Exercise 4

Due date : due 21/5 before 21:00, via email. Send a short pdf with your code, results and discussion.

Can be done individually or in pairs

File control.csv contains the data of a control group and exp.csv data on the experimental group

run a t-test to verify if the differences are significant

Equivalence tests

The package equivalence in R implements the TOST (two one sided t-test) test.

Let us assume that a difference of 2 or less in the data is irrelevant. Run the TOST test. Can you say that the two groups are equivalent?

compute the Cohen d from the treatment (use the pooled standard deviation formula
Either use an analytical formula based on the z-test or the formula based on the non-central t-distributions (implemented by the R package MBESS (function ci.smd (the smd parameter is the effect size computer above) compute the confidence interval for the effect size.
Let us assume that a effect size of 0.3 or less is irrelevant (please notice that this criterium of irrelevance does not correspond to the criterium used in the TOST question above). Can you state with 95% confidence that the difference between the experimental and the control groups is irrelevant?

Install the package BEST.

Run the BESTmcmc function on the data
What is the 95%HDI on the mean difference?
What is the 95%HDI on the effect size?
what is the probability that the experimental and the control group difference is irrelevant, given the 0.3 irrelevance on the effect size above? (see the ROPEeff parameter in the summary function)