May 01, 2023

### Introduction

A Repeated measures ANOVA and ANCOVA is a statistical test.  ANOVA refers as Analysis of Variance, it is a techniques for comparing the number of means based on observed sample, it done by comparing within group variances with between group variances. Repeated measure ANOVA tests also use to test the equality of means, but it is used to measures random samples under a number of different conditions (Crowder, & Hand, (2017), pp.152-157). ANCOVA refers as Analysis of Covariance, it is the combinations of ANOVA and regression analysis which allows analysts/ researcher to compare one variable in two or more groups considering the variability of other variables. Repeated measures of ANOVA and ANCOVA uses to solve many real life research problems using high level interpreted language known as Python. An analyst uses ‘Jupyter’ in python.

### Repeated Measures Of ANOVA

Fan, & Zhang, (2018), pp. 2760-2778 explained that In repeated measures of ANOVA, dependent variable measures are repeated several times on a same data sample. Standard ANOVA is not suitable because it fails to explain the correlation between repeated measures which violate the ANOVA assumptions of independence. Hypothesis Statement for repeated measures ANOVA explained by Langenberg, Helm, & Mayer, (2020), pp.12-19: All mean groups equal.  Vs.   Atleast one of the group means different from another.

### Applications

Applications has been explained by Murray, et., al, (2018), pp. 241-247 is as follows:

1] Suppose, researcher selects a group of peoples who are suffering from some condition or disease and which measures some characteristics related to that condition or disease, then researcher can match group of people into pairs which has similar level of the measured characteristics. One people from every matching pair is then given a proper treatment and then the level of measured characteristic of all sample is measured again.

2] Suppose, researcher wants to study the 4 different drugs which leads to different reaction times. To test this, researcher measures and observes the reaction time of 6 patients on 4 various drugs. However, every patient is measured on every 4 drugs, repeated measures ANOVA will be useful to understand if the mean reaction time between drugs differs or not.

In python, we can load this collected data using library ‘pandas’ or ‘numpy’. And can perform repeated measure of ANOVA using ‘statsmodel’ library using ‘AnovaRM’ function, in order to use this one have to import it as ‘from statsmodels.stats.anova import AnovaRM’. Through fitting data to AnovaRM researcher will get all the results from which one can find the mean reaction time between drugs differ or not.

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