to contact the physician directly to refer your patient, please use St. Luke's Provider Finder to find a physician by name, location, or specialty.


text:
West Virginia Voters Don't Want Their Lawmakers To Focus On Passing A 20-Week Abortion Ban
Tara Culp-Ressler Twitter Mar 3, 2014, 9:42 pm
CREDIT: AP PHOTO/MANUEL BALCE CENETA
West Virginia is currently advancing a bill that would ban abortion after 20 weeks of pregnancy. But according to a new poll, most West Virginia voters wish lawmakers would focus their attention on other issues.
The poll, conducted by Public Policy Polling (PPP) on behalf of Planned Parenthood Health Systems, found that voters are less likely to support a 20-week abortion ban once they have more information about the circumstances under which a woman may need later abortion care. The poll asked voters whether women should be able to have in abortion if she discovers serious fetal abnormalities, or if continuing her pregnancy poses critical health risks, or if she became pregnant from rape. When asked about women facing these specific circumstances, the majority of respondents said they should be able to access abortion services in those cases.
Ultimately, PPP found that up to 69 percent of voters believe a later abortion ban is the wrong issue for the legislature to spend its time on.
The polling results in West Virginia reflect the national polling that Planned Parenthood has conducted on this subject. Last August, a separate poll found that Americans oppose 20-week bans by 20 points once they're given more information about women's specific situations, and they overwhelmingly agree that the lawmakers pushing these restrictions have their priorities in the wrong place.
Nonetheless, the media typically doesn't provide this type of nuance in its coverage of 20-week bans, characterizing them simply as bans on late-term abortions that tend to have broad support. That plays into anti-choice advocates' hands, allowing them to construe later abortions as radically out of touch with Americans' values. Particularly after the illegal abortion provider Kermit Gosnell was found guilty of murder for preying on impoverished women in his Philadelphia-area clinic, later abortion bans became an area where conservatives could capitalize on emotional outrage.
"While women should not have to justify their personal medical decisions, the reality is that abortion later in pregnancy is rare and often happens under heartbreaking and tragic circumstances," Melissa Reed, the vice president of public affairs for Planned Parenthood Health Systems, said in a statement. "Unfortunately opponents of safe and legal abortion have tried to distort that reality, and it is important for us to get the truth out there."
The women who need later abortion care are often facing difficult decisions about wanted pregnancies that have gone terribly wrong. It's not exactly a casual decision that women make on a whim. And this type of legislation only applies to a very small number of procedures, since abortions after 20 weeks represent just 1.5 percent of abortions nationwide.
The GOP-controlled House of Representatives passed a national 20-week abortion ban last year, and state legislatures continue to push forward in this area. Nine states currently have 20-week bans on the books. This session, South Carolina and Mississippi are also advancing proposals to cut off legal abortion access at this arbitrary point.
#Abortion, #Health, #Reproductive Rights, #West Virginia

