Exercise 5
Due date : due 13/11 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 ne dsided t-test) test.
Let us assume that a difference of 2 or less in the data is
irrelevant. What does the TOST test says?
Effect size
- compute the effect size (Cohen d) from the treatment (use the
pooled standard deviation formula (with the -2)
- 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 nto
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?
Bayesian analysis
Install the pacakage BEST. The package need the JAGS MCMC program. I
recommend instaling the 3.X version (at least in my Mac the 4.0
version did not work).
- Run the BESTmcmc function on the data
- what is the 95%HDI on teh mean difference?
- What is the 95%HDI on the effect size?
- what is the probability that the experiemntal and the
control group differnce is irrelevant, given the 0.3 irrelevance
on the effect size above? (see the ROPEeff parameter in the
summary function)