What Is the Chi-Square Test? How to Read SPSS Results

What Is the Chi-Square Test

You open the SPSS output and see the Chi-Square Tests table, with a Pearson Chi-Square row and the columns Value, df, and Asymptotic Significance (2-sided). The chi-square test, commonly written as the Chi-Square test or χ² test, checks the association between categorical variables or compares an observed distribution with an expected distribution.

In a quantitative thesis, the most common application is testing independence between two categorical variables. For example, you may want to know whether gender is associated with purchase intention, or whether age group is associated with how often people use an application. The data are presented in a crosstabulation, such as the number of people in each combination of Gender and Purchase Intention.

For the Pearson Chi-Square test, SPSS calculates the statistic in the general form:

χ² = Σ (O - E)² / E

Here, O is the actual observed frequency in each cell of the crosstabulation, while E is the expected frequency if the two variables are not associated. SPSS then calculates df and the p-value in the Sig. column, which you use to decide whether to reject the independence hypothesis. If you are looking for background material in the Statistics category, distinguish Chi-Square from tests designed for means, such as the t test.

Why the Chi-Square Test Matters in Quantitative Research

This test answers a specific question: are two categorical variables independent in the research sample? For example, Gender may have two groups, Male and Female, while Service Usage may have two groups, Yes and No. The crosstabulation shows the number of observations in each group, while Chi-Square checks whether the difference between the groups is larger than what random variation could reasonably explain.

You usually begin with two hypotheses:

• H0: The two categorical variables are independent, meaning there is not yet evidence of an association in the population.
• H1: The two categorical variables are not independent, meaning there is evidence of an association in the population.

The conclusion is based on Asymptotic Significance (2-sided), usually shortened to Sig. or p-value. When Sig. < 0,05, you reject H0 and conclude that the two variables have a statistically significant association at the 5% level. When Sig. ≥ 0,05, you do not have sufficient evidence to reject H0.

Keep the interpretation within what the test can support. Chi-Square indicates a statistical association, but it does not by itself show that one variable causes the other. It also does not tell you whether the association is strong or weak if you only look at the p-value. To describe the direction and size of the association, inspect row or column percentages, residuals, and, where required by the research design, report Phi or Cramer's V as well.

Chi-Square is appropriate for categorical variables, such as gender, age group, usage status, or response category. If the dependent variable is a continuous mean score and you want to compare two groups, see the t test. If you have three or more groups and want to compare means, the appropriate analysis may be one factor ANOVA, rather than a chi-square test simply because both output tables contain a Sig. column.

What Is a Good Chi-Square Value

The search phrase “what is a good chi-square value” often leads you to focus on the Pearson Chi-Square column. There is no single χ² value that applies to every study. The χ² value depends on sample size, the number of groups, and the degrees of freedom. The value you usually use for the decision is the p-value, together with the expected-frequency condition.

The table below gives a practical way to read the output. It describes the decision rule for hypothesis testing, not a quality score for the entire research model.

The source rows in the table describe the formula and decision rule for the Chi-Square procedure itself. They are not thresholds taken from a source listed in this article. When writing your thesis, state the selected significance level, usually 5%, rather than describing a particular χ² value as “good.”

The important condition concerns the expected frequency in each cell. If too many cells have a small Expected Count, the Pearson approximation may be unreliable. SPSS usually places a note below the table, for example: “a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 8.40.” Read this note instead of looking only at the Pearson Chi-Square row.

How to Read the Chi-Square Test in SPSS Output

To run the most common version of the test in SPSS, select Analyze > Descriptive Statistics > Crosstabs. Put one categorical variable in Row(s) and the other in Column(s). Select Statistics, check Chi-square, and then select Cells to add Observed, Expected, and row or column percentages. Click Continue, then OK.

The table below is illustrative output, not the result of a real study. Assume that you are testing the association between Gender and Intention to Continue Using, with 180 observations.

For this illustrative table, start with the Pearson Chi-Square row. The Sig. = 0,009 value is smaller than 0,05, so you reject H0. An appropriate interpretation is: there is a statistically significant association between gender and intention to continue using the service in the survey sample.

You should not write that gender “affects” intention to continue using the service. This crosstabulation and test show an association only. To report which group has the higher percentage, return to the Crosstabulation table and inspect the row or column percentages. For example, if your aim is to compare the continuation rate between Male and Female respondents, row percentages are often easier to interpret.

If Sig. = 0,327, the conclusion changes to: there is insufficient statistical evidence to confirm an association between gender and intention to continue using the service at the 5% significance level. This does not mean that the two variables are certainly unrelated. The sample size, grouping method, or measurement quality may not be sufficient to detect the association.

What to Do When the Chi-Square Test Does Not Meet the Conditions

Work through the steps below, beginning with a data check rather than immediately deleting a variable.

Check the Coding and Crosstabulation

Open Variable View and check Values, Missing, and the data type. A gender variable may contain a mixture of the codes 1, 2, Male, and Female, which causes SPSS to create an unintended additional group. In Crosstabs, check the row labels, column labels, and the total N of Valid Cases.

If the number of valid observations is unusually low, inspect missing values in Data View. Record how many observations were excluded and why. Do not combine groups simply to make Sig. smaller or to make the results table look better.

