What Is Chi Square? How to Run and Read It in SPSS

What is chi square?

Chi square, commonly written as χ² or Chi-Square Test, is used to examine whether two categorical variables are associated. For example, you can test whether gender is related to purchase intention, whether age group is related to satisfaction level, or whether service use differs across occupational groups.

In SPSS, chi square is usually performed under Chi-Square Test of Independence. The test works with counts in the cells of a crosstabulation, such as the number of men who selected “Yes” and the number of women who selected “No”. The input must consist of categorical variables or variables that have been divided into groups.

The general formula for the Pearson Chi-Square statistic is:

χ² = Σ[(O - E)² / E]

Here, O is the observed frequency in each cell, while E is the expected frequency if the two variables were unrelated. When the difference between O and E becomes large enough, the χ² value increases. SPSS uses this value to calculate the p-value, usually displayed in the Asymptotic Significance (2-sided) column.

You can also browse the Statistics section if you are working through several types of tests. First, identify the type of variable before choosing a test. Chi square is not used to compare the mean of a quantitative variable, and it does not replace linear regression.

Why chi square matters in quantitative research

Chi square answers a specific question: are two categorical variables in your sample independent of each other? Here, “independent” means that the distribution of one variable does not change across the groups of the other variable.

Suppose you are studying purchase intention and have gender as a variable. If the proportion selecting “Intend to purchase” is almost the same for men and women, chi square may not be statistically significant. If the proportions differ clearly, the test may produce a small p-value, giving you grounds to reject the independence hypothesis.

Chi square is commonly used in three situations:

• Testing the association between two categorical variables, such as gender and purchase intention.
• Testing whether one categorical variable fits an expected proportion or distribution, which is One-Sample Chi-Square.
• Describing the distribution of data with frequency tables and crosstabulations before running the main model.

In a quantitative thesis, chi square is often used as an extended descriptive analysis or as an initial test of association. If your research model contains latent variables measured with multiple items, chi square does not replace Cronbach's Alpha, EFA, regression, or PLS-SEM. You can read what a scale is to distinguish categorical variables from a Likert scale.

A statistically significant result does not automatically prove causality. If the p-value is small, you should conclude only that there is evidence of an association between the two variables in the sample, given the current measurement and research design. You cannot write that gender “causes” higher purchase intention.

What chi square value is acceptable?

For Pearson Chi-Square, the decision is usually based on the p-value, specifically the Asymptotic Significance (2-sided) column. Before reading the p-value, check the expected-frequency condition. If too many cells have a very small Expected Count, the approximation used by Pearson Chi-Square may not be reliable.

The table below summarises how to read the criteria you will commonly see. Each threshold has a source that you can explain in the methods or results chapter.

Some sources present the Expected Count rule using the number and proportion of cells with low expected frequencies. The appropriate handling also depends on table size, number of groups, and software. Present the crosstabulation clearly instead of writing only that the “test passed”.

If the p-value is less than 0,05, you can write that there is a statistically significant association between the two variables. If the p-value is greater than or equal to 0,05, write that there is insufficient statistical evidence to conclude that the variables are associated. This wording is more cautious than saying that “the two variables are unrelated”, because a nonsignificant result may reflect a small sample size or an unbalanced data distribution.

How to read chi square in the output

In SPSS, open Analyze > Descriptive Statistics > Crosstabs. Put one variable in Row(s) and the other in Column(s). Then select Statistics, tick Chi-square, and optionally select Phi and Cramer's V if you want to report the strength of association. Under Cells, select Observed and Expected, and select row or column percentages if you need to explain the proportions.

The example below is illustrative output, not the result of a real study. Suppose you are testing the association between gender and purchase intention with a 2 x 2 table containing 200 observations.

In this example, the first row is Pearson Chi-Square. The test value is 6,482, df is 1, and the p-value is 0,011. Because 0,011 is less than 0,05, you reject H0 of independence between the two variables. The appropriate conclusion is that gender and purchase intention have a statistically significant association in the illustrative sample.

Do not look only at the Value column and draw a conclusion. A Pearson Chi-Square value of 6,482 does not, by itself, tell you whether the result is significant. Read df and the p-value together. You also need to open the Crosstabulation table to see which group has the higher proportion, because the Chi-Square Tests table shows that an association exists but does not show the direction of the difference.

If the crosstabulation contains two variables with several groups, read the row or column percentages consistently. If you want to know what percentage of each gender selected “Yes”, choose Row percentages. If you want to know how those who selected “Yes” are distributed by gender, choose Column percentages.

You should also distinguish chi square from handling outliers. An outlier is an unusual observation in quantitative or ordered data, while chi square uses the frequencies of categorical groups. Do not delete a small group simply because it makes the p-value nonsignificant.

What to do when chi square is not significant

If the p-value is greater than or equal to 0,05, first check whether you selected the correct test and the correct variables. Review Variable View, value labels, group coding, and missing values. A common error is entering the code “99” as a valid group, which adds a category that does not exist substantively.

Next, check the Crosstabulation table and the size of each group. When the sample size is small or some groups contain very few observations, the test may have low power. Do not merge groups automatically just to make the p-value smaller. Merge them only when the groups are theoretically similar in meaning, and state the merging rule clearly in the methods section.

