Chi-Square Test: Statistical Assumptions

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Statistical Assumptions

Chi-square test applies when the following assumptions prevail (Goodwin, 2010).

The test should aim to determine the association between two variables, which must be on an ordinal scale or a categorical scale.
The independent variables must have two or more nominal or categorical groups.
The categorical groups should be mutually exclusive to prevent redundancy of data.
The sample size should be sufficient to meet minimum distribution of frequencies.

Variables

The independent variable is the marital status.
The dependent variable is the perception of premarital sex.

Hypotheses

H₀: There is no significant association between the marital status and the perception of premarital sex.
H₁: There is a significant association between the marital status and the perception of premarital sex.

Chi-Square Analysis

From Table 2 in the appendix section, it is apparent that the perception of premarital sex varies according to the marital status of respondents. The table indicates that 56.6% of the married, 38.8% of the widowed, 59% of the divorced, 62.7% of the separated, and 66.3% of the never married hold that it is not wrong at all to engage in premarital sex. Overall, the cross-tabulation indicates that there is a skewed distribution of perceptions as most respondents, irrespective of their marital status, consider premarital sex as not wrong at all.

To test if the apparent association between the marital status and the perceptions of premarital sex is significant, chi-square analysis is appropriate. The chi-square test rejects the null hypothesis because the p-value is less than 0.05. Field (2013) states that the rejection of a null hypothesis happens when the p-value is less than the significance value. In this view, the hypothesis testing holds that there is a significant association between the marital status and the perception of premarital sex, χ(12) = 49.156, p = 0.000.

Table 1:

Chi-Square Tests
	Value	df	Asymp. Sig. (2-sided)
Pearson Chi-Square	49.156	12	.000
Likelihood Ratio	49.063	12	.000
Linear-by-Linear Association	19.410	1	.000
N of Valid Cases	1646

Multivariate Analysis

Multivariate analysis is appropriate for a quantitative study when a researcher wants to establish the influence of two or more independent variables on one or more dependent variables. Field (2013) argues that multivariate analysis allows determination of the complex interactions between the dependent variables and independent variables. Multivariate analysis also allows determination of how each independent variables influences respective dependent variables.

The dependent variables should have ordinal, ratio, or interval scales to allow the determination of the degree of variation. Furthermore, the independent variables should have nominal, ordinal, ratio, or interval scales to permit the assessment of the degree of influence. However, continuous scale provides robust multivariate analysis.

The data should follow the normal distribution without any significant outliers. Significant outliers create marked skewness and kurtosis, which reduce the validity of data (Weinberg & Abramowitz, 2008). Essentially, significant outliers distort the distribution of data and descriptive statistics, and hence, making data analysis to obtain biased results. Hence, the variables should contain data, which do not violate the assumption of normality.

I have developed interests in multiple regression analysis because it allows prediction of a dependent variable based on one or more independent variables. Multiple regression analysis is a form of multivariate analysis that researchers employ in modeling relationships among diverse variables. Multiple regression analysis is potentially useful in my future research because I will model relationships of diverse psychological variables and establish how each variable predicts certain psychological attribute or human behavior.

References

Field, A. (2013). Discovering statistics using SPSS (4th ed.). London: SAGE Publisher.

Goodwin, C. J. (2010). Research in psychology: Methods and design. Hoboken: John Wiley.

Weinberg, S. L., & Abramowitz, S. K. (2008). Statistics using SPSS: An integrative approach. Cambridge: Cambridge University Press.

Appendices

Cross-Tabulation Table

Table 2:

Marital Status Sex Before Marriage Cross-tabulation*
			Sex Before Marriage				Total
			Always Wrong	Almost Always Wrong	Sometimes Wrong	Not Wrong At All	Total
Marital Status	Married	Count	152	48	120	401	721
		% Within Marital Status	21.1%	6.7%	16.6%	55.6%	100.0%
		% Within Sex Before Marriage	46.9%	43.2%	46.7%	42.0%	43.8%
		% Of Total	9.2%	2.9%	7.3%	24.4%	43.8%
	Widowed	Count	46	14	25	54	139
		% Within Marital Status	33.1%	10.1%	18.0%	38.8%	100.0%
		% Within Sex Before Marriage	14.2%	12.6%	9.7%	5.7%	8.4%
		% of Total	2.8%	0.9%	1.5%	3.3%	8.4%
	Divorced	Count	61	17	36	164	278
		% Within Marital Status	21.9%	6.1%	12.9%	59.0%	100.0%
		% Within Sex Before Marriage	18.8%	15.3%	14.0%	17.2%	16.9%
		% of Total	3.7%	1.0%	2.2%	10.0%	16.9%
	Separated	Count	6	6	7	32	51
		% Within Marital Status	11.8%	11.8%	13.7%	62.7%	100.0%
		% Within Sex Before Marriage	1.9%	5.4%	2.7%	3.4%	3.1%
		% of Total	0.4%	0.4%	0.4%	1.9%	3.1%
	Never Married	Count	59	26	69	303	457
		% Within Marital Status	12.9%	5.7%	15.1%	66.3%	100.0%
		% Within Sex Before Marriage	18.2%	23.4%	26.8%	31.8%	27.8%
		% of Total	3.6%	1.6%	4.2%	18.4%	27.8%
Total		Count	324	111	257	954	1646
		% Within Marital Status	19.7%	6.7%	15.6%	58.0%	100.0%
		% Within Sex Before Marriage	100.0%	100.0%	100.0%	100.0%	100.0%
		% of Total	19.7%	6.7%	15.6%	58.0%	100.0%

Syntax

Table 3:

Notes
Syntax	CROSSTABS /TABLES=marital BY premarsx /FORMAT=AVALUE TABLES /STATISTICS=CHISQ PHI /CELLS=COUNT ROW COLUMN TOTAL /COUNT ROUND CELL.