Question
One-way Analysis of Variance (Use ‘BRFSS800. sav’ data file) Research Question: Does body-mass index differ based on perceived well-being among Washingtonians? In other words, are Washingtonians who feel differently about their well-being differ in their body-mass index? If so, how well does perceived well- being explain BMI or vice versa? How do the groups differ and by how much? (Are there statistically significant differences in body-mass index (@_BMI4) between Washingtonians who feel differently about their well-being (GÀNHLTH)? a. State the hypotheses and define the variables Null hypothesis: There is no statistically significant difference in BMI among Washingtonians who feel differently about their well-being Research/Alternative hypothesis: There is a statistically significant difference in BMI among Washingtonians who feel differently about their well-being Independent variable/level of measurement: General Health / categorical/ordinal Dependent variable/level of measurement: Body Mass Index(bmi) /continuous b. Screen the data on the two variables and clean/sort the data as needed first to ensure all problematic codes are excluded from analyses. c. Conduct One-way Analysis of Variance test using GENHLTH (General Health) as the independent categorical variable and @ BMI4 (Computed Body-Mass Index) as the dependent continuous variable. d. Address the following in your reporting and interpretation: 1. Descriptive statistics: 1.1 Means/SDs of BMI for each group: 1 1.1.1 Excellent, Mean-2574.69, St. Dev=389.048 1.1.2 Very good, Mean=2669.85, St. Dev=494.952 1.1.3 Good, Mean-2860.89, St. Dev-532.423 1.1.4 Fair, Mean-2957.28, St. Dev-807.284 1.1.5 Poor, Mean-3081.41, St. Dev=858.627 1.2 Range of means for the population for each group (1.e., 95% CI for each group): 1.2.1 Excellent: 2503.45-2645.93 1.2.2 Very good: 2599.21-2740.50 1.2.3 Good: 2784.08-2937.70 1.2.4 Fair: 2778.78-3135.79 1.2.5 Poor: 2795.11-3367.70 2. Do the data meet the homogeneity/equality of variance assumption? (Report and interpret the significance value Based on Mean.) 2.1 : The data does meet the homogeneity/equality of variance assumption because all values for the test of normality are p<0.05 3. Is the omnibus test statistically significant? (Also specify which omnibus test you are reporting (ANOVA/Welch)) 3.1 Yes, the omnibus test is statistically significant. We will interpret Welch test significance. This will tell us if there is any significant difference in the data. Will not tell us specifically which groups differ. Welch test of 0.000 tells us that at least 2 groups are statistically significantly different from each other. 4. Which groups differ significantly? (Also specify which post-hoc test you are reporting (Tukey/Games-Howell)) 4.1 The Excellent and Very Good group differ significantly 5. What is the magnitude of the difference (effect size) for each group mean difference that is statistically significant as Cohen’s d measure? Is the effect small, medium, or large? (Calculate, report, and interpret for each set of difference.) 5.1 E and VG: 0.21(small) 6. Are there any significant outliers? 6.1 Yes, there are some significant outliers in the data 7. Is the distribution of BMI scores similar to normal distribution for each group? If not, how would you characterize the shape of the distributions? (Hint: look at the skewness/kurtosis values and histograms) 7.1 The data has a slight positive skew 8. Are the variances of BMI scores equal across all groups? 8.1 No because each group is discrete from one another. 9. Would you accept or reject the null hypothesis? Why? 9.1 I would reject the null hypothesis because the p-value is less than 0.05 10. What do you conclude from the analysis? How would you explain your findings in lay language to someone who has no statistical background? (Write a paragraph that summarizes your findings and conclusions.) 10.1 After analyzing the data, I can conclude that there is no statistically significant difference between BMI and perceived well-being. I know this because using the Shapiro Wilks test, I figured out the p value is less than 0.05.
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