Independent T-test Assumptions

2021-04-30 17:39:25
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During the independent t-test analysis, several assumptions have to be put into consideration. They include; the dependent variable which should be measured on a continuous scale while the independent variable should consist of two independent categorical groups. Another assumption is that there should exist no relationship between observations in each group or between groups themselves, the data is assumed to have no significant outliers, the dependent variable should be normally distributed for each group of the independent variable and there should exist homogeneity of variances of the data (Bathke, 2008).

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Variables:

The dependent variable chosen is respondents employment status (WRKSF) which is measured on continuous scale and the independent variable chosen is the race of the respondent (RACE) which is categorized in whites, blacks and others. The objective question being; does race determine the employment status of an individual?

Hypothesis

Since our aim is to investigate if there exist a significant mean difference between blacks and whites then our hypothesis include:

- Results and discussion

- Group Statistics

- what race do you consider yoursefN Mean Std. Deviation Std. Error Mean

respondents employment status white 2213 1.86 .346 .007

black 429 2.07 .674 .033

The group statistics table gives us relevant information about the two groups, blacks and whites since the test requires this information. The sample (n) for black race is 429 and that for whites is 2213. The mean for whites is 1.86 while that for blacks is 2.07 and their respective standard deviations for whites is 0.346 while that for blacks is 0.674.

Independent Samples Test

Levene's Test for Equality of Variances t-test for Equality of Means

F Sig. t dfSig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference

Lower Upper

respondents employment status Equal variances assumed 35.086 .000 -9.278 2640 .000 -.204 .022 -.247 -.161

Equal variances not assumed -6.119 472.600 .000 -.204 .033 -.270 -.138

From the above table, our first aim is to find the row where we shall read our values from. Using the levenes test for equality of variance (homogeneity of variance), from the first row the levenes p-value is 0.000 which is less than default 0.05 alpha thus we reject the null hypothesis, this implies that the variances are different and thus we should use the second row for inference.

The p-value for the independent t-test is 0.000 and the 95% confidence interval for the mean difference is [-0.270, -0.138]. The confidence interval tells us that we are 95% confident that the mean differences between blacks and whites lies between -0.270 and -0.138.

Decision:

Since the p-value of the independent t-test (p=0.000) is less than the default 0.05 alpha then we reject the null hypothesis and accept the alternative hypothesis and conclude that; there is a significant difference between blacks and whites.

References

Bathke, A. (2008). A unified approach to nonparametric trend tests for dependent and independent samples. Metrika, 69(1), 17-29. http://dx.doi.org/10.1007/s00184-008-0171-x

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