Independent Samples t Tests with SPSS

In this paper, I will discuss the statistical assumptions of the independent samples t test as well as present a brief summation of results based on the SPSS analysis of the given data set.

Statistical Assumptions

The three assumptions underlying the independent-samples t test are that the test variable has a normal distribution in both populations of study; both populations have approximately equal variances; and both samples are randomly selected from the population and the observations in each sample are independent of the other (each has no influence on the other) (Green & Salkind, 2014).

Dependent and Independent Variables and Null and Alternative Hypothesis

I have used race of the respondents as the independent variable and how often respondent attends religious services as the dependent variable.

The null hypothesis is: Race (Black or White) does not influence frequency of attendance at religious services.

H0: µAttendance for Whites = µAttendence for Blacks.

The alternative hypothesis is: Attendance for Whites ≠ Attendance for Blacks (Race affects attendance).

H1: µAttendance for Whites ≠ µAttendence for Blacks.

The confidence level is .95. In this example, the variances are similar and consequently, the standard t test, t(1390) = -7.0, p = .00, and the t test for unequal variances, t(325.5) = -7.64, p = .00 yield similar results. I reject the null hypothesis: Race has an effect on how often respondents attend religious services, and in this case, Blacks attend religious services more frequently than Whites.

An independent-samples t test was conducted to evaluate whether race (Black or White) influences attendance at religious services. The test was significant, and the results were in agreement with the alternative hypothesis. The 95% confidence interval for the difference in means was quite narrow, ranging from -1.78 to -1.0. This means there is a 95% chance that the confidence interval range contains the true population mean. The eta square index indicated that 3% (η2 =.03) of the variance of the attendance variable was accounted for by whether the respondent was White or Black. The effect was small to medium.

Syntax and Output Files

T-TEST GROUPS=RACE(1 2)

  /MISSING=ANALYSIS

  /VARIABLES=ATTEND

  /CRITERIA=CI(.95).

T-Test

Notes
Output Created		25-JAN-2014 09:31:44
Comments
Input	Data	C:\Users\Deborah\Desktop\Stats\gss04student_corrrected.sav
	Active Dataset	DataSet1
	Filter	<none>
	Weight	<none>
	Split File	<none>
	N of Rows in Working Data File	1500
Missing Value Handling	Definition of Missing	User defined missing values are treated as missing.
	Cases Used	Statistics for each analysis are based on the cases with no missing or out-of-range data for any variable in the analysis.
Syntax		T-TEST GROUPS=RACE(1 2)   /MISSING=ANALYSIS   /VARIABLES=ATTEND   /CRITERIA=CI(.95).
Resources	Processor Time	00:00:00.00
	Elapsed Time	00:00:00.01

[DataSet1] C:\Users\Deborah\Desktop\Stats\gss04student_corrrected.sav

Group Statistics
	RACE OF RESPONDENT	N	Mean	Std. Deviation	Std. Error Mean
HOW OFTEN R ATTENDS RELIGIOUS SERVICES	WHITE	1176	3.65	2.734	.080
	BLACK	216	5.05	2.409	.164

Independent Samples Test
		Levene's Test for Equality of Variances		t-test for Equality of Means
		F	Sig.	t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
									Lower	Upper
HOW OFTEN R ATTENDS RELIGIOUS SERVICES	Equal variances assumed	24.358	.000	-6.997	1390	.000	-1.392	.199	-1.782	-1.001
	Equal variances not assumed			-7.635	325.484	.000	-1.392	.182	-1.750	-1.033

References
Green, S. B., & Salkind, N. J. (2014). Using SPSS for Windows and Macintosh: Analyzing and understanding data (7th ed.). Upper Saddle River, NJ: Pearson Education.