redpajama_set_name: RedPajamaCommonCrawl


text:
Home News EuroLeague FIBA and EuroLeague exchange new proposals, except it isn't happening until 2021
FIBA and EuroLeague exchange new proposals, except it isn't happening until 2021
EuroLeague Basketball executives met with FIBA in Geneva to discuss new proposals in order to "boost" its international cycle with ideas of altering the current model, which included a 26-page document highlighting such issues.
But, FIBA seemed to hold its ground once again, with a press release later on stating that it's always ready to study and take into consideration proposals that respect national teams and domestic leagues for the cycle after 2021.
The keyword being "after 2021". That said: the cycle is here to stay, whether people like it or not.
But it isn't all bad, as the two international windows all over the world have seen excellent matches, played at competitive levels in-front of near sell-out crowds. Plus, the fans are seeing countless new heroes shining through when they would have normally been hiding in the dark.
The EuroLeague though remains the top competition in Europe, domestically and while some players represented their country in both windows, their absence for the majority is noted. Therefore, EuroLeague Basketball presented FIBA with new proposals.
The agreement proposal included several points with the goal of discussing these with FIBA prior to reach an agreement that addresses them.
1. Competitions:Three international club competitions:
a. EuroLeague (EL)
b. EuroCup (EC)
c. Basketball Champions League (BCL)
As FIBA and the Domestic Leagues in October 2015 agreed that top leagues should have a maximum of 16 teams, Euroleague Basketball included this within the proposal.
2. Access:
Pyramidal System:
a. Domestic Leagues (DL) to have direct access to the EC and BCL in this order via sports ranking, after DL Playoffs
b. BCL to have direct access to the EC via sports ranking
c. EC to have direct access to the EL via sports ranking
3. International Calendar:
Three calendar alternatives with detailed calendar simulations for the upcoming four-year cycle. All three alternatives apply the following principles:
a. FIBA to have its National Team Competitions taking place on dates that do not compete head to head with any other major sports event, with the world's best players available to play, maximising the return for rights holders, sponsors and licensees
b. National Federations to organise their National Team qualification games on dates that do not compete head to head with any other major sports event, with all their best players available to play, maximising the return for rights holders, sponsors and licensees
c. Leagues worldwide to guarantee regularity in their competitions as they will not have the most talented players being released to their National Teams in-season, therefore the integrity of the competitions will be upheld, maximising the return for rights holders, sponsors and licensees
d. Clubs worldwide to work with their players on a regular basis, reducing the injury risk that comes from intracontinental travel and changes in training / playing style mid-season, maximising the return for rights holders, sponsors and licensees, holding a shortened pre-season preparation period but with the complete roster available
In addition, all alternatives ensured five or six weeks of complete rest every season for all players competing in European clubs.
4. Conditions for the release of players for national teams:
As it happens in other team sports EB proposed that:
a. Players to be exclusively released for official games and without any increase in the number of games currently existing in the FIBA Calendar. As is currently the case this includes friendly games in the lead up to national team tournaments
b. Insurance under conditions to be agreed guaranteeing 100% salary for each player in case of temporary or permanent inability
c. Agreed maximum of practice days including conditions for practices; safety of players
d. Club medical staff to have access to players during practices
5. Youth to senior pathways:
a. All domestic leagues / national federations to include a minimum quota of U22 players enrolled in higher education per club for all leagues below the domestic championship
b. Establish compensation scales for clubs that develop youth players based on:
i. Age
ii. Seasons in the club
iii. Competition level
c. The contractual clause will prevail in the case that this is higher among the two
6. Financial Fair Play Regulations:
a. All domestic leagues / national federations must implement a homologated Financial Fair Play system for the domestic championship
7. Economy:
a. A compensation system must be established for clubs that release players to National Teams as is already the case in football, handball, ice hockey; based on the principles of:
i. Solidarity
ii. Transparency
iii. Proportionality
Euroleague Basketball remains fully available to further discuss the proposal with FIBA after their internal evaluation, since in its view there are matters that need to be urgently resolved, as flagged by Euroleague Basketball to FIBA on numerous occasions in the past seasons.
EuroLeague Basketball, who were made aware of FIBA's international cycle in 2015, when this was first revealed during Eurobasket of that year in Lille, France, had opportunities to address the problems that they had, and have reported to FIBA directly. However, nothing has worked.
And while EuroLeague's top dogs came prepared and arrived in Switzerland brimmed with the hope that things might go their way, the meeting itself lasted exactly 50 minutes due to what they said was "unwillingness of the FIBA executives to discuss the agreement proposal in any depth."
Hopefully, the proposals will be reviewed by FIBA but after this meeting in Geneva, one thing is for sure: FIBA are taking the lead.
Previous articleWas a game in Istanbul the reason for Baskonia's second half turnaround against Valencia?
Next articleTwo sweeps in the EuroCup quarter-final series, while other two games live to fight another day
ASVEL prevail against Khimki in a high-scoring "battle"
ALBA Berlin cruise past Baskonia
Jeremy Evans on Talkbasket: "I thought about coming to Olympiacos last summer "
European basketball is the best style
Zack LeDay on TalkBasket.net: "We didn't play like ourselves"
Othello Hunter on Talkbasket: "We have a special group"
Hawks' Chandler Parsons has potentially career-ending injuries
EuroLeague Round 20 MVP: Shane Larkin
Lebron James with one-handed no-look pass to Danny Green
Ognen Kuzmic inks two-year deal with Real Madrid
Tornike Shengelia out for at least four weeks
Benetton announced Hackett and Kalnietis


