Chi-Square Calculator with APA 7 Results
Test of independence on a contingency table, or goodness of fit for one variable. Type your counts and get χ², df, p, expected counts, Cramér’s V or φ, Yates’ correction and Fisher’s exact test for 2×2 tables, and the results sentence written in APA 7 style.
How to use this calculator
1. Choose the test. Independence asks whether two categorical variables are related, for example gender and preferred learning mode. Goodness of fit asks whether one variable’s counts differ from what you expected, for example equal numbers on each day.
2. Type the counts. Each cell is the number of participants, never percentages. Add rows and columns up to 6×6. The labels you type are used in the APA sentence and the tables.
3. Read the expected counts. They appear in parentheses next to each observed count. If any is below 5 the calculator says so and, for a 2×2 table, marks Fisher’s exact test as the one to report.
4. Look at the highlighted cells. Cells whose standardised residual is beyond ±1.96 are the ones that produce the result. That is what you describe in words after the statistics.
5. Copy the APA sentence. It goes into your results chapter as it is. The full chapter, every hypothesis with tables, is what the Chapter 4 Interpreter writes from your SPSS output.
Which chi-square test do you need?
The chi-square test of independence checks whether two categorical variables are associated. The data are a contingency table, a crosstab in SPSS: rows are the categories of one variable, columns the categories of the other, and each cell holds how many participants fall in that combination. The null hypothesis is that the row variable tells you nothing about the column variable.
The chi-square goodness-of-fit test looks at one categorical variable and asks whether the observed counts match an expected distribution: equal proportions by default, or proportions you specify, such as national census figures. In SPSS it lives under Nonparametric Tests → Legacy Dialogs → Chi-square.
Both use the same statistic, χ² = Σ (O − E)² / E, summed over all cells, and the same distribution with df = (rows − 1)(columns − 1) for independence and df = categories − 1 for goodness of fit. The p-value is the upper tail of that distribution, computed here with the regularized incomplete gamma function that every statistics package uses; all values are checked against scipy to six decimals.
Expected counts, Yates and Fisher
The chi-square approximation is only reliable when the expected count in every cell is at least 5 (some texts allow up to 20% of cells below 5 as long as none is below 1). SPSS prints this check as a footnote under the Chi-Square Tests table. The calculator prints the same check under its table.
For a 2×2 table two remedies exist. Yates’ continuity correction makes the statistic more conservative; SPSS reports it as “Continuity Correction”, and it is shown here for completeness but is no longer recommended by most methodologists. Fisher’s exact test computes the exact probability from the hypergeometric distribution and is the accepted report when expected counts are small. When any expected count is below 5 the calculator marks Fisher as the reported line and the APA sentence says why.
For larger tables with small expected counts, merge sparse categories that make sense together, or collect more data. Do not delete rows to make the test work.
Effect size: Cramér’s V, φ and Cohen’s w
A significant χ² tells you an association exists, not how strong it is. Cramér’s V = √(χ² / (N × (k − 1))), where k is the smaller of the number of rows and columns, ranges from 0 to 1 and is the standard effect size for a contingency table. For a 2×2 table it equals the absolute value of φ, which also carries a sign. For goodness of fit the equivalent is Cohen’s w = √(χ² / N).
Cohen (1988) labelled .10 small, .30 medium and .50 large for one degree of freedom; the thresholds shrink for larger tables (divide by √df*, where df* = k − 1), and the calculator applies that adjustment before choosing the word.
How to report a chi-square test in APA 7
State the test and the two variables, then χ²(df, N = n) = value, p, and the effect size: for example χ²(2, N = 140) = 11.43, p = .003, Cramér’s V = .29. Then describe the cells that carry the association in plain words, using the percentages: “women chose online learning more often than men (49% vs 26%)”. Add the contingency table as an APA table with counts and row percentages. The calculator writes the sentence; change the variable names so it reads like your study.
A results chapter repeats this for every hypothesis and adds the tables, the descriptive statistics, the assumption checks and the reliability of each scale. See a real one in the Chapter 4 Interpreter demo.
Frequently asked questions
Can I enter percentages instead of counts?
No. The test depends on the actual number of participants; the same percentages from 20 people and from 2,000 people give completely different p-values. Enter counts.
My table has expected counts below 5. What now?
For a 2×2 table report Fisher’s exact test, which the calculator already marks. For a bigger table merge categories that belong together, for example “strongly agree” with “agree”, and run it again. Say in the chapter that you merged them and why.
Which cells explain a significant result?
The ones the calculator highlights: standardised residuals beyond ±1.96 mean that cell has noticeably more or fewer people than independence predicts. Describe those cells with their row percentages.
Does chi-square tell me which variable causes which?
No. It only tells you the two variables are not independent in your sample. Direction and causation come from your design, not from the test.