Module 8: Persona of ANOVA

 Hi everyone! 

This week we learned another form of testing, specifically for analyzing variances of a categorical variable like being male or female and if that has a true mean difference with a quantitative variable like hours spent studying for a test. This form of hypothesis testing is called ANOVA. The characteristics or persona that makes ANOVA different from a t-test for difference in means is we can have more than 2 variables with multiple categories. Let's get started!

A researcher is interested in the effects of drug against stress reaction. She gives a reaction time test to three different groups of subjects: one group that is under a great deal of stress, one group under a moderate amount of stress, and a third group that is under almost no stress. The subjects of the study were instructed to take the drug test during their next stress episode and to report their stress on a scale of 1 to 10 (10 being most pain).

High StressModerate StressLow Stress
1084
9106
866
974
1082
882

Report on drug and stress level by using R. Provide a full summary report on the result of ANOVA testing and what does it mean. More specifically, report  using the following R functions: Df, Sum, Sq Mean, Sq, F value, Pr(>F)










F(2,15) = 21.36; p <0.05

The ANOVA test tells us the stress groups of high(h), moderate(l), or low(l) have a true mean difference with the subjects stress scale level from 1 to 10. The p-value is low at 0.0000408 which is lower than a normal alpha level 0.05, thus we can say there is truly a relationship between the group stress type and the stress scale levels due to the drugs.

2. From our Textbook:Introductory Statistics with R. Chapter # 6 Exercises 6.1 pp. 127.

The zelazo data (taken from textbook's R package called ISwR) are in the form of a list of vectors, one for each of the four groups. Convert the data to a form suitable for the user of lm, and calculate the relevant test. Consider t tests comparing selected subgroups or obtained by combining groups.  

2.1  Consider ANOVA test (one way or two-way) to this dataset (zelazo)



















From the ANOVA test, we can tell the differences in age of the infants is not truly related to the test group type the infants were part of because the p-value is greater than 0.05 and the F ratio is very small.

-Ramya's POV

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