[Last update: 7/7/04]
(8.1) REVIEW QUESTIONS
(A) How do independent samples differ from paired samples?
(B) Indicate whether each of the following samples are paired or independent :
(a) Weekly hours of television viewing by third-grade boys with and
without ADHD
(b) Cortisol levels of husbands and wives
(c) Psychological stress scores of engineering students and social
science students
(d) Problem-solving skills of scientists and artists
(e) Problem-solving skills of scientists and artists matched on IQ
(f) Number of medical services errors in
nurse practitioners before and after attending a quality improvement workshop
(g) Weight for subjects before and after partaking in the
Atkins diet.
(h) Presence of type A behavior in husbands and wives.
(i) Comparison of self-reported and actual
weights in dieters
(j) Number of needle stick accidents in two groups of nurses.
(C) How would you set up an SPSS data file in preparation for comparing
independent groups?
(D) Suppose you wanted to study anxiety in undergrad and grad students. A
psychological profile is administered to study participants. How would you code this information
within SPSS?
(E) How are boxplots used to compare the spreads of
distributions?
(F) What statistic do we use as the point estimator for population mean
difference �1 - �2?
(G) [M/C]: The pooled estimate of variance is a
weighted average of group variances with weights based on group (a) sample sizes
(b) means (c) variances (d) degrees of freedom.
(J) [M/C] The pooled estimate of variance is an estimate of
the variance [(a) between groups (b) within groups].
(I) [M/C] The standard error of the mean difference quantifies [(a) mean difference (b) average spread
(c) precision of the sample mean difference (d) precision of the population mean difference].
(J) How many degrees of freedom does the t percentile have when
calculating a confidence interval for an independent mean difference?
(K) A 95% confidence interval for an independent mean difference is (-3.3, 1.7).
Interpret this interval.
(L) In plain language, describe the null hypothesis tested by the independent t test.
(M) In statistical notation, write the null hypothesis tested by the independent t test.
(N) List the distribution assumptions of the [equal variance/ Student] independent t test.
(O) [True or false?] Even though Student's t tests requires distribution assumptions, numerous studies have proven that the test is
able to withstand departures from these assumptions while still providing
reliable results, especially when samples are moderate to large in size.
(P) When and why do you conduct sample size calculations?
(U) What information must be specified to determine the sample size for a t test?
(8.2) MONKEY2 (Effects of Two Treatments on Monkey Intelligence): This exercise will demonstrate how to take paired measurements on independent groups and then compare the change between the the groups. Twelve monkeys are randomly assigned to receive either Monkey Tonic (GROUP = 1) or a course in Applied Monkey Training (GROUP = 2). Each Monkey's Intelligence Quotient is recorded at BASELINE and WEEK12s following treatment. Data are:
ID GROUP BASELINE WEEK12 DELTA
--- ----- -------- ------ -----
1 1 100
104
2 1 88 93
3 1 106 109
4 1 116 117
5 1 102 104
6 1 106 106
7 2 114 113
8 2 106 108
9 2 100 102
10 2 92 100
11 2 112 110
12 2 92 95
(A) Calculate mean IQs of the two group at BASELINE. Is a paired or independent
comparison?
(B) Calculate the change (DELTA) in Monkey IQ associated with therapy
for each monkey. Store
this information under the DELTA
variable.
(C) Calculate the mean change in group 1 Is this a paired or independent
comparison?
(D) Calculate the mean change in group 2. Is this a paired or independent
comparison?
(E) Compare the mean changes in the two groups. Is this a paired or
independent comparison?
(8.3)TWOGRPS: Symptomatic and asymptomatic patients with HIV demonstrated the following scores on a psychological exam. (Data are ordered arrays.)
Symptomatic: 72 73 86 95 95 95 96 97 99 125
Asymptomatic: 89 92 93 98 105 106 110 126 127 130
(A) Construct side-by-side boxplots of these data. Interpret your plot. Is
there evidence unequal averages? Is there evidence of unequal variance?
(B) Descriptive statistics for the groups are
n1 = 10, 
1 = 93.3, s1 = 14.86;
n2 = 10 , 2 = 107.6 , s2 = 15.37. Test H0: �1 = �2 at a = .05. List all hypothesis testing
steps and show all calculations. State your conclusion and interpret your results.
(8.4) HISTIDINE: Total histidine excretion (mg.) in 24-hour urine samples from men and women on protein-restricted diets are:
Men: 172 204 229 236 256
Women: 115 135 138 174 197 224
(A) Construct side-by-side boxplots of these data. Compare the two distributions.
