## power of test and importance of effect size

Hello,

This questions been troubling me.

An investigator wants to show that mental training can increase mental functioning in a way similar to that of physical training increasing physical fitness.

A goup of 26 children is selected. their average IQ at the beginning of the training is Xbar=100. at the end of three months of training the average IQ is assessed as 103.*

There are two possibilites for the increase:

-pure chance and random fluctuation; subsequent testing may show IQs of 100 or even below 100

-a genuine increase as a result of mental fitness training, subsequent testing will show similar increases

Supposing that the increase is real, what is the probability that the results will be attributed to chance if N=26, if N=50, if N=101, if N=200, N=500

as n increases how does the p-value change and how does the effect size change?

2. describe typical types of experiements with two or more groups using repeated measures

3. explain what we mean by an interaction between variables? What forms can interaction take? give examples

Not question 2 and 3 as much as the first.

How do you solve and find out the p-values using all the sample sizes?