Lab 5- One and Two Way ANOVA_Final

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Name: Miranda Yount T.A. name: Zhengming Li 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 11:59 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. (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. There are no outliers represented on the side-by-side boxplot. The plot displays population data. 1

2. (1 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 screenshot is pasted below. 2

Because the largest standard deviation value (3: 14.029) is less than twice the smallest standard deviation value (1: 11.655), it is indicated that there is not a significant variation in the data and it is reasonable to pool variances. 3. (1 points) State your hypotheses relating to the One-Way ANOVA test for this story. Ho: μ1 = μ2 = μ3 Ha: μ1 ≠ μ2≠ μ3 4. (1 points) Identify the following from your One-Way ANOVA output. F = 9.075 P-value = < .001 5. (2 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 . Because the significance value is less than the significant threshold 0.05 the null hypothesis is rejected. 6. (1 point) Discuss whether, in this particular case, sample observations point in the same direction as the conclusions reached for the population means. Since the null hypothesis is rejected, it suggests that the sample observations do not point in the same direction as the conclusions reached for the population means. 7. (2 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 3 decimal places. 3

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R 2 = .066 s p = 88.295 Sp2 =(n1 - 1)S12 + (n2 - 1)S2^2 / n1 + n2 - 2 Sp2 =(250 - 1)*0.7942 + (250 - 1)*13.2652 / 250 + 250 – 2 = 88.295 8. (1 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. Because the results of the multiple comparisons test shows the means are the same for Turkey and Bonferroni, it isn’t appropriate to utilize the Bonferroni to determine which means are different Part 2 4

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. (1 points) Using your output, is it reasonable to pool the variances? Why or why not? Because the largest standard deviation is less than twice the smallest deviation, it is indicated that there is not a significant variation in the data and it is reasonable to pool variances. 10. (1 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. There is a significant interaction effect between sleep_quality num 1 and 2 because they do not run parallel. This direction and degree difference can be seen by examining the slopes or deviations in the plot. The plot shows sleep quality 1 is less pronounced in males than sleep quality 2 while the opposite is true for females. Sleep quality 1 and 3 however run parallel so there is less of a significant interaction between males and females. 5

11. (3 points) State the hypotheses (including variable names) for the Two-Way ANOVA tests. a. Ho: (gender); ufemale=umale Ha (gender: ufemale =/= umale b. Ho: (sleep_quality_num); u1 = u2= u 3 Ha: (sleep_quality_num) u1=/= u2 =/= u3 c. Ho (gender x sleep_qual_num) Sleep_qual_num does not depend on gender Ha (gender x sleep_qual_num) Sleep_qual_num does depend on gender 6

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12. (3 points) Report the F-test statistics and p-values (include outputs showing these values). a. Gender F = ___ 2.412 _____ P-value = ____ 0.122 ____ b. Sleep_qual F = __ 9.296 ______ P-value = ___ <.001 _____ c. Gender x sleep_qual F = __ 2.127 ______ P-value = ___ .121 _____ 13. (2 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. In our gender hypothesis, we fail to reject the null hypothesis because there is not a significant difference in the population means at the .05% threshold. b. In our gender hypothesis, we reject the null hypothesis because there is a significant difference in the population means at the .05% threshold. c. In our gender * sleep_qual_num hypothesis, we fail to reject the null hypothesis because there is not a significant difference in the population means at the .05% threshold. 7