What is a Chi-square Test for Independence?

    1. Using Chi-Square Statistic in Research

    This easy tutorial will show you how to run the Chi-Square test in SPSS, and how to interpret the result.

    The chi-square test of independence uses to investigate the relationship between two categorical variables that have two or more categories. In addition, the test compares the proportions, that is, the frequency of cases observed in each of the categories with values that would be expected to have if there is no relationship between the variables.

    First of all, the chi-square test based on a contingency table that shows the intersection of each category of one variable with each group of the other variable.

    2. The Assumptions of the Chi-Square Test include:

    • The data in the cells should be frequencies or counts of cases rather than percentages or some other transformation of the data.
    • The levels (or categories) of the variables are mutually exclusive. In other words, a particular subject fits into one and only one level of each of the variables.
    • Each subject may contribute data to one and only one cell in the χ2. If, for example, the same subjects are tested over time such that the comparisons are of the same subjects at Time 1, Time 2, Time 3, etc., then χ2 may not be used.

    The Study Groups must be independent for Chi-Square Test

    • The study groups must be independent. That is to say, a different test must be used if the two groups are related. For example, a different test must be used if the researcher’s data consists of paired samples, such as in studies in which a parent is paired with his or her child.

    • There are 2 variables, and both are measured as categories, usually at the nominal level. However, data may be ordinal data. Interval or ratio data that have been collapsed into ordinal categories may also be used. While Chi-square has no rule about limiting the number of cells (by limiting the number of categories for each variable), a very large number of cells (over 20) can make it difficult to meet assumption #6 below and to interpret the meaning of the results.

    • The value of the cell expects should be 5 or more in at least 80% of the cells, and no cell should have an expected of less than one (). This assumption is most likely to be met if the sample size equals at least the number of cells multiplied by 5. Essentially, this assumption specifies the number of cases (sample size) needed to use the χ2 for any number of cells in that χ2. This requirement will be fully explained in the example of the calculation of the statistic in the case study example. (Mary L. McHugh, 2013)

    3. An Example for the Chi-Square Test

    This guide will explain, step by step, how to run the Chi-Square Test in SPSS statistical software by using an example.
    We will test whether education (primary school, secondary school, BA, Master, Ph.D.) is independent of gender (male, female).

    Null hypothesis:

    The education level is not independent of gender.

    Alternative hypothesis:

    The education level is independent of gender.

    This easy tutorial will show you how to run the Chi-Square test in SPSS, and how to interpret the result.


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    How to Run Chi-square Test in SPSS: Explanation Step by Step

    From the SPSS menu, choose Analyze – Descriptive Statistics – Crosstabs.

    A new window will open. Transfer variables from the left box to the right boxes. One variable transfer into box Row(s) and other into box Column(s). Checkbox Display clustered bar charts.

    Click on the Cells… tab and a new window will appear. Check Observed in the Counts box. Check Row, Column, Total in the Percentages box. Click Continue and then OK.

    Click on the Statistics tab. A new window will appear. Choose Chi-square and Phi and Cramer’s V from the Nominal box. Click Continue.

    The results of the Chi-square test for independence will appear in the output box.

    How to report a Chi-square test for independence results: Explanation Step by Step

    How to Report Case Processing Summary Table in SPSS Output?

    The first table is the Case processing Summary. It shows the number of valid, missing, and total cases.

    How to Report Crosstabulation Table in SPSS Output?

    The second table is Crosstabulation. It shows the number of cases in each group. For example, there is 11 male finished primary school, 11 male finished secondary school, 13 male finished BA, 8 male finished Master, and 7 male finished Ph.D. There is a female finished primary school, 15 females finished secondary school, 21 female finished BA, 10 female completed Master, and 10 female finished Ph.D. There are 50 males and 66 females in the sample. 21 respondents finished primary school, 26 finished secondary schools, 34 finished BA, 18 completed Master, and 17 finished Ph.D. The total number of respondents is 116.

    How to Report P-Value in Chi-Square Table SPSS Output?

    The third table shows the Chi-square test statistic and its significance.

    If the p-value (Asymp. Sig. (2-sided)) for Pearson Chi-square statistic is higher than .05 (p > .05), the education is not dependent on gender (we fail to reject the null hypothesis).

    If the p-value (Asymp. Sig. (2-sided)) for Pearson Chi-square statistic is lower than .05 (p < .05), the education is dependent on gender (we reject the null hypothesis).

     Since the results show that p = .892 > .05, we fail to reject the null hypothesis.

    How to Report Cramer’s V and Phi Measures in SPSS output?

    The following table shows the results of Cramer’s V and Phi measures. If Cramer’s V/Phi is 0.10, there is a small impact, 0.30 medium, and 0.50 high.

    How to Show Clustered bar Char in SPSS Output?

    In the end, there are clustered bar charts.

    How to Interpret a Chi-Square Test for Independence Results in APA Style ?

      A chi-square test for independence was computed to determine whether education (primary school, secondary school, BA, Master, Ph.D.) is independent of gender (male, female). The results are not significant, χ2(4) = 1.111, p = .892, Cramer’s V/phi = .892. We fail to reject the null hypothesis that education is the same across gender (male, female) and conclude that education is not related to gender.

    Visit our Reporting Chi-Square Test Page for more details.

    Are you in trouble with Chi Square Test?

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