The following research questions can be answered using 1 of the 5 tests you have learned so far: single-sample t-test, paired-samples t-test, independent-samples t-test, one-way ANOVA, or two-way ANOVA. Use the information in the tables to construct your SPSS data file, just as you have been doing in Part 2 of each homework assignment. There is only 1 correct choice of analysis for each question, and note that some tests are 1-tailed and some are 2-tailed. The assessment is open-book/open-notes.
For each problem involving a test of significance, your answer must include: A) SPSS output; B) an appropriate graph from SPSS; C) a Results section in current APA style including a statistical statement (i.e., t(19) = 1.79, p = .049); a sentence summarizing the results "in English" (i.e., "There was a significant difference between the two groups on the variable..." or "There was no significant difference..."); and a decision about the null hypothesis.
For ANOVA problems: Report statistical findings and make statements for all main effects and interaction effects. Use Tukey's test for any analyses requiring post hoc tests.
Submit this assignment by 11:59 p.m. (ET) on Monday of Module/Week 5.
1. Children who experience chronic pain as a result of medical procedures are the focus of a psychiatrist's study. Specifically, the psychiatrist wants to measure whether a new program helps decrease feelings of chronic pain in the short-term. He measures children's self-reports of pain levels before treatment on a standardized scale with a range of 0-10, with 10 being the most severe. He then administers the new program, and measures children's pain levels after treatment. Does the new treatment decrease self-reported levels of chronic pain? (16 pts)
Patient Pain before tx Pain after tx
a) SPSS output
Paired Samples Statistics
Mean N Std. Deviation Std. Error Mean
Pair 1 Pain_before_tx 6.13 16 2.446 .612
Pain_after_tx 5.38 16 1.928 .482
Paired Samples Correlations
N Correlation Sig.
Pair 1 Pain_before_tx & Pain_after_tx 16 .710 .002
Paired Samples Test
Paired Differences t df Sig. (2-tailed)
Mean Std. Deviation Std. Error Mean 95% Confidence Interval of the Difference
Lower Upper
Pair 1 Pain_before_tx - Pain_after_tx .750 1.732 .433 -.173 1.673 1.732 15 .104
b) SPSS graph
c) Current APA-style Results section
From the correlation table we see that there is a correlation between pain before tx and pain after tx at 5% level of significance because the p value corresponding to r=0.710 is 0.002 which is less than 0.05 at 5% level of significance and also the correlation between them is strong and positive.
We can determine from a paired samples t-test that the mean pain score after treatment was not significantly lower than before treatment, t (15) = 1.732, p = 0.052>0.05 at 5% level of significance, one-tailed. The mean score of self-reported pain in children after treatment was 5.38 (SD = 1.93) and before treatment was 6.13 (SD = 2.45). Conclusion: the treatment is not significantly associated with decreasing pain scores in children. The null hypothesis must not be rejected.
2. A health psychologist in a northern climate wants to evaluate the claim that UV lamps help lower depressive symptoms in middle-aged women. She recruits volunteers who meet the criteria for clinical depression and assigns them to two groups: one group receives a standard treatment for depression and undergoes a half hour of UV lamp therapy each day; the other group receives the same standard treatment for depression but without UV lamp therapy. At the end of two months, she administers a depression inventory where lower scores indicate fewer depressive symptoms (lower levels of depression). Assume all other variables are controlled for in the study. Evaluate the claim that depression treatment plus the UV lamp results in lower depression scores than depression treatment alone. (16 pts)
Depression Treatment + UV Depression
Treatment Only
34
29
46
31
28
27
12 14
33
27
24
19
35
42 39
29
12
41
26
23
47 31
25
14
24
37
42
42
a) SPSS output
Group Statistics
Therapy N Mean Std. Deviation Std. Error Mean
Depression_Scores UV_Lamp 14 28.64 9.548 2.552
Without_UV 14 30.86 10.833 2.895
Independent Samples Test
Levene's Test for Equality of Variances t-test for Equality of Means
F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference
Lower Upper
Depression_Scores Equal variances assumed .772 .388 -.574 26 .571 -2.214 3.859 -10.147 5.719
Equal variances not assumed -.574 25.596 .571 -2.214 3.859 -10.154 5.725
b) SPSS graph
c) Curren APA-style Results section:
An independent samples t test was conducted to evaluated the hypothesis that UV lamps help lower depressive symptoms in middle aged women. The test results were not significant, with t(26) = -.574, p = .571/2 = .286. Thus, we are unable to reject the null hypothesis and conclude that the use of UV light therapy results in lower depression levels.