Border has established health and safety guidelines and practices for employees and subcontractors involved in all projects and fieldwork. The health and safety program contains detailed information pertaining to site activities, personal protection, potential hazards, chemical information, contingency plans, and communication procedures; aimed at maintaining the health and safety of site personnel, subcontractors, the general public, and the environment. All personnel and visitors that visit our job sites are briefed on site safety practices.
Projects work best when performed as a cooperative effort between the customer and contractor, and that is how Border approaches every project. We apply our policies of quality, timelines, and superior customer service to every project we perform. Our goal is to be the most responsive contractor you have ever worked with, and we demonstrate our commitment to that goal. Border's experience and proven competence, coupled with our personnel and financial strength make us the ideal contractor for your project.


text:
Amrita Acharia in charity drive
Nepali Times November 27, 2018
Game of Thrones actress Amrita Acharia has joined the online appeal for funds for the charity ChoraChori that has rescued 147 trafficked and displaced Nepali children from slavery and abuse in India.
The 31-year-old Nepali-Ukrainian actress is based in Norway and acted in HBO's Game of Thrones, UK tv series The Good Karma Hospital, the Norwegian tv series Acquitted and in the forthcoming animation The Missing Link.
Says Acharia: "My father was educated, and he made sure we were educated and taught self-respect. When we moved away from Nepal, it was that education that gave us stability and the chance to follow our dreams. I love it that ChoraChori works on empowering young girls after these experiences, and gives them tools rather than just rescuing and dumping them in an orphanage".
Acharia was born in Kathmandu but her family moved to England when she was seven and after spending some years in the Ukraine, attended High School in Norway where her father is an obstetrician. She is now looking forward to going back to Nepal after 16 years to visit ChoraChori's facilities in Thaukel.
Most of the rescued children are boys whom ChoraChori has reunited with their families who hadn't heard from the boys in years and had come to believe them to be dead. Most of the children had left home in search of work before being trafficked, were apprehended by the Indian authorities and later rescued and brought back to Nepal.
Some of the children were runaways from domestic abuse whom ChoraChori funds through vocational training and into good employment. ChoraChori last year rescued Nepali girls from a notorious children's home in Muzaffarpur where at least 34 residents were gang raped by care home officials and outsiders. These girls are currently supported at ChoraChori's child trauma management centre alongside a growing number of domestic child rape victims.
"We've only just begun" says ChoraChori Founder Lt Col (retd.) Philip Holmes. "We know that there are still scores of Nepali children trapped in Indian institutions and the Muzaffarpur case has brought into sharp focus just how dangerous these centres are for children."
With Brexit, ChoraChori is feeling the effects of a financial squeeze in the UK charitable sector. Which is why it is launching 'The Big Give' online Christmas appeal. For one week only from noon GMT on Tuesday 27 November, all online donations are automatically being doubled in value in the charity's main annual fundraising drive.
Says Holmes: "The truth is that some of the rescued children are so young that they even lack the vocabulary to describe what has been done to them. That is heart-breaking, but I have been encouraged and inspired by how ChoraChori-Nepal has risen to the challenge."
To see Amrita's video appeal and donate to ChoraChori through The Big Give visit www.chorachori.org
Cranes, nature and godliness
Spicy foods from the coast
Wintering in Mongolia March 15, 2018 Photos: Lisa Choegyal "I don't think we get many…
Crackdown on anti-road expansion protesters March 28, 2018 Police have arrested 16 people following a clash with anti-road…
Nissan's festive drive offer September 14, 2018 ioneer Moto Corp, the authorized distributor of Nissan four-wheeler in…


Newyorkonlineservices is a professional Translation company providing high quality translation services in Schuylerville, New-york. The rates that is being charged by us are moderate and feasible. We make sure that we deliver much fabulous and sensational translation services in Schuylerville, NY.
Market Research, Insurance, Conference, Corporate and Financial.
Our Translation agency Schuylerville, NY has major resource it needs to deliver superb services in Schuylerville, NY like document, academic, immigration, legal and certificate translation.
Our Certified Translation Services Schuylerville, Newyorkonlineservices is trusted by all organizations. As a certified translation company Schuylerville, NY we provide services like Immigration, USCIS Acceptance, Sworn and Certified for Immigration .
Rush and super rush, Speed, Immediate, Best, Quality, Emergency , 24-hour translation, Same Day, Instant, Rapid, Fast, Urgent, Quick, Accuracy and professional translation.


