Question

1a.) You assigned 400 depressed patients to receive either 1) medication, 2) psychotherapy, 3) placebo, or 4) no treatment for 12 weeks, and now want to compare these groups on levels of demoralization (scale from 1-5). What kind of statistical test does this call for?

1. Chi-square for independence
2. Dependent Samples t-test
3. Chi-square for goodness of fit
4. Independent Samples t-test
5. Correlation
6. ANOVA
7. Single Mean

1b.) Imagine you have conducted the appropriate test for the above design, with α = .05 and p = .002. What would you conclude?

1. There were no significant differences in demoralization between groups.
2. The placebo effect was observed.
3. Participants were not randomly assigned to groups.
4. There was at least one significant difference in demoralization between groups.
5. Participants were randomly assigned to groups.

Answer 1

1a) Answer is

f) ANOVA

Note : Since we are comparing means for four groups , we use Analysis of Variance (ANOVA) . For comparing means for two groups we use Independent or dependent sample t test . For more than two groups ANOVA is used . We cannot use Chi square and correlation , as they are tested for association between two variables.

b) Answer is

d) There was at least one significant difference in demoralization between groups

Note : The null hypothesis for this test

H0: Means for 4 groups are equal

the alternative hypothesis is

Ha: At least one significant difference between groups ( that is means of atleast two groups are different)

Test criteria : We reject H0 , if P value < significance level

P value is , P= 0.002

level of significance is ,

Since P value < 0.05

Reject H0 ( that is may accept Ha)

There was at least one significant difference in demoralization between groups