3. As part of a new prevention program, a clinical psychologist wants to see whether feelings of alienation differ as a function of immigration status in a local high school. She divides volunteer students into three categories: first-generation immigrants, second-generation immigrants, and non-immigrants. She then administers an instrument assessing feelings of alienation, where higher scores indicate stronger feelings of alienation from peers, adults, and society in general. Is there a difference in alienation scores among these three groups? (16 pts)
First-generation
immigrants Second-generation
immigrants Non-immigrants
35
39
35
37
36
24
39 36
37
37
29
37
35
25 29
32
17
28
19
30
32
a) SPSS output
Descriptive Statistics
Dependent Variable: Alianation_scores
Immigrants Mean Std. Deviation N
First_generation 35.00 5.132 7
Second_generation 33.71 4.786 7
Non_immigrants 26.71 6.157 7
Total 31.81 6.329 21
Tests of Between-Subjects Effects
Dependent Variable: Alianation_scores
Source Type III Sum of Squares df Mean Square F Sig. Partial Eta Squared
Corrected Model 278.381a 2 139.190 4.792 .021 .347
Intercept 21248.762 1 21248.762 731.515 .000 .976
Immigrants 278.381 2 139.190 4.792 .021 .347
Error 522.857 18 29.048
Total 22050.000 21
Corrected Total 801.238 20
a. R Squared = .347 (Adjusted R Squared = .275)
b) SPSS graph
c) Current APA-style Results section
4. In response to media reports of violence on college campuses, a psychologist who works at a local community college decides to study students' perceptions of campus safety. He hopes to use these results to help develop an on-campus violence prevention program. The administration has asked him additionally to look at whether perceptions of safety differ depending on students' year in school and gender. The psychologist administers a questionnaire with possible scores ranging from 1-70, with higher scores indicating higher perceptions of safety on campus, and lower scores indicating perceptions that the campus is less safe. Based on the data collected below, do year in school and/or gender have an effect on perceptions of campus safety? (16 pts)
Male Freshmen Sophomore Junior Senior
39
67
54
66
61 45
32
63
59
30 63
67
46
51
41 42
53
68
56
60
Female 51
46
43
57
32
32
21
37
49
53 56
52
60
47
59 61
55
43
57
60
a) SPSS output
Descriptive Statistics
Dependent Variable: Safety_Score
Gender Students_Year Mean Std. Deviation N
Males Freshmen 57.40 11.502 5
Sophomore 45.80 15.090 5
Junior 53.60 11.082 5
Senior 55.80 9.550 5
Total 53.15 11.904 20
Females Freshmen 45.80 9.365 5
Sophomore 38.40 12.954 5
Junior 54.80 5.357 5
Senior 55.20 7.225 5
Total 48.55 11.038 20
Total Freshmen 51.60 11.626 10
Sophomore 42.10 13.820 10
Junior 54.20 8.230 10
Senior 55.50 7.990 10
Total 50.85 11.568 40
Levene's Test of Equality of Error Variancesa
Dependent Variable: Safety_Score
F df1 df2 Sig.
1.216 7 32 .323
Tests the null hypothesis that the error variance of the dependent variable is equal across groups.
a. Design: Intercept + Gender + Students_Year + Gender * Students_Year
Tests of Between-Subjects Effects
Dependent Variable: Safety_Score
Source Type III Sum of Squares df Mean Square F Sig. Partial Eta Squared
Corrected Model 1577.500a 7 225.357 1.980 .089 .302
Intercept 103428.900 1 103428.900 908.866 .000 .966
Gender 211.600 1 211.600 1.859 .182 .055
Students_Year 1099.700 3 366.567 3.221 .036 .232
Gender * Students_Year 266.200 3 88.733 .780 .514 .068
Error 3641.600 32 113.800
Total 108648.000 40
Corrected Total 5219.100 39
a. R Squared = .302 (Adjusted R Squared = .150)
Multiple Comparisons
Dependent Variable: Safety_Score
(I) Students_Year (J) Students_Year Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval
Lower Bound Upper Bound
Tukey HSD Freshmen Sophomore 9.50 4.771 .212 -3.43 22.43
Junior -2.60 4.771 .947 -15.53 10.33
Senior -3.90 4.771 .846 -16.83 9.03
Sophomore Freshmen -9.50 4.771 .212 -22.43 3.43
Junior -12.10 4.771 .073 -25.03 .83
Senior -13.40* 4.771 .040 -26.33 -.47
Junior Freshmen 2.60 4.771 .947 -10.33 15.53
Sophomore 12.10 4.771 .073 -.83 25.03
Senior -1.30 4.771 .993 -14.23 11.63
Senior Freshmen 3.90 4.771 .846 -9.03 16.83
Sophomore 13.40* 4.771 .040 .47 26.33
Junior 1.30 4.771 .993 -11.63 14.23
Based on observed means.
The error term is Mean Square(Error) = 113.800.
*. The mean difference is significant at the .05 level.
b) SPSS graph
c)
d) Current APA-style Results section
5. A cross-cultural psychologist living in an overseas, non-Western rural area has a background studying culture bias in traditional psychological testing procedures. She contends that members of a rural community who normally score lower than average on traditional Western-style IQ tests will score better than the general population on a new test that emphasizes practical and social intelligence. Scores on the test can range from 1-100. She recruits 18 volunteers and administers the new test. Their scores are as follows:
Practical/Social IQ Scores on New Test
78
63
82
87
74
61
58
89
86
82
64
61
70
67
51
78
54
88
Based on early normative data in Western countries, the mean for the general population is 65. Do members of this community score significantly higher on the new IQ test? (16 pts)
a) SPSS output
One-Sample Statistics
N Mean Std. Deviation Std. Error Mean
Social_IQ_Scores 18 71.83 12.411 2.925
One-Sample Test
Test Value = 18
t df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the Difference
Lower Upper
Social_IQ_Scores 18.403 17 .000 53.833 47.66 60.01
b) SPSS graph
c)
d) Current APA-style Results section
A single-sample t-test was conducted