INSTRUCTIONS: This part of the exam is closed-book and should take approximately 10-15 minutes. When you are done with this part of the exam, please turn it in and pick up Part B. Please write your name on the back of the last page in the upper right-hand corner of each item you turn in. Do not write your name elsewhere, so as to allow for blinded review. Total exam time:1.25 hours.
(1) Briefly, describe the main difference between experimental studies and observational studies. [2 pts]
(2) What two key factors determine the sample size requirements of a study that wishes to estimate a mean with given confidence and power? [2]
(3) Define "simple random sample." [1]
A simple random sample is a sample in which everyone from the population has the same probability of being selected. [1]
(4) Define "double blinding." [3]
Double blinding is a study technique in which subjects (e.g., patients) [1] and observers (e.g., clinicians taking measurements) [1] are kept in the dark about treatment types [1].
(5) For (standard) ANOVA to be valid, three assumptions must be met. Provide the brief reference names we use to denote each of these assumptions. [3]
(6) An ANOVA analysis looks at 4 groups. How many degrees of freedom are there between groups (i.e., df1 =)? [1]
df1 = k - 1 = 4 - 1 = 3
(7) What summary statistics contribute to the drawing of a quartile plot? [1]
minimum, 25th percentile (Q1), median, 75th percentile (Q3), maximum [all components must be correct]
SOME.REC: A social psychologist develops a scale that measures one's ability to see life as meaningful and coherent. Let us call this scale the Sense Of Meaning and Experience ("SOME") scale. The Stewart Smalley positive affirmations is put in place to see if has an effect on one's SOME. Baseline measurements are listed as SOME1. After 6 months of therapy, SOME is measured again (SOME2). Data are:
(1) Create an Epi Info REC file with these data. (No output required.) [5 pts]
Fully valid data set - [5 pts]; points deducted during exam if help provided.
(2) Statistically describe the initial sample. [3]
n = 10, sample mean = 112.3 SD = 39.9 [3]
(Optionally, one could report selected points from the 5-point summary: 55, 82, 111, 142, 171)
(3) Statistically describe the subsequent sample. [3]
n = 10, sample mean = 121.2, SD = 38.6 [3]
(5-point summary: 71, 85, 122, 156, 178)
(4) Statistically describe the change in SOME associated with the intervention.[3]
n = 10, sample mean = 8.9, SD = 6.4) [3]
(5-point summary: -4, 4, 11, 13, 17)
(5) Plot this change in the form of a stem-and-leaf plot, and interpret this graph. [5]
|-0|4
|+0|339
|+1|022347
(x 10 - positive scores indicate an increase in SOME)
All but one of the subjects showed an improved SOME score. The average seems to be about +10.
(6) Using the step-by-step approach discussed in class, test whether the observed change is significant. (Report the null and alternative hypotheses, set the alpha level, report the test statistic and p value using an APA-like format, state your conclusion.) [8]
H0: �d = 0 [1]
H1: �d is not equal to 0 [1]
Let alpha = .05 (or .01 or whatever, as long as it is explicit) [1]
t(9) = 4.42 [3 pts: t stat, df, reporting style]
p = .0020 [1]
Reject H0 [1]
(7) Has the increase been significant? [1]
Yes.
SOME-TRI.REC: The effect of three different interventions on a person's Sense Of Meaning and Experience (SOME) are tried. The first intervention is Stewart Smalley positive affirmations (see above). The second intervention is Prozac®. The third intervention is whisky and gambling. Data are contained in SOME-TRI.REC (located in J:\Gerstman on the network) as the variable DELTA (indicating change in the SOME score following interventions). The independent GROUP is coded 1 = affirmations, 2 = Prozac, 3 = whisky and gambling.
(8) Report summary statistics by group. (Round appropriately.) [10]
Group 1: n = 10; mean = 9.0; SD = 6.3 [3]
Group 2: n = 10; mean = 10.6; SD = 5.6 [3]
Group 3: n = 10; mean = 8.4; SD = 6.2 [3]
[1 pt] for proper rounding of the mean and SD to one or two decimal places
(9) Perform Bartlett's test to help determine whether group variances differ significantly. (Report the null and alternative hypotheses, set alpha, report the test statistic and p value using an APA-like format, state the conclusion of the test.) [8]
H0: s�1 = s�2= s�3 [1]
H1: at least one population variance differs [1]
Let alpha = .05 [1]
Chi-squared (2, N = 30) = 0.11 [3]
p = .94 [1]
Retain H0 [1]
(10) Interpret Bartlett's test results.[2]
No significant difference in variances. [1]
(A common mistake is to say that Bartlett's test shows the population variances to be equal.)[1].
(11) Calculate the standard error of the mean for group 1. [3]
se(sample mean 1) = sqrt (MS Within / n1) = sqrt (36.548 / 10) = sqrt (3.6548) = 1.91175 ~= 1.9
(12) In testing whether the average change in SOME scores differs by group, what test will you use. Justify your response. [2]
One could make an argument for using either the ANOVA test or Kruskal-Wallis (non-parametric) ANOVA test. The grading will be based on naming one or the other test [1] and its justification [1].
(13) Test whether group averages differ significantly. (Report the null and alternative hypotheses, set alpha, report the test statistic and p value, state the conclusion of the test.) [8]
H0: �1 = �2 = �3 [1]
H1: At least one �i differs [1]
Let alpha = .05 (or .01) [1]
F(2, 27) = 0.35 [3 pts: F stat, dfs, reporting style]
p = .71 [1]
Retain H0 [1]
(14) Is there a significant difference associated with the treatment types? [1]
No.
(15) Review the results of both the SOME.REC analysis and this SOME-TRI.REC analysis. Provide an interpretative comment on your findings. (Two or three sentences, maximum.) Please be concise, restricting your response to interpretations only, using the allotted space, only. [2]