Inspect Expected Count and Consider a Defensible Grouping

If many cells have a low expected frequency, first check whether some groups are too small. Combine groups only when the new grouping has theoretical meaning and can be explained in the methods chapter. For example, combining adjacent age groups may be reasonable if the revised grouping is stated before the test is run.

After making a defensible adjustment, rerun the crosstabulation and save both the before and after versions. The committee may ask why the groups were combined, so your answer should be based on the variable design, not on a desire to obtain a particular p-value.

Use Fisher's Exact Test for a Small Table

For a 2×2 table with small expected frequencies, SPSS may provide Fisher's Exact Test. In the Crosstabs dialog box, select Exact, then request the appropriate test if your SPSS version supports it. Read the Fisher p-value rather than relying only on Pearson Chi-Square.

If the table has several rows or columns, the appropriate treatment may be more complicated. Report clearly which test you used and why. Do not run multiple versions and then select only the result that is statistically significant.

Consider Whether the Analysis Matches the Variable Type

If a variable is actually a continuous score but you divided it into several groups, Chi-Square may have discarded useful information. If your research question concerns a comparison of means, see the ANOVA table or another test that matches the design. If both variables are ordinal, also consider whether a Pearson crosstabulation answers the research question correctly.

Chi-Square Test Compared with the t Test

Chi-Square and the t test can both appear in a thesis, but they answer different questions. Chi-Square analyses the frequencies of categorical groups. The t test usually compares the mean of a quantitative variable between two groups.

For example, Gender and Service Usage: Yes/No are both categorical variables, so Chi-Square can be used to test their association. If you use Gender to divide respondents into two groups and then compare their mean Satisfaction scores, the t test may be more appropriate. The gender variable is the same, but the other variable has changed, so the test also changes.

Chi-Square also differs from ANOVA. ANOVA compares means across three or more groups, such as the average satisfaction score for three age groups. If you code satisfaction into “low,” “medium,” and “high” groups and analyse the frequency table, you are working in a Chi-Square context. See ANOVA if your question concerns mean differences across several groups.

Common Errors

Calling χ² an Effect Coefficient

Pearson Chi-Square = 6,842 is a test statistic, not a regression coefficient, and it cannot be written as the effect of gender on intention. If you need to describe the strength of the association, consider an appropriate measure such as Phi or Cramer's V and explain how that measure was calculated.

Reporting Only Sig. and Omitting the Crosstabulation

A p-value does not tell you which group has the higher percentage. Also report counts, percentages, and the total number of valid observations. The reader needs to see the data that produced the conclusion, not only a number smaller than 0,05.

Using Chi-Square for Scale Data Without Explanation

Individual Likert items can be coded into groups, but dividing them into groups loses information and requires a reason. If you are analysing items to create a mean score or assess a scale, Chi-Square is usually not the default step. Base the choice on your research question and the actual type of data.

Writing “There Is No Association” When the p-value Is Large

p ≥ 0,05 shows only that there is insufficient evidence to reject H0 in the sample and at the selected significance level. A more cautious sentence is “no statistically significant association was found.” This is a small wording difference, but it matters when you defend the thesis.

How to write this in your thesis

You can adapt the following paragraph to your actual output: “The Pearson Chi-Square test indicates that the association between [variable 1 name] and [variable 2 name] is statistically significant, χ²([df]) = [Chi-Square value], p = [Sig.]. Because p is [smaller/larger] than 0,05, the study [rejects/does not have sufficient grounds to reject] the H0 hypothesis.” If the table contains small expected counts, replace the test and interpretation with the corresponding Fisher's Exact Test result.

Frequently asked questions

What variables can be used in the chi-square test?

The chi-square test is usually used for categorical variables, where the data are represented by the number of observations in each group. Examples include gender, age group, usage status, product choice, or a classification level that has been clearly defined.

What is a good chi-square value?

There is no single Pearson Chi-Square value that is considered good. Read Sig. together with df, Expected Count, and the crosstabulation. At the 5% significance level, p < 0,05 leads to rejection of H0, while p ≥ 0,05 means there is insufficient evidence to reject H0.

What does a Chi-Square Sig. value of 0,000 mean?

In SPSS output, 0,000 usually means that the p-value is very small and below 0,001. You should not write that the p-value is exactly 0. Report it as p < 0,001, then state the conclusion at the selected significance level.

What should I do when Expected Count is small?

Check the coding, the number of groups, and the size of each group. If a 2×2 table contains a small expected count, consider Fisher's Exact Test. Combine groups only when there is a clear theoretical or design-based reason, not simply to change the p-value.

Do I need to run Chi-Square after Cronbach's Alpha?

There is no rule requiring you to run Chi-Square after Cronbach's Alpha. Cronbach's Alpha evaluates the reliability of a scale made up of items, while Chi-Square tests the association between categorical variables. Choose the procedure according to your hypothesis and the type of data in your study.

Open your SPSS file, identify the two categorical variables, run Analyze > Descriptive Statistics > Crosstabs, and check the Pearson Chi-Square, Sig., df, and Expected Count note before writing the conclusion. If you need to run the analysis on your own .sav or .csv file, M4 analysis supports this step.