(B) Descriptive statistics for the men in the sample are n1 = 5,
1 = 219.4; s1 =
32.37. Descriptive statistics for the women are n2 = 6, 2 =
163.83, s2 = 41.73. Test the means for inequivalence at a = .01. Show all
work and hypothesis testing steps (H0, H1, etc.)
Interpret your results in plain language.
(8.5) JOGGERS: Maximal V02 uptake
(ml/kg) measurements can be used as an index of physiologic conditioning. A
random sample of 25 joggers had a mean V02 uptake of 47.5 (s = 4.8).
Twenty-size (26) non-joggers show a mean of 37.5 ml/kg (s = 5.1)
(A) Calculate a 95% confidence interval for �1 - �2.
Provide a brief narrative interpretation of results.
(B) Calculate a 99% confidence interval for �1 - �2. Interpret
these results.
(8.6) BONE: A study was conducted to determine whether maternal cigarette smoking affects bone mineral density of newborns. A sample of 77 infants from mothers who smoke had a mean bone mineral content of 0.098 g/cm� (s1 = 0.026 g/cm�). A sample of 161 children whose mothers had not smoked have mean bone mineral content of 0.095 g/cm� (s2 = 0.025 g/cm�). Estimate the mean difference in bone mineral content with 95% confidence (i.e., calculate a 95% confidence interval for �1 - �2). Interpret your results.
(8.7) CMV: One theory suggests that cytomegalovirus (CMV) infection causes coronary narrowing in patients with narrowed coronary vessels. To test this theory, 75 patients undergoing angioplasty were studies following their procedures. (Angioplasty is a procedure with a balloon-tipped catheter to enlarge a narrowing in a coronary artery.) Six months following surgery, the 49 patients who were seropositive for CMV (group 1) experienced an average luminal diameter reduction of 1.24 mm (s1 = 0.83 mm). In contrast, 26 patients who were seronegative for CMV (group 2) experienced an average luminal reduction of 0.68 (s2 = 0.69). Test whether this differences is significant at a = .05. Discuss the meaning of this finding.
(8.8) ANXIETY: Severe anxiety occurs often in patients who must undergo chronic hemodialysis. To help counteract this anxiety, a set of progressive relaxation exercises was shown on videotape to a group of 38 experimental subjects. A control group of 23 patients viewed a set of neutral videotapes (Rosner, 1990, p. 280; Alarcon, 1982). Following these interventions, a psychiatric questionnaire (the State-Trait Anxiety Inventory) was administered to both groups. For the experimental group, the mean State-Trait Anxiety Inventory score was 33.42 (standard deviation = 10.18). For the control group, the mean State-Trait Anxiety Inventory was 39.71 (standard deviation = 9.16). Test whether this difference was effective at a = .01. Show all hypothesis testing steps, and summarize your results in plain language.
(8.9) ASPIRIN: In a randomized clinical trial of women with pregnancy-induced hypertension, 23 women received aspirin and 24 received a placebo. After several weeks on treatment, the mean arterial blood pressure of the aspirin-treated group was 111 mm Hg (s1 = 8 mm Hg) and the mean blood pressure of the control group was 109 mm Hg (s2 = 8 mm Hg). Perform at test to determine whether aspirin treatment was effective. Include all hypothesis testing steps, and show all work.
(8.10) FEV: Download the data set fev.sav. This data file contains a variable named FEV representing forced expiratory volume (liters / second), which measures respiratory function based on the amount of air a person can forcibly expel through a tube in a period of time. Use methods learned in this chapter to compare the forced expiratory volumes of smokers and non-smokers. Compute and analyze summary statistics. You might also show data in the form of a side-by-side boxplot. Show all work.
(8.11) INDTSIZE: You are planning a study to compare serum cholesterol levels in vegetarians and non-vegetarians. Previous studies suggest that the standard deviation of cholesterol levels in these two populations is approximately 40 mg/dl. You want to conduct a two-sided test of H0: at a level of .05 (two-sided), want power to exceed 80%, and have an equal number of subjects in each group. Based on these assumptions, how many subjects should be studied to detect a mean difference of 10 mg/dl?
(8.12) PATIENT-SATIS: In a study of patient satisfaction we expect a mean difference in satisfaction scores of 0.25 between traditionally-treated patients and holistically-treated patients. The pooled estimate of standard deviation from is estimated at 0.67 units. Using this information, determine the size of a study to achieve 80% power.
Key to Odd Numbered Problems
Key to Even Numbered Problems (may not be posted)