Our activity started in 1983, and in these 35 years we have progressively increased our presence in the market. The sale of our products is targeted exclusively towards optical businesses, distributing wholesale via a network of sales representatives. In Yodel Internacional we want to satisfy the demands of the market, with regular new products in the latest colors and materials. Our web www.yodel.es shows all the details of our products, collections of frames and sunglasses with the latest models and innovations.


text:
Most Popular Movies and TV Shows With Brian Holloway
Sport (12) Talk-Show (9) News (5)
American Football Conference (1)
Former Athlete (1)
Live Television (1)
Morning Show (1)
Performer Name In Title (1)
Roman Numeral In Title (1)
1. Fox and Friends (1998– )
180 min | News, Talk-Show
A morning news show that includes interviews, features and banter among the hosts.
Stars: Steve Doocy, Brian Kilmeade, Ainsley Earhardt, Heather Nauert
2. NFL Monday Night Football (1970– )
Coverage of professional football featuring teams from the National Football League airing on Monday nights during the NFL's regular season.
Stars: Frank Gifford, Al Michaels, Howard Cosell, Dan Dierdorf
3. The NFL on NBC (1965–1998)
Stars: Charlie Jones, Dick Enberg, Curt Gowdy, Paul Maguire
4. Justice with Judge Jeanine (2011– )
60 min | Talk-Show
Justice with Judge Jeanine is a legal and current program of Fox News.
Stars: Jeanine Pirro, John Bolton, Chris Hahn, David Hunt
5. Huckabee (2008–2015)
Former Arkansas Governor Mike Huckabee's talk show.
Stars: Mike Huckabee, Lauren Green, Reggie Brown, Tara Setmayer
6. On the Record w/ Brit Hume (2002–2016)
60 min | News, Talk-Show
Stars: Greta Van Susteren, Ainsley Earhardt, Ted Williams, Bernie Grimm
7. Super Bowl XX (1986 TV Special)
Director: Ted Nathanson | Stars: Dick Enberg, Merlin Olsen, Bob Griese, Bob Costas
8. 1981 NFL Draft (1981 TV Special)
Stars: Bob Ley, Chris Berman, Dave Ahrens, Robert Alexander
9. 1985 AFC Championship Game (1986 TV Special)
Stars: Dick Enberg, Merlin Olsen, Bob Griese, Bob Costas
10. The NFL on NBC (1965–1998)
Episode: AFC Divisional Playoff: New England Patriots vs. Denver Broncos (1987)
Stars: Dick Enberg, Merlin Olsen, Greg Baty, Ken Bell
Episode: AFC Divisional Playoff: New England Patriots vs. Los Angeles Raiders (1986)
Stars: Dick Enberg, Merlin Olsen, Julius Adams, Marcus Allen
Episode: AFC Wild Card Game: New England Patriots vs. New York Jets (1985)
Stars: Marv Albert, Bob Griese, Julius Adams, Dan Alexander
13. On the Record w/ Brit Hume (2002–2016)
Episode: Episode dated 20 September 2013 (2013)
News, Talk-Show
Stars: Michele Bachmann, Ben Carson, Brian Holloway, Greta Van Susteren
14. Fox and Friends (1998– )
Stars: Heather Childers, Steve Doocy, Ainsley Earhardt, Elisabeth Hasselbeck
15. Huckabee (2008–2015)
Stars: Michele Bachmann, Five for Fighting, Elisabeth Hasselbeck, Brian Holloway
Stars: Morgan Brennan, Alisyn Camerota, Tucker Carlson, Linda Chavez
17. Justice with Judge Jeanine (2011– )
Stars: Carl Cameron, Ben Carson, Brian Holloway, Jeanine Pirro
Episode: New England Patriots vs. Baltimore Colts (1983)
Stars: Phil Stone, John Brodie, Julius Adams, Raul Allegre
Stars: Bob Costas, Bob Griese, Julius Adams, Larry Anderson
Episode: New England Patriots vs. Dallas Cowboys (1984)
Stars: Dick Enberg, Merlin Olsen, Gary Allen, Bill Bates
21. NFL Monday Night Football (1970– )
Episode: New England Patriots vs. Miami Dolphins (1985)
Stars: Frank Gifford, O.J. Simpson, Joe Namath, Woody Bennett


