Chi-Square with SPSS

The purpose of this paper is to state the statistical assumptions of the chi-square, choose dependent and independent variables, develop the null hypothesis and the alternative hypothesis, use SPSS to calculate a chi-square, and decide whether to reject or retain the null hypothesis. In addition, the statistical results of the chi-square will be analyzed.

Statistical Assumptions

The statistical assumptions underlying the one-sample chi-square test are that the observations made must be from a random sample, and results from the observation are independent of each other (Green & Salkind, 2014). In addition, when the sample size is relatively large, the one-sample chi-square will produce a resulting statistic that is approximately distributed as a chi-square (Green & Salkind, 2014).

Brief Analysis

A one-sample chi-square test was conducted to assess whether race has an effect on feelings about the bible. The independent variable is race and the dependent variable is feelings about the bible.

The research question is: is there a relationship between race and feelings about the bible.

The null hypothesis is: there is no relationship between race and feelings about the bible.

H0: ρ = 0

The alternative hypothesis is:

H1: ρ ≠ 0

The results of the test were significant, x2 (6, N = 706) = 40.45, p < .01. There is a relationship between race and feelings about the bible. I reject the null hypothesis.



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.

Laureate Education, Inc., (n.d.) Correlation and introduction to regression [Streaming Video]. Author.

CROSSTABS

  /TABLES=RACE BY BIBLE

  /FORMAT=AVALUE TABLES

  /STATISTICS=CHISQ

  /CELLS=COUNT EXPECTED ROW COLUMN TOTAL

  /COUNT ROUND CELL.

Crosstabs

Notes
Output Created		12-FEB-2014 07:00:14
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 table are based on all the cases with valid data in the specified range(s) for all variables in each table.
Syntax		CROSSTABS   /TABLES=RACE BY BIBLE   /FORMAT=AVALUE TABLES   /STATISTICS=CHISQ   /CELLS=COUNT EXPECTED ROW COLUMN TOTAL   /COUNT ROUND CELL.
Resources	Processor Time	00:00:00.00
	Elapsed Time	00:00:00.01
	Dimensions Requested	2
	Cells Available	131029

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

Case Processing Summary
	Cases
	Valid		Missing		Total
	N	Percent	N	Percent	N	Percent
RACE OF RESPONDENT * FEELINGS ABOUT THE BIBLE	706	47.1%	794	52.9%	1500	100.0%

RACE OF RESPONDENT * FEELINGS ABOUT THE BIBLE Crosstabulation
			FEELINGS ABOUT THE BIBLE				Total
			WORD OF GOD	INSPIRED WORD	BOOK OF FABLES	OTHER
RACE OF RESPONDENT	WHITE	Count	169	293	102	4	568
		Expected Count	193.9	272.7	95.7	5.6	568.0
		% within RACE OF RESPONDENT	29.8%	51.6%	18.0%	0.7%	100.0%
		% within FEELINGS ABOUT THE BIBLE	70.1%	86.4%	85.7%	57.1%	80.5%
		% of Total	23.9%	41.5%	14.4%	0.6%	80.5%
	BLACK	Count	53	22	9	1	85
		Expected Count	29.0	40.8	14.3	.8	85.0
		% within RACE OF RESPONDENT	62.4%	25.9%	10.6%	1.2%	100.0%
		% within FEELINGS ABOUT THE BIBLE	22.0%	6.5%	7.6%	14.3%	12.0%
		% of Total	7.5%	3.1%	1.3%	0.1%	12.0%
	OTHER	Count	19	24	8	2	53
		Expected Count	18.1	25.4	8.9	.5	53.0
		% within RACE OF RESPONDENT	35.8%	45.3%	15.1%	3.8%	100.0%
		% within FEELINGS ABOUT THE BIBLE	7.9%	7.1%	6.7%	28.6%	7.5%
		% of Total	2.7%	3.4%	1.1%	0.3%	7.5%
Total		Count	241	339	119	7	706
		Expected Count	241.0	339.0	119.0	7.0	706.0
		% within RACE OF RESPONDENT	34.1%	48.0%	16.9%	1.0%	100.0%
		% within FEELINGS ABOUT THE BIBLE	100.0%	100.0%	100.0%	100.0%	100.0%
		% of Total	34.1%	48.0%	16.9%	1.0%	100.0%

Chi-Square Tests
	Value	df	Asymp. Sig. (2-sided)
Pearson Chi-Square	40.455a	6	.000
Likelihood Ratio	37.008	6	.000
Linear-by-Linear Association	5.549	1	.018
N of Valid Cases	706
a. 2 cells (16.7%) have expected count less than 5. The minimum expected count is .53.