Download Comparing GRE Scores and Performing Statistical Analysis: A Case Study and more Assignments Data Analysis & Statistical Methods in PDF only on Docsity!
- An institutional researcher at U of X was interested in comparing the GRE scores of potential graduate students who apply to the School of Liberal Arts (SOLA) vs. the School of Public Health (SOPH). The researcher’s assistant obtains a random sample of GRE Quantitative (GREQ) and Verbal (GREV) scores from the Graduate School Admissions office and reports the following:
SOLA SOPH GREQ GREV GREQ GREV Q (^) (LA) = 522 V (^) (LA) = 614 Q (^) (PH) = 602 V (^) (PH) = 604 s Q(LA) = 86 s V(LA) = 96 s Q(PH) = 105 s V(PH) = 95 n Q(LA) = 72 n V(LA) = 72 n Q(PH) = 70 n V(PH) = 70 r QV(LA) = 0.62 r QV(PH) = 0.
For GREQ, the assistant found: Pooled Variance = 9184.5786; SE = 16.0864; Critical value: t (.975;df=140) = 1. Pooled 95% CI: -80 ± 31.804 [-111.804, -48.196] t (140) = (-80/16.0864) = -4.97, 2-tailed p < 0.
1.a. Are there any statistical issues with using the Pooled Variance for the GREQ scores? ( 3 points )
The assistant quit shortly thereafter. Due to security and confidentiality issues, the raw data file is destroyed; however, the researcher wants to know if there is a significant difference between SOLA and SOPH scores on the GREV.
1.b. For GREV, Construct a Pooled 95% Confidence Interval for the Mean Difference between SOLA and SOPH. ( 3 points )
1.c. For GREV, Conduct a Pooled two-sample t-test for Mean Difference between SOLA and SOPH. ( 3 points ) t = df = Significant? (two-tailed, α = 0.05) Yes No
Since the GRE Combined score (GREC = GREQ+GREV) is often used for admission decisions and reporting, the Provost wants to know if there is significant difference between SOLA and SOPH in the GREC.
1.d. Calculate the following: ( 10 points ) SOLA SOPH GREC GREC C (^) (LA) = C (^) (PH) = s C(LA) = s C(PH) = n C(LA) = n C(PH) =
1.f. For GREC, Construct a Pooled 95% Confidence Interval for the Mean Difference between SOLA and SOPH. ( 3 points )
1.g. For GREC, Conduct a Pooled two-sample t-test for Mean Difference between SOLA and SOPH. ( 3 points ) t = df = Significant? (two-tailed, α = 0.05) Yes No
Note: Partial credit will be given so show your work.
- Suppose a test statistic has a Type I error rate of α = 0.05. That is, 5% of the time the test will reject the null hypothesis when the null hypothesis is actually true. Now suppose the K =3 tests conducted in the previous analyses were independent.
2.a. What is the probability of at least one failure, P( r ≥ 1) = _____________. (3 points)
2.b. Is it reasonable to assume that these tests were independent? Explain. ( 3 points )
- An obesity researcher wanted to investigate the effects of a 12-week diet and exercise program on obese women. The participants were N=25 females recruited from a local bariatric physician. All participants had a body mass index (BMI) in excess of 26. The participants BMI and resting metabolic rate (RMR) were measure before and after the 12-week program. The data for this is in the Microsoft Excel file ( BST621-Assign4-BMI.xls )
SPSS: Use Analyze-Compare Means-Paired Samples T-Test and choose PRE and POST variables as pairs Use Analyze-Compare Means One Sample T Test and use the DIFF variables as Test Variables
JMP: Use Analyze-Matched Pairs enter the PRE and POST variables as Y, Paired Response Use Analyze-Distributions enter the PRE POST and DIFF variables Under the DIFF Banner select the Test Means Option
SAS: Use PROC MEANS N MISS MEAN STD VAR STDERR T PROBT;VAR PRE POST DIFF; Use PROC TTEST; PAIRED PRE*POST; RUN; and
3.a. In symbolic notation, what was the null hypothesis for the previous analysis? (The null hypothesis was the same for both variables.) ( 2 points )
3.b. Enter the following Results. ( 28 points total ) 95% CI (Mean Diff) Pre Post Mean Diff Lower Bound Upper Bound BMI Mean SD t p-value SE(MDiff) n r df 95% CI (Mean Diff) Pre Post Mean Diff Lower Bound Upper Bound RMR Mean SD t p-value SE(MDiff) n r df
3.c. For both the BMI and RMR, interpret each 95% CI. ( 4 points )
3.d. How would missing data affect the interpretation of these results? ( 3 points )
3.e. What other limitations does this study have? ( 3 points )
- Based on Schwartz et al. (1991), a researcher investigated the effect of cigarette smoking on lung functioning in patients with idiopathic pulmonary fibrosis. The researcher collected the patient’s smoking history and measured their percent predicted residual volume (PPRE).
Never Former Current 65 120 105 100 60 99 82 52 103 57 80 104 84 103 115 86 107 90 109 107 94
7.a. State the omnibus null hypotheses for this one-way analysis of variance (ANOVA). ( 3 points ).
7.b. Complete the ANOVA Source Table with SS, df , MS, and F , and test the null hypothesis in (1) at the α = .05 level of significance. ( 5 points )
Source SS df MS F p-value
Between ______ ___ _____ ____ _____
Within _______ ___ _____
Total ________ ___
7.c. What is the Model R 2? R^2 = _______ ( 2 points )
7.d. Compute Tukey HSD for each pairwise comparison. ( 9 points ). Mean Diff Lower Bound Upper Bound Never vs Former Never vs Current Current vs Former
7.e. Based on these results explain which groups are significantly different and which group if any has worse lung functioning. ( 4 points ).
- Do you think there is a causal relationship between these variables? Explain. ( 3 points ).
9.a. What was the “Observed Power” for these results at a two-tailed α = 0.05? (3 points)
9.b. Holding these data (Means and SDs) constant, what would a future sample size need to be for a similar to have 80% Power (1 – β = 0.80) at a two-tailed α = 0.05.? (3 points)
- Write a brief interpretation of these results. ( 4 points )
Directions for 7.b. – 7.d. SPSS: Use Analyze-Compare Means –One Way ANOVA and Select PPRE as the Dependent Variable and Group as Factor Select Options – Descriptive statistics, Homogeneity of Var Test, Welch Select Post-Hoc and Check the Tukey option
JMP: Change the X variable to Nominal, then Use Analyze-Fit Y by X Under the Oneway Analysis Banner select the Means/Anova/Pooled t and Means and Std Dev Compare Means – All Pairs, Tukey HSD options
SAS: Use PROC GLM; CLASS group; model PPRE = group / solution; MEANS group / tukey; RUN;
