Week 11 project

Running Head: REPEATED MEASURES SPSS IN ANNOVA

REPEATED MEASURES SPSS IN ANNOVA

Jamiah Riddick Walden University RSCH - 8260F; Advanced Quantitative Dr. Marker July 18th, 2021

Factorial ANOVA

Factorial ANOVA is the statistical procedure that is used to analyze the impact of the two or more independent variables on the given dependent variable. In this regard, this study is analyzing the interaction of the use of marijuana and the family income on the number of children. Therefore, in this regard, factorial ANOVA deals with the efficient testing for checking such association deals with the “comparison of different means between the groups which are split into independent variables (called factors)”. This study is using the general social science database for analyzing such interaction. For this purpose, a number of children have been taken as the dependent variable and the use of marijuana and family income has been taken as the independent variables or factors. Therefore, two-way ANOVA has been analyzed where the “should marijuana be made legal and respondents’ income served as the factors for measuring the number of children.

Hypothesis:

HO: There is no interaction between the factors.

H1: There is an interaction between the factors.

The results of two categorical variables (factors) have been obtained through the factorial ANOVA estimation on the SPSS.

Conclusion:

All the results obtained through the SPSS regarding the social set database are available in the appendices section. In this way, appendix 2 of the appendices deal with the “between-subjects factors whose sample size is slightly different from the sample size before estimating the factorial analysis and the sample size changes because of factorial ANOVA”. Moreover, the descriptive statistics in this regard which have been obtained through the ANOVA factorial analysis are available in appendix 03 of the appendices. These statistics are also “presenting the different means as compared to the observed means which are depicting clearly in marginal expected means appendix section”. Furthermore, appendix 4 is dealing with “the Levene’s test of equability of error variances” which is clearly indicating the normal distribution of the given model and presents the facts of the significance of the given actors. Therefore, this analysis has not been violated any assumption which is clearly depicting by the mean-based approach presented in the appendices section. So, the main findings of the study i.e., “between-subjects effects” are available in the appendix 5 section of the appendices, which deals with the representation of the statistics regarding the one-way and two-way ANOVA, due to which the researcher will draw the inferences regarding the hypothesis of the study i.e., whether or not any interaction found between the factors or actors of the model. in the way, it is found that the significant value of the corrected model is 0.00 which postulates that the corrected model is highly significant which is based on the factorial ANOVA. Furthermore, the value of the intercept of the corrected model is also found highly significant which has a p-value of 0.000. therefore, it is concluded that the factors in the corrected model are highly significant. Moreover, the observed power found is 0.98 and 1 for the corrected model which is indicating the sample size is large enough for estimating the effect. The partial Eta squared values in this regard are .175 and .172 which is also representing the efficiency of factorial ANOVA. In this way, the probability values obtained should marijuana be made legal and respondents’ income in the one-way factorial ANOVA has been found insignificant i.e., .5 and .6. Therefore, it is concluded that in one-way factorial analysis there is no interaction between the factors, and should marijuana be made legal and the respondent’s income have an insignificant interaction with the number of children. While the results of the two-way Factorial ANOVA postulates that the probability value of the interaction between the factors is 0.05. Therefore, it is concluded that the factors have an interaction with the number of children. However, this interaction has not been found significant. Therefore, based on the results of the test of between subjects’ effects it is concluded that the null hypothesis is rejected, and the alternative hypothesis is accepted i.e., there is an interaction. Below is the plot graph, which is depicting the facts in this regard.

APPENDICES

Appendix 1

Model Summary
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.312a	.097	.088	1.407
a. Predictors: (Constant), RESPONDENTS INCOME, SHOULD MARIJUANA BE MADE LEGAL

Coefficientsa
Model	Unstandardized Coefficients	Standardized Coefficients	t	Sig.
	B	Std. Error	Beta
1	(Constant)	-.599	.561		-1.068	.287
	SHOULD MARIJUANA BE MADE LEGAL	.898	.207	.292	4.339	.000
	RESPONDENTS INCOME	.080	.042	.129	1.910	.058
a. Dependent Variable: NUMBER OF CHILDREN

