significant and we are more than 99% confident when we say that there is a difference between the groups’ means. This is an overall difference and even if we have an indication from the graph, we cannot tell which mean is significantly different from which. This is because the ANOVA is an test: it tells we that there is (or not) an overall difference between “omnibus” our means but not exactly which means are significantly different from which other ones. This is why we apply post-hoc tests. Post hoc tests could be compared to t-tests but with a more stringent approach, a lower significance threshold to correct for familywise error rate. We will go through post-hoc tests more in detail later. Example (File: protein expression.csv) Let’s do it in more details. We want to find out if is a significant difference in terms of protein expression between 5 cell types. As usual, we start by designing our experiment, we decide to go for an analysis of variance and then, we get to the point where we have to decide on the sample size. Power analysis with an ANOVA We are quite confident in our hypothesis so we decide to go ahead. First we need to see whether the data meet the assumptions for a parametric approach. Well it does not look good: 2 out of 5 groups (C and D) show a significant departure from normality (See Table below). As for the homogeneity of variance, even before testing it, a look at the box plots (see Graph above) tells us that there is no way the second assumption is met. The data from groups C and D are quite skewed and a look at the raw data shows more than a 10-fold jump between values of the same group (e.g. in group A, value line 4 is 0.17 and value line 10 is 2.09). A good idea would be to log-transform the data so that the spread is more balanced and to check again on the assumptions. The variability seems to be scale related: the higher the mean, the bigger the variability. This is a typical case for log-transformation.
significant and we are more than 99% confident when we say that there is a difference between the groups’ means. This is an overall difference and even if we have an indication from the graph, we cannot tell which mean is significantly different from which. This is because the ANOVA is an “omnibus” test: it tells we that there is (or not) an overall difference between our means but not exactly which means are significantly different from which other ones. This is why we apply post-hoc tests. Post hoc tests could be compared to t-tests but with a more stringent approach, a lower significance threshold to correct for familywise error rate. We will go through post-hoc tests more in detail later. Example (File: protein expression.csv) Let’s do it in more details. We want to find out if is a significant difference in terms of protein expression between 5 cell types. As usual, we start by designing our experiment, we decide to go for an analysis of variance and then, we get to the point where we have to decide on the sample size. Power analysis with an ANOVA We are quite confident in our hypothesis so we decide to go ahead. First we need to see whether the data meet the assumptions for a parametric approach. Well it does not look good: 2 out of 5 groups (C and D) show a significant departure from normality (See Table below). As for the homogeneity of variance, even before testing it, a look at the box plots (see Graph above) tells us that there is no way the second assumption is met. The data from groups C and D are quite skewed and a look at the raw data shows more than a 10-fold jump between values of the same group (e.g. in group A, value line 4 is 0.17 and value line 10 is 2.09). A good idea would be to log-transform the data so that the spread is more balanced and to check again on the assumptions. The variability seems to be scale related: the higher the mean, the bigger the variability. This is a typical case for log-transformation.
Introduction%20to%20Statistics%20with%20GraphPad%20Prism%20manual.docx