Factorial ANOVA of Variance

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Liberty University *

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820

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Sociology

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Feb 20, 2024

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Camesha Walters HSCI820 Qualitative Topic: Case Study Factorial Analysis of Variance February 18, 2023 Factorial Analysis of Variance In this study, we will consider multiple factors. We measured skin temperature over a period of time, with an environmental factor (hot or cold environment) present. Research question: “Is there a statistical difference in skin temperature across time while taking into account the “factor” “environment” (hot versus cold)?” Assumptions Testing 1. Data level of measurement – what is the level of measurement for the data used in this case study? ______________________________________________________________ 2. Would the amount of skewness and kurtosis in these affect the analysis? How do you know? Give numerical values to support your conclusion. ______________________________________________________________________________________________________ __________________________________________ Table 1. PASTE TABLE with skewness and kurtosis (EACH FACTOR) BELOW
Descriptive Statistics N Minimum Maximum Mean Std. Deviation Skewness Kurtosis Statistic Statistic Statistic Statistic Statistic Statistic Std. Error Statistic Std. Error Time_0 32 21.70 35.40 32.9406 2.22085 -4.365 .414 22.499 .809 Time_15 32 31.80 38.90 35.3709 2.21342 -.004 .414 -1.535 .809 Time_30 32 33.30 37.40 35.8406 .91011 -.736 .414 .471 .809 Valid N (listwise) 32 3. Was the assumption of normality met and how do you know? Table 2. PASTE Tests of NORMALITY table BELOW Tests of Normality
Kolmogorov-Smirnov a Shapiro-Wilk Statistic df Sig. Statistic df Sig. Time_0 .259 32 <.001 .532 32 <.001 Time_15 .195 32 .003 .907 32 .009 Time_30 .112 32 .200 * .958 32 .247 *. This is a lower bound of the true significance. a. Lilliefors Significance Correction Figure 1. PASTE Histogram with normal curve (EACH FACTOR) BELOW
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Figure 2. PASTE Normal Q-Q Plot (EACH FACTOR) BELOW
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4. Were there any outliers; how do you know? ______________________________________________________________________________________________________ __________________________________________
Table 3. PASTE Box-and-Whiskers Plot (EACH FACTOR) BELOW
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Factorial ANOVA – Between-Within (Split-Plot) Design
Table 4. PASTE Within-Subjects Factors table BELOW Table 5. PASTE Between-Subjects Factors table BELOW Table 6. PASTE Descriptive Statistics table BELOW Table 7. PASTE Box’s Test of Equality of Matrices table BELOW
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Table 8. PASTE Mauchley’s Test of Sphericity table BELOW Table 9. PASTE Tests of Within-Subjects Effects table(s) BELOW Table 10. PASTE Levene’s Test of Equality of Error Variances table BELOW Table 11. PASTE Tests of Between-Subjects Effects table BELOW
Table 12. PASTE Pairwise Comparisons table(s) (FOR EACH FACTOR) BELOW This could include the table for the interaction comparison which (may) require the use of the Syntax calculation. Table 13. PASTE Univariate Tests table(s) (FOR EACH FACTOR) BELOW
Figure 3. PASTE Profile Plots figure BELOW Abstract The write-up must include the following. Use these questions as a guide. 1. What is the research question? 2. What is the mean and standard deviation for skin temperature at minutes 0, 15, and 30 while working in a hot or cold environment? 3. Was Levene’s test significant? How do you know? 4. What did Mauchley’s Test of Sphericity met, how do you know? 5. Was the ANOVA statistically significant? (Hint: look at the p sig value in the Test of Within-Subjects table) 6. List all (if any) significant posthoc comparisons including the interaction comparison 7. What do the statistical findings of these data suggest about the research question? 8. What are your thoughts on the finding of this analysis, and what are the practical application(s) of this finding? Elaborate on the study's meaning, why, and how you know, and relate the findings to exercise physiology knowledge. Use references if needed. (Hint- does this study “make sense?” What could influence results?)
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