Stat 322 – HW 5

Due Thursday, Feb. 15

1) problem 1 (p. 453)

2) problem 18 (p. 464), feel free to use Minitab

Note: You can get Minitab to store the fitted values and residuals automatically!

3) A 1989 study (Capron & Duyme found in Ramsey and Schafer) investigated the effect of heredity and environment on intelligence. From adoption registers in France, researchers elected samples of adopted children whose biological parameters and adoptive parameters came from either the very highest or the very lowest socioeconomic status (SES) categories (based on years of education and occupation). They attempted to obtain samples of size 10 from each combination: (1) high adoptive SES and high biological SES, (2) high adoptive SES and low biological SES, (3) low adoptive SES and high biological SES, and (4) low SES for both parents. They 38 selected children were given intelligence quotient (IQ) tests.

SES of Adoptive	SES of biological	IQ scores of adopted children
High	High	136	99	121	33	125	131	103	115	116	117
High	Low	94	103	99	125	111	93	101	94	125	91
Low	High	98	99	91	124	100	116	113	119
Low	Low	92	91	98	83	99	68	76	115	86	116

(a) Identify the observational units, explanatory variable(s), and response variable in this study. Identify each variable as quantitative or qualitative. Is this an observational study or an experiment?

(b) Enter these data into a blank Minitab worksheet, being careful to treat each column as a different variable. How many rows should you end up with?

(c) Run a one-way ANOVA to see if the mean IQ scores differ significantly depending on the SES of the adoptive parents. Report the F statistic, p-value, and your conclusion.

(d) Run a two-sample t-test to decide whether there is a difference in the mean IQ scores for the high and low SES adoptive parents. How does your p-value compare to that in (d)? What technical condition is required by the procedure in (c) but not in (d).

(e) What happens if you try to run Stat > ANOVA > Two-Way, using the IQ scores as the response, the SES of the adoptive parents as one factor and the SES of the biological parents as the other?

(f) Instead, choose Stat > ANOVA > General Linear Model, entering the IQ scores as the response, and using the two SES variables in the Model box. Click OK.

- What is the p-value for the SES adoptive factor? What hypotheses are being tested?

- What is the p-value for the SES biological factor? What hypotheses are being tested?

(g) Return to Stat > ANOVA > General Linear Model. This time, enter the “model” as:

adding the vertical line between the factors. Also click the Factors button and request an “Interactions Plot” of the two factors:

Click OK twice.

- What does the interactions plot reveal about the overall effect of the adoptive parents’ SES?

- What does the interactions plot reveal about the overall effect of the biological parents’ SES?

- Does the difference in mean scores for those with high and low SES biological parents depend on whether the adoptive parents were high or low SES?

(h) Return the Session window and report the p-value for the Interaction effect. Does the size of this value make sense based on the graph?

(i) If there is no interaction (your answer to the last question in (f) is no), then how much is the mean IQ score affected by the SES of adoptive parents, and how much is it affected by the SES of the biological parents? Is one of these effects larger than the other? Hint: Use multiple comparison procedures to help answer this question.

Writing Assignment 5, due March 5

Attend one of the research talks of the statistics department job candidates and write a summary of your impressions of the talk. This could be which context issues you found most interesting, the technical aspects you did or did not understand, your evaluation of the quality of the presentation, etc. In particular, what did you hear that sounded related to anything we have discussed in class? What questions do you have about what the speaker presented?