SPPA 619
Study Guide for Exam 2: Inferential Statistics
Notes: (1) you will need calculator, (2) the exam will cover only the material on inferential
statistics, although there is overlap in the concepts that were used, (3) this is just a guide; it is not
intended to be comprehensive, (4) bring all of the tables (z, t, etc.) that we used in class.
1. What is the difference between descriptive and inferential statistics?
2. What kind of theoretical sampling experiment forms the basis of the z test? In your answer,
explain the standard error of the mean and tell what factors affect it.
3. What kind of theoretical sampling experiment forms the basis of the t test? In your answer,
explain the standard error of the difference between the means.
4. Under what conditions would a z test be used?
Answer: When comparing a sample mean to a population mean.
5. Under what conditions would a t test be used?
Answer: When comparing two sample means.
6. What are the Null and Alternative Hypotheses?
7. When inferential statistics are used to compare groups, what kinds of errors can occur? Which of
these error probabilities can be calculated using inferential statistics?
Answer: All that Type I/Type II stuff.
8. What is sampling error, and what factors control it? For each factor, tell whether large values
increase or decrease the amount of sampling error.
10. Give an example of an experimental design that would call for the use of:
a. a t test for independent groups
b. a t test for correlated samples
Note: Your examples need not be very detailed; just enough to get the idea across.
*** NOTE: We may or may not get to all three parts of the item below ***
11. We studied three inferential statistics for analyzing group difference (z, t and F). The formulas
differ in detail, but these tests have quite a lot in common. Explain what these tests have in
common.
12. An analogy was drawn between the decision making process that is used in inferential statistics
and the decision making process that is used in a court of law. Explain this analogy.
13. Under what conditions should a two-tailed statistical test be used?
*** NOTE: We may or may not get to this one ***
14. An experimenter tests visual memory for 20 children with attention deficit disorder. The
children are tested with medication and, on a separate day, without medication. The mean for
the medicated condition is 10.0, the mean for the non-medicated condition is 9.1, and the
standard error of the difference between the means is 0.6. Does the presence versus absence of
medication have a significant effect on visual memory? Would a correlated (repeated measures)
test be used or a test for independent groups?
Answer:
t = 10.0-9.1/0.6 = 1.5
df = n-1 = 20-1 = 19
The critical value at 0.05 for a directional test is 1.729. (A directional test is used because the
hypothesis would presumably be that the medication helps.) Since the t value obtained is less
than this threshold, the effect of medication is nonsignificant; that is, we do not reject the null
hypothesis. A correlated test would be used since the same subjects are being tested under two
conditions.
15. IQ scores are measured from 30 children who participated in Head Start and from 32 otherwise
comparable children who did not participate in Head Start. The mean for the Head Start group
is 103, the mean for the No Head Start Group is 95, and the standard error of the difference
between the means is 4. Does Head Start have a significant effect on IQ? Would a correlated
(repeated measures) test be used or a test for independent groups?
Answer:
t = 103-95/4 = 2.0
df = n1+n2-2 = 30+32-2 = 60
The critical value at 0.05 for a directional test is 1.671. (We are assuming here that the
hypothesis is that Head Start helps, not just that it produces a difference in one direction or the
other.) Since the t value obtained is greater than this threshold, the effect of Head Start is
significant; that is, we reject the Null Hypothesis. A t-test for independent groups would be
used since two separated groups of subjects are being tested.
16. 20 children are tested on their mastery of grammatical structures using tasks involving
imitation, comprehension, and production. Between-group variance for percent correct
scores on the three tasks = 1200, while within-group variance = 220. Is there a significant
effect for task (imitation vs. comprehension vs. production)? Is this is a repeated-measures
test or a test for independent groups.
Answer:
F = 1200/220 = 5.45
df = k-1, n-k = (3-1),(20-3) = 2,17
The critical value at 2,17 for 0.05 = 3.59. The computed F value is larger than this. Therefore
we reject the Null. This is a repeated-measures test: the same kids are tested on all 3 tasks.