Bivariate Analysis : Categorical Variables

Doing Crosstabulation in SPSS

The following working examples refer to the dataset from the US General Social Survey 1993 .

1. Analyze -> Descriptive Statistics -> Crosstabs

2. Select and put independant variable in "Column(s) " box, dependent variable in "Row(s)"

• this "Column(s)" and " Row(s)" arrangement facilitates the "percentage downward" convention in the output crosstabulation table
  
• if on no ground we could distinguish independent from dependent variable, it doesn't matter putting the variables in which box
  

3. Then press the Statistics button

• in most questionnaire surveys, researchers are interested not only in the sample statistics, but also in generalizing the findings to the target population
• click to choose Chi-square to do the test for significance of the relationship between two variables, this is a MUST to choose
• below the Chi -square, there are measures of the strength of the relationship , choose the appropriate ones corresponding to the level of measurement
• press Continue to return to the above dialog box
  

4. Having returned to the first dialog box, press Cells

• each classification in the crosstabulation table is named a cell
  
• click to choose Observed Counts to obtain actual number of cases in each classification 
• if the positions of independent and dependent variables can be assumed, choose Column Percentages to produce the "percentage downward" output
• however, if independent-dependent cannot be assumed, both Column Percentages and Row Percentages must be chosen
• press Continue to return to the first dialog box
• press OK if you want to get the results immediately, or 
• press Paste to copy out the command syntax, then run it in the Syntax window to get the output
  

5. SPSS Output for Crosstabulation

5.1  Number of cases in each cell and the "percentage downward" results

• we want to know whether males and females behaved differently in the 1992 election

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VOTE92 Voting in 1992 Election * SEX Respondent's Sex Crosstabulation

			SEX Respondent's Sex		Total
			1 Male	2 Female
VOTE92 Voting in 1992 Election	1 voted	Count	448	584	1032
		% within SEX Respondent's Sex	72.1%	70.3%	71.1%
	2 did not vote	Count	173	247	420
		% within SEX Respondent's Sex	27.9%	29.7%	28.9%
Total		Count	621	831	1452
		% within SEX Respondent's Sex	100.0%	100.0%	100.0%

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• the cells with yellow background show the "percentage downward" result:
• 72.1% of male respondents voted in the 1992 election, and 27.9% did not
• 72.1% + 27.9% = 100% as shown in the Total row at the bottom
• compare the yellow column with the blue column, we could draw an initial conclusion that males and females did not behave differently
• however, we are interested more in inferring the sample finding to the target population, the above conclusion must be tested for statistical significance by the Chi-squre test shown below

5.2 Test for significance of the relationship between sex and voting behaviour - Chi-square test

• the null hypothesis is: no relationship between sex and voting behaviour
• normally, the row starting with Pearson Chi-Square is what we need to examine
• the column labelled "Asymp. Sig. (2-sided) " is the level of significance for the chi-square value (0.601) with the corresponding degree of freedom (df=1)
• the significance shows p=0.438
• in sociological research, typical level of significance adopted to reject the null hypothesis is p  0.05
• in the current example, 0.438 is much greater than 0.05, we are much confident in accepting the null hypothesis
• hence, we may conclude that sex and voting behavior have no relationship existing in our target population
• the Chi-square test is nonparametric, which means the strict assumption of population distribution is relaxed
• however, there is still requirement to fulfill: the expected frequency (not observed or actual frequency) in each cell must be 5 or more
• should such requirement is not fulfilled, a warning will be issued in the SPSS output
• in any circumstances if the proportion of cells with expected frequency less 5 is as high as 25% or more, the chi-square is not reliable
• you should consider again the classifications in the variables involved in the analysis, 
• regroup some categories to yield more cases
• exclude categories with almost no or very few cases
  

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Chi-Square Tests

	Value	df	Asymp. Sig. (2-sided)	Exact Sig. (2-sided)	Exact Sig. (1-sided)
Pearson Chi-Square	.601(b)	1	.438
Continuity Correction(a)	.514	1	.473
Likelihood Ratio	.602	1	.438
Fisher's Exact Test				.448	.237
Linear-by-Linear Association	.601	1	.438
N of Valid Cases	1452
a Computed only for a 2x2 table
b 0 cells (.0%) have expected count less than 5. The minimum expected count is 179.63.

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