What do I do if my building has been completely or partially shut for part of the reporting timeline?
Please report your energy and water usage for the entire year regardless of whether you have been open to the public.
If you have been unable to monitor your impacts for the full year, due to building closure, please report the data you have and let us know the situation in the notes box within the general tab of your account.
If no energy and water usage data is available, please contact us directly. You will still be required to create an Environmental Policy and Action Plan.
What are the IG Tools?
What is an Environmental Policy and Action Plan?
Are there any repercussions if we don't reduce our carbon footprint?
What is going to happen to the information we give you?
Where can I get more information (webinars/guides/case studies)?
What should I do if I am based in the same building as another Arts Council funded organisation?
How do I enter my data if I am in a shared space and my energy and water consumption is built into my rent or charged as a service fee?
What will happen after 31st May?
What do I do if my policy and/or action plan is not yet live/has not been board approved?
How do I upload my Environmental Policy and Action Plan?


text:
Executive Program on Evaluation in the Middle East
Hamad Bin Khalifa University (HBKU)
16 Jan, 2022 - 13 Feb, 2022 08:00 AM - 3:00 PM Doha Time + Add to CalendarMinaretein (Education City Mosque)
Hamad Bin Khalifa University (HBKU), member of Qatar Foundation (QF), is organizing this course. The course has been designed to empower program administrators, managers and policymakers in the Middle East and North Africa region with the necessary tools to design and use performance measures that can monitor program efficiency and effectiveness and implement management techniques that apply performance data to improve programs.
Upon completion of the program, HBKU and The University of Maryland (UMD) will provide a joint certification of completion to participating students.
It is noteworthy that the course fees are USD 3,000.
For more details and registration, you can check the event information page on QF website.
Minaretein (Education City Mosque)
Other Events You May Like
Culture , Arts and Media
Qatar Museums (QM)
Kufic Script for Beginners
20 Jun, 2021 - 23 Jun, 2021 10:00 AM - 12:00 PM Doha TimeMuseum of Islamic Art, DohaIntended Audience
Education and Training Health
Ahed (Agreement) for Post-COVID Humanity
20 Mar, 2021 - 21 Mar, 2021 2:00 PM - 4:00 PM Doha TimeHamad Bin Khalifa University, Intended Audience
Visitor:Student
Qatar National Library
International Day Against Illicit Trafficking of Cultural Property
15 Nov, 2021 - 15 Nov, 2021 6:30 PM - 7:30 PM Doha TimeZoom, Intended Audience
Teaching and Learning Forum 2021
10 Oct, 2021 - 10 Oct, 2021 12:00 AM - 12:00 AM Doha Timevirtual event , Intended Audience
Ministry of Transport and Communications
Local Registration in World Summit Awards 2020 for Digital Innovation
28 Jun, 2020 - 16 Jul, 2020 12:00 AM - 11:00 PM Doha TimeDoha, DohaIntended Audience
Culture , Arts and Media Religion and Community
Cultural Village Foundation (Katara)
Katara Children's Festival
20 Nov, 2021 - 20 Nov, 2021 11:00 AM - 9:00 PM Doha TimeCultural Village Foundation (Katara) , DohaIntended Audience
Program Evaluation: Determining What Works
28 Jun, 2021 - 30 Jun, 2021 4:00 PM - 7:30 PM Doha TimeQatar Foundation, Al RayyanIntended Audience
Qatar Development Bank (QDB)
EntelaQ Pre-Accelerator Program
29 Aug, 2021 - 25 Nov, 2021 12:00 AM - 12:00 AM Doha TimeIntended Audience
Culture , Arts and Media Education and Training
Intellectual Property for Entrepreneurs and SMEs
11 Apr, 2021 - 11 Apr, 2021 1:00 PM - 2:00 PM Doha TimeQatar National Library , Intended Audience
Business and Finance Education and Training
Cross Pollination - Enabling Impactful Collaboration between Academia and Industry
10 Nov, 2021 - 10 Nov, 2021 11:00 AM - 12:00 PM Doha TimeOnline event , Intended Audience