Then check the Expected Count condition. For a 2 x 2 table, if the expected frequencies are small, you can inspect Fisher's Exact Test in the output. Fisher's Exact Test is often more appropriate when the table is small or cells have low frequencies. In your report, state clearly that you used the Fisher's Exact Test row rather than simply taking the Pearson Chi-Square result.

If your research objective is to predict or explain the size of an effect, review the model. Chi square tests the association between categorical variables. It does not provide a regression coefficient, report the percentage of explained variance, or test a mediator or moderator. Those roles require a more suitable model and test.

Do not run many alternative groupings until you obtain p < 0,05 and then report only the attractive result. If several reasonable coding schemes exist, explain your choice using the theory, sample context, and research objective. The committee often asks about this when the number of groups changes between Chapter 3 and Chapter 4.

Distinguishing chi square from correlation tests

Chi square and correlation tests can both be used to examine whether variables are associated, but their data types and outputs differ.

Chi square is suitable for two categorical variables. For example, gender may consist of Men and Women, while purchase intention may consist of Yes and No. The main results are χ², df, and the p-value, usually accompanied by a frequency table and percentages.

Pearson Correlation is more suitable when you analyse a linear association between quantitative variables or composite scores. The result is a correlation coefficient r ranging from -1 to 1, showing the direction and strength of the linear association. Spearman Correlation is often considered for ordinal data or when the conditions for Pearson are not suitable.

Chi square also differs from logistic regression. Logistic regression can be used when the dependent variable is binary, but it allows multiple explanatory variables to enter the same model and can report coefficients, odds ratios, or confidence intervals. If you have only two categorical variables and your research question is whether they are associated, chi square is usually the more direct choice.

You may see the terms “chi-square”, “Chi-Square Test”, and “χ² test”. In the SPSS context, they usually refer to the same group of tests, but you still need to identify the specific variant, such as Pearson Chi-Square, Likelihood Ratio, or Fisher's Exact Test.

Common errors

The first error is using chi square for a Likert mean without deciding how the variable will be handled. If you use response levels such as “1, 2, 3, 4, 5” as categorical groups, chi square can technically be run, but the research question must genuinely concern a comparison of frequency distributions. If you want to analyse the effect of several scales, consider a regression model or PLS-SEM.

The second error is confusing the p-value with the strength of association. The p-value indicates evidence against H0, but it does not show whether the association is strong or weak. Also inspect Cramer's V and the percentage table, then interpret the result in the context of your topic.

The third error is reporting “Sig. = 0,000”. SPSS displays 0,000 because of the limit on the number of decimal places. This does not mean that the p-value is exactly 0. You can write p < 0,001 when that matches the way the output should be reported.

The fourth error is ignoring missing values and incorrect coding. Before running the test, go to Analyze > Descriptive Statistics > Frequencies to check the count, value labels, and distribution of each variable. If unusual data require handling, record the decision and the number of observations remaining after processing.

The final error is drawing a causal conclusion from a crosstabulation. The statement “gender affects purchase intention” is stronger than what chi square demonstrates. A safer formulation is “gender is associated with purchase intention in the survey sample”.

Frequently asked questions

What is chi square and when is it used?

Chi square is used to examine whether two categorical variables are associated. You use it when the data are represented by the number of observations in groups, such as the number of people selecting Yes or No within each gender group.

If your variable is a quantitative score or the average score of a scale, review the analysis objective before choosing chi square.

What chi square value is acceptable?

In general, a p-value below 0,05 is considered statistically significant, so you reject H0 of independence. A p-value greater than or equal to 0,05 means that there is insufficient evidence to conclude that the two variables are associated.

In addition to the p-value, you must check Expected Count and read the crosstabulation. A significant p-value with an unsuitable expected-frequency condition still requires explanation.

Where is the SPSS chi-square test located?

Go to Analyze > Descriptive Statistics > Crosstabs, place the two variables in Row(s) and Column(s), select Statistics, tick Chi-square, and then use Cells to view Observed, Expected, and percentages.

The result appears in the Chi-Square Tests table. The row usually read first is Pearson Chi-Square, but if the table is small or Expected Count is low, inspect Fisher's Exact Test.

What should I do if the chi square p-value is greater than 0,05?

Check the variable coding, missing data, group sizes, and Expected Count condition. If everything is correct, report that there is insufficient statistical evidence of an association in the sample, rather than altering the data to make the p-value smaller.

If the research question requires an effect or prediction analysis, chi square may not match the objective. In that case, review the model and the type of variables.

Can chi square be calculated by hand?

Yes. Create a table of observed frequencies, calculate the expected frequency for each cell, apply the formula χ² = Σ[(O - E)² / E], and compare the result with the chi-square distribution using df. However, for thesis data with several groups, SPSS reduces calculation errors and provides the Expected Count table, p-value, and alternative tests.

When you submit your thesis, what matters is that you understand the data coding, application conditions, and output. Software does not replace the explanation of the result.

How to write this in your thesis

Open the .sav file again, check Frequencies and Variable View first, and then run Analyze > Descriptive Statistics > Crosstabs with the two variables from your actual topic. If you need to run the analysis on the actual data file and prepare result tables for your thesis, you can use the M4 data analysis module.