Week 11 project

Jamiah Riddick Walden University RSCH - 8260F; Advanced Quantitative

Dr. Marker

July 25th, 2021

ANCOVA

ANCOVA is like the ANOVA, as they are the analysis of variance, except the ANCOVA which takes the effect of covariant into account, so covariant is another variable that we have measure as a part of this study that we might have believed that it has some influence on the outcome on the dependent variable. So, ANCOVA allows us to measure the effect of treatment while controlling for a covariant that could also affect our dependent variable. Therefore, “ANCOVA, analysis of covariance is used to test the main and interaction effects of categorical variables on a continuous dependent variable, controlling for the effects of selected other continuous variables, which co-vary with the dependent and the control variables are called the covariates." Therefore, our research question in this regard is that sex does not determine the family income while holding the number of hours worked per week.

Assumptions

· There should be an independent observation.

· Within each subpopulation dependent variable should be normally distributed.

· The variance of the dependent variable should be equal to the overall sub-populations.

Hypotheses: Null: “There is no relationship between family income and sex controlling for the number of hours usually work for a week”

The dependent variable in the case is the family income, which is measured in constant dollars and has been estimated through the social science research database. In this way, family income (dependent variable) is measuring through sex i.e., independent variable while assuming or holding constant the number of hours worked for the week. This control variable (number of hours worked for the week) is a covariate, which is controlling in the model for the ANCOVA analysis. Hence, the model of the study assumes that sex defines or measures the family income while holding the number of hours worked for a week and there is no relationship between the type of sex and family income. Test of between-subject effects (see appendix 1), first assumption of the ANCOVA holds, in the case the sex has the 0.9 value which is depicting that it is insignificant. So, a number of hours per week have been taken as a covariate variable into the account as a change in sex does not determine the number of hours per week. So, there is no statistically significant difference between the sex as measured by the dependent variable in the case. Based on the above discussion, it has been analyzed that ANOVA analysis postulates that sex has a positive impact on the family income (see appendix 2) without taking the covariate (number of hours worked per week) into account. In this case, it has been estimated that sex has a significant value of 0.002. Moreover, the value of the intercept is 0.00 which is also highly significant in the case. Hence, by employing the ANCOVA analysis, results of the regression analysis postulate the difference in the statistical analysis (see appendix 3). In this case, the number of hours worked for a week has been taken as control or covariate variable and the influence of sex has been analyzed on the family income. In this regard, it has found a difference in the Statistical results i.e., when the number of hours per week is taken as covariate then the statistical results of the sex changes. In the way, it has been found that sex is insignificant i.e., not influencing the family income. Moreover, sex is also not closed to significance as it has a value of 0.8.

APPENDICES

Appendix 1

Tests of Between-Subjects Effects
Dependent Variable: NUMBER OF HOURS USUALLY WORK A WEEK
Source	Type III Sum of Squares	df	Mean Square	F	Sig.
Corrected Model	.445a	1	.445	.003	.959
Intercept	5920.445	1	5920.445	37.155	.000
sex	.445	1	.445	.003	.959
Error	1434.100	9	159.344
Total	19599.000	11
Corrected Total	1434.545	10
a. R Squared = .000 (Adjusted R Squared = -.111)

Appendix 2

Tests of Between-Subjects Effects
Dependent Variable: FAMILY INCOME IN CONSTANT $
Source	Type III Sum of Squares	df	Mean Square	F	Sig.
Corrected Model	19089625078.966a	1	19089625078.966	9.813	.002
Intercept	962227019084.370	1	962227019084.370	494.647	.000
sex	19089625078.965	1	19089625078.965	9.813	.002
Error	885101974342.096	455	1945279064.488
Total	1850315909749.398	457
Corrected Total	904191599421.062	456
a. R Squared = .021 (Adjusted R Squared = .019)

Appendix 3

Tests of Between-Subjects Effects
Dependent Variable: FAMILY INCOME IN CONSTANT $
Source	Type III Sum of Squares	df	Mean Square	F	Sig.	Partial Eta Squared
Corrected Model	654335383.996a	2	327167691.998	.182	.837	.044
Intercept	60016648.794	1	60016648.794	.033	.859	.004
hrs2	608403888.754	1	608403888.754	.339	.576	.041
sex	40215569.614	1	40215569.614	.022	.885	.003
Error	14357406602.393	8	1794675825.299
Total	31222932211.128	11
Corrected Total	15011741986.389	10
a. R Squared = .044 (Adjusted R Squared = -.196)

RESPONDENTS SEX
Dependent Variable: FAMILY INCOME IN CONSTANT $
RESPONDENTS SEX	Mean	Std. Error	95% Confidence Interval
			Lower Bound	Upper Bound
MALE	32341.988a	42369.595	-65362.474	130046.450
FEMALE	38994.120a	13396.740	8101.182	69887.059
a. Covariates appearing in the model are evaluated at the following values: NUMBER OF HOURS USUALLY WORK A WEEK = 40.64.

Descriptive Statistics
Dependent Variable: FAMILY INCOME IN CONSTANT $
RESPONDENTS SEX	Mean	Std. Deviation	N
MALE	31927.50	.	1
FEMALE	39035.57	40778.276	10
Total	38389.38	38744.989	11

Levene's Test of Equality of Error Variancesa
Dependent Variable: FAMILY INCOME IN CONSTANT $
F	df1	df2	Sig.
1.152	1	9	.311
Tests the null hypothesis that the error variance of the dependent variable is equal across groups.
a. Design: Intercept + hrs2 + sex