text:
Valtário foi um rei lombardo, filho do rei Vacão que subiu ao trono com a morte de seu pai por volta de 540, quando ainda era menor de idade. Assumiu então a regência Audoíno que substituiu o rei quando ele morreu ainda jovem em 547, pondo fim à dinastia Letingi. Audoíno provavelmente matou Vátário antes de sua maioridade, de forma a obter o trono em ca. 546, e liderou os lombardos à Panônia. Procópio de Cesareia afirma que Valtário morreu de doença.

Bibliografia
Paolo Diacono, Historia Langobardorum (Storia dei Longobardi, Lorenzo Valla/Mondadori, Milano 1992)
Origo Gentis Langobardorum, ed. G. Waitz in Monumenta Germaniae Historica SS rer. Lang.
 Jörg Jarnut. Storia dei Longobardi. Torino, Einaudi, 2002. ISBN 8846440854
 Sergio Rovagnati, I Longobardi (Milano, Xenia 2003)

Reis lombardos
Lombardos do século VI

redpajama_set_name: RedPajamaWikipedia


A drunk driving charge or arrest can be extremely damaging to one's professional and personal reputation. If you have been charged with a DWI, you need to reach out to a seasoned New Jersey DWI attorney who can help. With years of experience, we are committed to defending our clients and protecting their rights at every step of the way.
According to the Centers for Disease Control and Prevention, over a million people across the country were arrested for driving under the influence in 2016. That same year, about 28 percent of all traffic-related deaths in the country involved alcohol-impaired driving. While states have tried to implement many different anti-DWI measures over the years, it is hard to know which ones have truly been effective.
In New Jersey, the basic offense of driving while intoxicated (DWI) occurs when a person operates a motor vehicle with a blood alcohol content (BAC) of 0.08 or above. It is important to note that a person can be charged with a DWI if they are under the influence of a drug that impairs their ability to drive safely. This can be a legal or illegal drug.
A new study published in the Journal of the American Medical Association reveals that strengthening state alcohol policies by a mere 10 percent can reduce the odds of an alcohol-impaired crash fatality by that same amount. For example, a 1 percent increase in restrictive polities led to a 1 percent drop in the likelihood that a crash was alcohol-related. Across all states, a 10 percent increase in the restrictiveness of policies would translate to about 800 fewer deaths each year.
One potential policy would be lowering the BAC limit to 0.05 percent or less to match most other developed nations in the world. Another potential policy would be alcohol taxes and limits on the number of places in communities that could sell alcohol. Measures such as sobriety checkpoints and enforcement of legal blood-alcohol limits could also be helpful.
If you have been charged with a DWI in New Jersey, you may be feeling hopeless, but you don't have to feel this way. A charge or an arrest does not mean you are guilty. There may be a number of defenses that are applicable in your case. We can examine the circumstances of your stop and subsequent arrest to ensure that none of your rights was violated. For example, the officer must have had probable cause to make the initial traffic stop. If the officer who pulled you over lacked probable cause, your charges could be reduced or dropped altogether. Another potential defense could be related to the administration or accuracy of the portable breathalyzer test. Did the officer administer the test correctly? Were there intervening factors, such as vomiting or indigestion? In addition, we could look into whether the breath test device was calibrated properly.
If you or someone close to you has been charged with drunk driving, you need a reliable New Jersey DWI attorney on your side. Whether it is your first DWI, second DWI, or subsequent DWI charge, we can help. You can rest assured that we can meticulously examine your case and help you understand your options moving forward. For more details, call us today at 877-450-8301 or contact us online.


