Answers to Practice Questions for Final:
Part I: Review of Basics: Hypothesis testing
1. Piano lesson problem
a. Do piano lessons improve spatial skills in children?
b. Piano lessons (this is what experimenter controls, expected to be the "cause")
c. Spatial ability (this is something experimenter measures, DV is what should show the "effect")
d. 3 months lessons / no lessons ..... or just lessons / no lessons
e. Ho: Mu-lessons = Mu-no lessons
Ha: Mu-lessons not equal to Mu-no lessons
Note: the research question focuses on "improvement" so question itself is directional. However, a change in the opposite direction is both plausible and would be interesting. So a 2-tailed test would be the best choice. In actual exam, if you are not told which to use, nondirectional is always a safe choice. If you do decide to set up directional hypotheses, however be sure and be consistent as you proceed--directional hypotheses go with one-tailed test, single critical region/value etc. Don't switch back and forth as you proceed through the problem. For directional, be sure the two hypotheses cover all possibilities:
Ha: Mu-lessons > Mu-no lessons & Ho: Mu-lessons < or = Mu-lessons
f. .05 or .01 (both are standard choices). What it measures: the significance level, chance of Type I error (a false positive). For .05, chance is 5%, for .01, chance is 1%. Note: Because this is a small n experiment, .05 will give a better balance between chance of Type I and Type II errors. .01 will give you a very low power test.
g. t-test for independent samples [independent measure also okay -- same test, two different name]
Note: Why independent? You have two DIFFERENT sets of children, some who get lessons, some who don't. A dependent means approach would be to give all the children lessons, and test them both before and after. Same research question, different approach to collecting data.
h. Conclude that piano lessons have an effect on spatial skills, with confidence level of 95% (or 99% if you chose alpha = .01). Will need to look at means to determine whether spatial skills were improved or worsened by piano lessons. NOTE: Don't automatically conclude that significant result shows improvement! This is a two-tailed test, remember
i. No. Results are inconclusive. There is always some chance of a Type II error. Power is low because of small n (only 20 in each group).
j. Use larger samples. Other correct answers: If you had .01 alpha, change to .05 alpha. Or give piano lessons for a longer time to strengthen the effect (increase effect size)
Symbols and formulas:
chi-square, z-score, sample mean, mean, significance level / probability of Type I error, degrees of freedom, chi-square, population variance, estimated population variance, degrees of freedom for chi-square independence (if you just said chi-square, would get half points) , s2, sigma2, proportion of variance accounted for [Note: book uses little r2, sorry, forgot to change this from last class, when I used a different book. Same thing with S2 versus s2-forgot to update notation to match the current book]