Appendix 2 Between-Subjects Factors
	Value Label	N
SHOULD MARIJUANA BE MADE LEGAL	1	LEGAL	131
	2	NOT LEGAL	72
RESPONDENTS INCOME	1	LT $1000	3
	2	$1000 TO 2999	2
	3	$3000 TO 3999	3
	4	$4000 TO 4999	1
	5	$5000 TO 5999	2
	6	$6000 TO 6999	3
	7	$7000 TO 7999	3
	8	$8000 TO 9999	4
	9	$10000 - 14999	12
	10	$15000 - 19999	5
	11	$20000 - 24999	21
	12	$25000 OR MORE	144

Appendix 3

Descriptive Statistics
Dependent Variable: NUMBER OF CHILDREN
SHOULD MARIJUANA BE MADE LEGAL	RESPONDENTS INCOME	Mean	Std. Deviation	N
LEGAL	LT $1000	.33	.577	3
	$3000 TO 3999	.00	.000	3
	$4000 TO 4999	1.00	.	1
	$5000 TO 5999	1.00	.	1
	$6000 TO 6999	1.00	.	1
	$7000 TO 7999	.00	.	1
	$8000 TO 9999	2.00	.	1
	$10000 - 14999	1.29	1.113	7
	$15000 - 19999	4.00	2.828	2
	$20000 - 24999	.64	.809	11
	$25000 OR MORE	1.25	1.336	100
	Total	1.18	1.323	131
NOT LEGAL	$1000 TO 2999	2.00	.000	2
	$5000 TO 5999	2.00	.	1
	$6000 TO 6999	1.00	1.414	2
	$7000 TO 7999	1.50	2.121	2
	$8000 TO 9999	2.33	2.082	3
	$10000 - 14999	1.40	1.673	5
	$15000 - 19999	.67	1.155	3
	$20000 - 24999	2.40	1.265	10
	$25000 OR MORE	2.20	1.665	44
	Total	2.06	1.573	72
Total	LT $1000	.33	.577	3
	$1000 TO 2999	2.00	.000	2
	$3000 TO 3999	.00	.000	3
	$4000 TO 4999	1.00	.	1
	$5000 TO 5999	1.50	.707	2
	$6000 TO 6999	1.00	1.000	3
	$7000 TO 7999	1.00	1.732	3
	$8000 TO 9999	2.25	1.708	4
	$10000 - 14999	1.33	1.303	12
	$15000 - 19999	2.00	2.449	5
	$20000 - 24999	1.48	1.365	21
	$25000 OR MORE	1.54	1.505	144
	Total	1.49	1.474	203

Appendix 4

Levene's Test of Equality of Error Variancesa
Dependent Variable: NUMBER OF CHILDREN
F	df1	df2	Sig.
1.614	19	183	.057
Tests the null hypothesis that the error variance of the dependent variable is equal across groups.
a. Design: Intercept + grass + rincome + grass * rincome

Appendix 5

Tests of Between-Subjects Effects
Dependent Variable: NUMBER OF CHILDREN
Source	Type III Sum of Squares	df	Mean Square	F	Sig.	Partial Eta Squared	Noncent. Parameter	Observed Powerb
Corrected Model	76.756a	19	4.040	2.042	.008	.175	38.804	.981
Intercept	75.348	1	75.348	38.092	.000	.172	38.092	1.000
grass	.704	1	.704	.356	.552	.002	.356	.091
rincome	18.113	11	1.647	.832	.608	.048	9.157	.454
grass * rincome	28.257	7	4.037	2.041	.052	.072	14.285	.779
Error	361.983	183	1.978
Total	891.000	203
Corrected Total	438.739	202
a. R Squared = .175 (Adjusted R Squared = .089)
b. Computed using alpha = .05

Appendix 6

Grand Mean
Dependent Variable: NUMBER OF CHILDREN
Mean	Std. Error	95% Confidence Interval
		Lower Bound	Upper Bound
1.400a	.221	.964	1.837
a. Based on modified population marginal mean.

Estimates
Dependent Variable: NUMBER OF CHILDREN
SHOULD MARIJUANA BE MADE LEGAL	Mean	Std. Error	95% Confidence Interval
			Lower Bound	Upper Bound
LEGAL	1.137a	.324	.498	1.776
NOT LEGAL	1.723a	.292	1.147	2.299
a. Based on modified population marginal mean.