With progress in clinical studies on recently developed diagnostic medicine approaches for dementia, there is an emerging demand for dedicated brain PET scanners to provide early diagnosis of the disease. Therefore, we have proposed the Helmet-Chin PET, a novel geometry for highly sensitive brain imaging based on a hemispheric arrangement of detectors. For a proof-of-concept, last year we developed the first prototype using 4-layered depth-of-interaction (DOI) detectors. Following successful realization of phantom imaging, we conducted the first clinical test which we describe in this paper.
The Helmet-Chin PET prototype was developed using 54 DOI detectors, each of which consisted of 16×16×4 Zr-doped GSO crystals (2.8×2.8×7.5 mm3) and a high sensitivity 64-channel flat-panel photomultiplier tube. In the prototype, 47 detectors were used to form a hemisphere of 25 cm inner diameter and 50 cm outer diameter, and 7 detectors were used for the chin detector. First of all, we compared sensitivity for the brain region with a commercial scanner to determine injection activity. We measured the count rate performance of the prototype and that of a whole-body PET, Biograph mCT Flow 64-4R PET/CT system (Siemens Medical Solutions USA, Inc.). The mCT consisted of four detector rings 84 cm in diameter, having 192 detectors, each of which consisted of 13×13 LSO crystals (4×4×20 mm3). We made a pool phantom with a shape of hemisphere with inner diameter of 20 cm filled with 18F solution. The phantom was measured with the prototype and the mCT for 5 min. Following the sensitivity assessment, we conducted the initial clinical test using the prototype. A healthy volunteer was measured for 18 min beginning 85 min after 18F-FDG injection of 70 MBq. For attenuation correction, the separately scanned CT image was registered.
The measured sensitivity for the brain region was 17.4 kcps/MBq for the Helmet-Chin PET prototype and 9.3 kcps/MBq for the mCT, where the energy windows were 400-600 keV and 435-650 keV, respectively. The sensitivity of the Helmet-Chin PET for the brain region was almost twice as high as that of the mCT, even though the number of detectors was less than 30% that of the mCT. For the initial clinical test, we could obtain a clear image of the brain with low radioactivity injection.
Our initial clinical test using the first prototype showed that the Helmet-Chin PET has promising performance for highly sensitive brain imaging.


Visit Taronga Zoo where the extraordinary parts of the wilderness come close enough for a truly unique experience.
Home to more than 4,000 animals from 350 species the best way to get there is on a Yellow Water Taxi. Soak in the magnificent sights of Sydney Harbour as you cruise over to your destination.
We have created a bundle to give you the best possible experience for the lowest price. By purchasing a Taronga Zoo transfer and your Taronga Zoo entry through us you save money and are ensured of a return journey at the end of the day!
With a combined package, Taronga Zoo ticket + Yellow Water Taxi Shuttle, you can skip the queues and spend the maximum amount of time exploring the "Zoo with a view." A Taronga Zoo shuttle is a short trip that significantly adds to the experience of visiting the wondrous wildlife of Taronga Zoo.
*Other departures & pick up times available on request. Please call our store for availability.
If you've ever dreamed of getting up-close and personal with whales, now is your chance! Here in Sydney, we observe the annual migration of humpback whales from May through until November.
Jump on board to enjoy Sydney Harbour on the 20-minute journey to Sydney's largest outlet centre, Birkenhead Point.
Rated "Excellent" by 200+ Travellers!
"It was an absolutely great whale watching experience. We saw a lot of humpback whales and dolphins. Beautiful day. Staffs were very friendly. The boat was large, comfy and clean. It was really enjoyable and I'll definitely come back. :)"
"Amazing view of the lights without the crowds. The boat was clean and comfortable and not over crowded. Lots of room to move about and get photos. All the staff were friendly and pointed out things of interest. Highly recommended!"
"We had a great morning with the Fantasea crew and saw a lot of humpback whales, really amazing experience. The staff was friendly and the facilities very good. We would definitely go again!"
"Great deal booked online and a really lovely 1 1/2 hrs cruising the harbour. We enjoyed the outdoor deck upstairs, but the inside area was just beautiful for those who preferred to be inside. Staff were lovely and overall experience was terrific. We were blessed with the weather... would highly recommend!"