Lab 5- One and Two Way ANOVA_student

docx

School

Purdue University *

*We aren’t endorsed by this school

Course

301

Subject

Statistics

Date

Feb 20, 2024

Type

docx

Pages

Uploaded by AdmiralScorpionPerson691

Name: Connor Wood T.A. name: Ziyi Wang Lab 5: One and Two- Way ANOVA NOTE: SPSS outputs are necessary to show full completion of the lab. Please paste all SPSS outputs into your lab report and submit the completed reports including all requested tables and graphs via Brightspace (under the "Lab" folder) by 11:50 pm Friday. Two points will be deducted for each SPSS requested output that is not included in the submitted lab document. Also, 30% points will be deducted for late submission, up to 24 hours. Dataset : This lab uses the dataset ( SleepPatterns ), located on Brightspace under Lab in the Datasets submodule. Instructions for opening the dataset in SPSS are found as follows.  SPSS installed on a computer: Reference page 4 of the SPSS Instruction Manual  SPSS running remotely: Reference the slide “Opening your Dataset Remotely in SPSS via Go Remote” in the document “SPSS using Citrix access guidelines” on Brightspace. Two hundred fifty college students in Indiana participated in a study examining the associations among sleep habits, sleep quality and physical/emotional factors. Participants completed an online survey about sleep habits that included the Pittsburgh Sleep Quality Index (PSQI), the Epworth Sleepiness Scale (ESS), the Horne-Ostberg Morningness Eveningness Scale (MES), the Subjective Units of Distress Scale (SUDS), and questions about academic performance and physical health. Part 1 Use SPSS to create a side-by-side box plot, descriptive statistics table and run the One-Way ANOVA for Morningness Eveningness Scale (MES) by the different levels of sleep quality(Sleep_quality) (Please refer to page 15 in the SPSS Instruction Manual, section 2 of One-Way ANOVA/Bonferroni). Use the output to answer the following questions (make sure you upload all outputs to Brightspace as part of your work ). The column Sleep_quality _ num contains the numerical values corresponding to each group. While the boxplot allows categorical groups, the ANOVA in SPSS requires categorical values be represented by numbers. This has already been done for you. Note: “ Sleep_quality _ num ”: 1 = optimal, 2 = borderline, 3 = poor 1

Descriptives MES N Mean Std. Deviation Std. Error 95% Confidence Interval for Mean Minimum Maximum Lower Bound Upper Bound 1 82 58.57 13.732 1.516 55.56 61.59 24 92 2 88 49.99 12.864 1.371 47.26 52.71 16 82 3 80 45.78 13.963 1.561 42.67 48.88 11 76 Total 250 51.46 14.451 .914 49.66 53.26 11 92 ANOVA MES Sum of Squares df Mean Square F Sig. Between Groups 6925.016 2 3462.508 18.975 <.001 Within Groups 45073.000 247 182.482 Total 51998.016 249 1. (1 point) Looking at the side-by-side boxplot, are there any outliers? Discuss between what groups you would expect to see significant differences, and why. Be sure to state whether the side-by-side boxplot displays sample or population data. 2

Yes, I would expect to see significant differences between the optimal and poor groups, because those who get optimal sleep should have a higher MES score. The boxplot represents the population data. 2. (2 points) Is it reasonable to pool the variances for One-Way ANOVA? Why or why not? Show your work. Note: You should have already run the One-Way ANOVA in SPSS, which gives you the descriptive statistics table. Make sure your descriptive statistics table output is uploaded to Brightspace. Yes, because the standard deviations are all fairly close there is little variance among groups. 3. (4 points) State your hypotheses relating to the One-Way ANOVA test for this story. H o : μ 1 = μ 2 = μ 3 H a : Not all means are the same 4. (2 points) Identify the following from your One-Way ANOVA output. F = 18.975 P-value = < 0.001 5. (4 points) What are your conclusions in terms of the story (using a significance level of 0.05)? Be sure to state whether your results refer to the sample or the population . Reject the null hypothesis because the p-value is less than 0.05. There is evidence that at least one of the MES scores is different from the population mean of MES scores. 6. (1 point) Discuss whether, in this particular case, sample observations point in the same direction as the conclusions reached for the population means. Sample observations point in the same direction the conclusions reached for the population means because the optimal sleep quality group has several outliers. 7. (4 points) Report the R-squared and the pooled estimate of the standard deviation. These calculations should be done by hand using information from the SPSS output. Show all your calculations. Round to 4 decimal places. R 2 = 0.1332 s p = 13.3897 3

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

8. (2 points) Is it legitimate to use Bonferroni to establish which means are different (at a significance level of 0.05)? Give your reason why or why not. If you believe it is legitimate, please identify which means are significantly different. Please include the output from the multiple comparisons procedure. 4

No, because there wasn’t much significance of any data being incorrectly significant. Part 2 Part 2 is optional and will not be graded. If you choose to complete it, your TA will provide feedback so that you can practice running a 2-way ANOVA. Some researchers have mentioned that Gender might affect their Morningness Eveningness Scale (MES), and thus we should also investigate the interaction between Gender and sleep_quality. Now re-run the analysis for MSE using the variables Sleep_quality (or Sleep_quality _num) and Gender in a Two-Way ANOVA, make a means plot and descriptive statistics table. 9. (0 points) Using your output, is it reasonable to pool the variances? Why or why not? 10. (0 points) Looking at your means plot (“Estimated Marginal Means” in your SPSS output), what does it tell you about each of the main effects and their interaction? Please explain how the plot tells you this. 11. (0 points) State the hypotheses (including variable names) for the Two-Way ANOVA tests. 12. (0 points) Report the F-test statistics and p-values (include outputs showing these values). a. F = ________ P-value = ________ b. F = ________ P-value = ________ c. F = ________ P-value = ________ 13. (0 points) State your conclusion to the hypotheses tested above in terms of the story. Assume α=0.05. Be sure to state whether your results refer to the sample or the population . a. b. 5

c. 6

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version