Question

-For a particular study, your alpha is .01 and your beta is .32. What is the probability
of correctly rejecting a false null hypothesis?

-You have a group of 32 individuals whom you have divided into four equal groups of 8  Using these groups, you want to see if type of classroom instruction (traditional
lecture, distance learning, self-guided discovery, classroom debate) has an impact on
test scores. Using this information and an alpha of .05, what would the critical value
for a Fisher’s LSD test be?

Answer 1

- Probability of correctly rejecting a false null = power of the test = 1- beta = 1-0.32 = 0.68

- We are assuming that we are using a CRD, given by:

We want to do a multiple comparison using Fisher's LSD. Now, LSD consists of two steps.

In step 1: We test,

For this, we use the usual ANOVA test. In this CRD, trt df is 4-1=3 and error df is 32-4=28.

The ANOVA test is an Ftest, and the cutoff is given by:

If, step 1 is rejected, we go to step 2.

Step 2: We test .,

Here we a use t test statistic with error df (=28 in our case). We use a two sided test, so the cutoff is given by:

Hence, cutoff for the first stage is: 2.95 and for the second stage is 2.05,-2.05