Music treatment on patient on agitation level in early and middel stage alzheimer using: Two way analysis of variance

Testing a New Technique but not sure how it stack up against all the alternative is very difficult as most of the options sound similar to each other so picking the best out of them is a challenge. Consider a scenario we have three music treatment to be apply on patient who are in early and middle stage Alzheimer I conduct a survey on randomly selected patients. Each Class of patient is provided with a different environment i.e. Piano interlude, Mozart, Easy listening in order to make a confident and reliable decision we need a evidence to support our approach. ANOVA is defined as a statistical measure that analyze the variance of two, three or more comparable series for determining the significance of the difference in their mean values with the help of statistical technique known as F-test. The methodology was originally developed by Sir Ronald A. Fisher, the pioneered innovator of the use and application of statistical methods in experiment design who coined the name “Analysis of variance”-ANOVA There are commonly two types of ANOVA tests for univariate analysis-One way ANOVA and Two-Way ANOVA. One way-ANOVA is used when one can interested in studying the effect of one independent variable factor on population, whereas Two-way ANOVA is used for studying the effects of two factors on population at the same time.


Introduction
The most important and fundamental application of F-distribution is the Analysis of Variance or ANOVA. It is defined as a statistical measure that analyze the variance of two, three or more comparable series for determining the significance of the differences in their mean values with the help of statistical technique known as F-test. In others words, technique of ANOVA is used to test the equality of three or more sample means by comparing the sample variance using F-distribution. This technique split up the variance into two parts, namely (a) Variance between the samples (b) Variance within samples

Characteristics of Anova
The characteristics of the analysis of variance (ANOVA) are as follows: i) It makes statistical analysis of variance of two, three or more samples.
ii) It determines whether the difference in the mean values of the different samples is due to Chance, or due to any significant cause and thereby it reveals the true characteristics of the given series. iii) It gives the desired result by finding the appropriate variance ratio through the F-test technique.

Assumptions of Analysis of Variance
The analysis of variance (ANOVA) is made on the basis of some assumptions which are as follows: i) Each sample is drawn from the normally distributed population. If samples are large, this assumption is not required.
ii) The samples drawn at random for study are homogeneous and independent of each other. iii) There is no significant difference amongst the variance of the different universe from which the samples have been drawn. iv) It begins with the null hypothesis that µ1 =µ2= µ3=……=µk. v) It is assumed that critical values of the variance ratio, (F) as estimated by the Snedecar for Different degrees of freedom at different level of significance viz., 5% or 1% etc. holds good testing the significance of the calculated values of F-that represents the variance ratio of the Sample.

Technique of Analysis of Variance (Anova)
For the sake of clarity this technique be divided into two categories, namely. i) One-way-classification ii) Two-way-classification

Analysis of Variance in Two-Way Classification
In Two-way classification, the data are classified according to two factors. For example, the production of a manufacturing concern can be studied on the Basis of workers as machines. A company can analyses it's sales according to salesmen and seasons. In tow-way classification, the following procedure is adopted in the analysis of variance: i) Coding method can used to simplify the calculation. ii) Find the correction factor by using the formula: Correction  Table: In a two-way classification, the analysis of variance (ANOVA) table is prepared in the following way:

Assumption
There some assumption to do Two Ways ANOVA or we can say that there are the condition for Two Way ANOVA Assumption #1: Your dependent variable should be measured at the continuous level (i.e., they are interval or ratio variables). Assumption #2: Your two independent variables should each consist of two or more categorical, independent groups. Assumption #3: You should have the independence of observation, which means that there is no relationship between the observations in each group or between the groups themselves.
Assumption #4: There should be no significant outliers. Outliers are data points within your data that do not follow the usual pattern Assumption #5: Your dependent variable should be approximately normally distributed for each combination of the groups of the two independent variables. Assumption #6: There needs to be the homogeneity of variances for each combination of the groups of the two independent variables.

Validity of Two-Way Anova
ANOVA is based on two assumptions:  the observations are random samples from normal distributions  the populations have the same variance [variance = (standard deviation)2]  observations are independent of each other 7. Two -Way Anova Practical Problem I want examine the effect of various types of music on agitation levels in patients who are in the early and middle stages of Alzheimer's disease. Patients were selected to participate in the study based on their stage of Alzheimer's disease. Three forms of music were tested: Easy listening, Mozart, and piano interludes. While listening to music, agitation levels were recorded for the patients with a high score indicating a higher level of agitation. Suppose you want to determine whether the early and middle stage Alzheimer's react to piano interlude, Mozart and Easy listening. In this example, I are interested in testing Null Hypotheses H0D: The amount of relief does not depend on type of Alzheimer's H0T: The amount of relief does not depend on the piano interlude, Mozart, and Easy listening One says the experiment has two factors (Factor Stages of Alzheimer's, Factor various music treatment at a = 2(early and middle) and b = 3(Piano interlude, Mozart, easy listening). Thus there are ab = 3 × 2 = 6 different combinations. With each combination we have r =5 loads. r is called the number of replicates. This sums up to n = abr = 30 loads in total.