Module 5 Assignment One-way Analysis of Variance (Use 'M5A Data BRFSS Wi22.sav' data file) Research Question: Does weight differ based on perceived well-being among Washingtonians? In other words, are Washingtonians who feel differently about their well-being differ in their weight? If so, how well does perceived well-being explain change in weight or vice versa? How do the groups differ and by how much? (Are there statistically significant differences in weight (WEIGHT2) between Washingtonians who feel differently about their well-being (GENHLTH)?

Part 1: a. State the hypotheses and define the variables Null hypothesis: Research/Alternative hypothesis: Independent variable/level of measurement: Dependent variable/level of measurement: 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 WEIGHT2 (Reported weight in pounds) as the dependent continuous variable. d. Address the following in your reporting and interpretation:

Part 2: 1. Descriptive statistics: 1.1 Mean/SD of weight for each group: 1.2 Range of means for the population for each group (i.e., 95% CI for each group): 2. Do the data meet the homogeneity/equality of variance assumption? (Report and interpret the significance value Based on Mean.) 3. Is the omnibus test statistically significant? (Also specify which omnibus test you are reporting (ANOVA/Welch)) 4. Which groups differ significantly? (Also specify which post-hoc test you are reporting (Tukey/Games-Howell)) 5. What is the magnitude of difference (effect size) for each group mean difference that is statistically significant (i.e., Cohen's d estimate)? Is the difference small, modest or large? (Calculate, report and interpret for each set of difference.) 6. Are there any significant outliers? 7. Is the distribution of weight scores similar to normal distribution for each group? 8. Are the variances of weight scores equal across all groups? 9. Would you accept or reject the null hypothesis? Why? 10. What do you conclude from the analysis? How would you explain your findings in lay language to someone who has no statistical background? ( A paragraph that summarizes your findings and conclusions.) 11. What type error are you likely to be committing, and why?

DATA TABLE TO BE USED TO ANSWER THIS QUESTIONS:

Oneway

Descriptives
COMPUTED BODY MASS INDEX
	N	Mean	Std. Deviation	Std. Error	95% Confidence Interval for Mean	Minimum	Maximum
Lower Bound	Upper Bound
excellent	117	2574.69	389.048	35.967	2503.45	2645.93	1941	4836
very good	191	2669.85	494.952	35.813	2599.21	2740.50	1844	4892
good	187	2860.89	532.423	38.935	2784.08	2937.70	1801	4876
fair	81	2957.28	807.284	89.698	2778.78	3135.79	1720	5803
poor	37	3081.41	858.672	141.165	2795.11	3367.70	1798	5650
Total	613	2772.79	585.580	23.651	2726.34	2819.24	1720	5803

Tests of Homogeneity of Variances
	Levene Statistic	df1	df2	Sig.
COMPUTED BODY MASS INDEX	Based on Mean	12.518	4	608	.000
Based on Median	10.072	4	608	.000
Based on Median and with adjusted df	10.072	4	446.743	.000
Based on trimmed mean	11.538	4	608	.000

ANOVA
COMPUTED BODY MASS INDEX
	Sum of Squares	df	Mean Square	F	Sig.
Between Groups	14347653.583	4	3586913.396	11.155	.000
Within Groups	195509510.848	608	321561.695
Total	209857164.431	612

Robust Tests of Equality of Means
COMPUTED BODY MASS INDEX
	Statistica	df1	df2	Sig.
Welch	11.089	4	170.225	.000

a. Asymptotically F distributed.

Post Hoc Tests

Multiple Comparisons
Dependent Variable: COMPUTED BODY MASS INDEX
	(I) GENERAL HEALTH	(J) GENERAL HEALTH	Mean Difference (I-J)	Std. Error	Sig.	95% Confidence Interval
Lower Bound	Upper Bound
Tukey HSD	excellent	very good	-95.161	66.573	.609	-277.30	86.98
good	-286.195*	66.843	.000	-469.08	-103.31
fair	-382.592*	81.965	.000	-606.85	-158.34
poor	-506.713*	106.954	.000	-799.34	-214.09
very good	excellent	95.161	66.573	.609	-86.98	277.30
good	-191.034*	58.337	.010	-350.64	-31.43
fair	-287.431*	75.190	.001	-493.15	-81.71
poor	-411.552*	101.855	.001	-690.23	-132.88
good	excellent	286.195*	66.843	.000	103.31	469.08
very good	191.034*	58.337	.010	31.43	350.64
fair	-96.396	75.429	.705	-302.77	109.98
poor	-220.518	102.032	.196	-499.67	58.64
fair	excellent	382.592*	81.965	.000	158.34	606.85
very good	287.431*	75.190	.001	81.71	493.15
good	96.396	75.429	.705	-109.98	302.77
poor	-124.121	112.520	.805	-431.97	183.73
poor	excellent	506.713*	106.954	.000	214.09	799.34
very good	411.552*	101.855	.001	132.88	690.23
good	220.518	102.032	.196	-58.64	499.67
fair	124.121	112.520	.805	-183.73	431.97
Games-Howell	excellent	very good	-95.161	50.757	.333	-234.50	44.18
good	-286.195*	53.005	.000	-431.68	-140.71
fair	-382.592*	96.641	.001	-650.80	-114.38
poor	-506.713*	145.675	.010	-922.41	-91.02
very good	excellent	95.161	50.757	.333	-44.18	234.50
good	-191.034*	52.901	.003	-336.05	-46.02
fair	-287.431*	96.584	.029	-555.46	-19.40
poor	-411.552	145.637	.053	-827.15	4.05
good	excellent	286.195*	53.005	.000	140.71	431.68
very good	191.034*	52.901	.003	46.02	336.05
fair	-96.396	97.784	.861	-367.55	174.76
poor	-220.518	146.436	.565	-637.99	196.95
fair	excellent	382.592*	96.641	.001	114.38	650.80
very good	287.431*	96.584	.029	19.40	555.46
good	96.396	97.784	.861	-174.76	367.55
poor	-124.121	167.252	.946	-593.18	344.94
poor	excellent	506.713*	145.675	.010	91.02	922.41
very good	411.552	145.637	.053	-4.05	827.15
good	220.518	146.436	.565	-196.95	637.99
fair	124.121	167.252	.946	-344.94	593.18

*. The mean difference is significant at the 0.05 level.

Homogeneous Subsets

COMPUTED BODY MASS INDEX
	GENERAL HEALTH	N	Subset for alpha = 0.05
1	2	3
Tukey HSDa,b	excellent	117	2574.69
very good	191	2669.85	2669.85
good	187		2860.89	2860.89
fair	81			2957.28
poor	37			3081.41
Sig.		.808	.180	.083

Means for groups in homogeneous subsets are displayed.

a. Uses Harmonic Mean Sample Size = 85.466.

b. The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error levels are not guaranteed.

Means Plots