Chi-Square Expected Count Less Than 5: What to Do

You run your chi-square test, scroll to the bottom of the SPSS output, and find this footnote: "2 cells (33.3%) have expected count less than 5. The minimum expected count is 2.47." Your p-value sits right there above it, looking perfectly normal. Can you still use it? Usually not. This article explains what the warning means and walks through the three standard fixes, with APA reporting examples for each.

What the Warning Actually Means

A chi-square test compares the counts you observed against the counts you would expect if the two variables were unrelated. SPSS computes each expected count from the table margins: row total multiplied by column total, divided by the overall sample size. In a study of 90 nursing students where 12 chose the night-shift option and 18 were in the part-time group, the expected count for that cell is 12 × 18 / 90 = 2.4, no matter what you actually observed there.

The test statistic follows the chi-square distribution only approximately. That approximation is good when expected counts are reasonably large and falls apart when they are small. The standard rule, based on Cochran's 1954 criteria, has two parts: no more than 20% of cells may have an expected count below 5, and no cell may have an expected count below 1. SPSS checks the first part for you in that footnote.

Note the word expected. Students often look at their crosstab, see observed counts of 6 or 8 everywhere, and assume the warning is a mistake. It is not. A cell can hold 7 observed cases and still have an expected count of 3.1. Observed counts play no role in this assumption.

Why You Cannot Just Ignore It

With small expected counts, the true sampling distribution of the test statistic becomes lumpy and discrete while the chi-square distribution stays smooth. The p-value SPSS prints can then be too small, meaning you might report a significant association that a valid test would not support. For a thesis, that is the worst kind of error: an examiner who checks the footnote will spot it in seconds, and your Results chapter comes back with red ink.

The good news is that every fix takes minutes. Which one applies depends on the size of your table.

Fix 1: Fisher's Exact Test (for 2×2 Tables)

If your table has exactly two rows and two columns, the solution is already in your output. SPSS automatically adds Fisher's exact test to the Chi-Square Tests table for every 2×2 crosstab. Instead of approximating, it computes the exact probability of your table (and more extreme ones) directly, so the expected-count rule does not apply to it at all.

Read the "Exact Sig. (2-sided)" value in the Fisher's Exact Test row and report that as your p-value. In APA format: Because two cells had expected counts below 5, Fisher's exact test was used. The association between treatment completion and relapse was significant, p = .021. There is no test statistic or degrees of freedom to report for Fisher's method, which surprises many students. The p-value stands alone.

Fix 2: Combine Categories (for Larger Tables)

Sparse cells usually come from thin categories, not small samples. A 5-point satisfaction item crossed with gender produces a 5×2 table, and if only 4 people chose "very dissatisfied," that whole row drags expected counts down. Merging "very dissatisfied" with "dissatisfied" turns the table into 4×2 and often clears the warning in one step.

Two conditions make merging defensible. The combined categories must be conceptually adjacent (you can merge two levels of disagreement; you cannot merge "unemployed" with "retired" just to fix a number), and you must disclose the change: Due to low expected frequencies, the "very dissatisfied" and "dissatisfied" categories were combined prior to analysis. Decide on the merge before looking at how it changes your p-value. Rerunning the test with different groupings until something turns significant is p-hacking, and it is one of the mistakes that get theses sent back.

Fix 3: Exact or Monte Carlo Methods (When Merging Is Not an Option)

Sometimes categories cannot be merged without destroying the research question. For those cases, SPSS offers an Exact button inside the Crosstabs dialog (if your license includes the Exact Tests module). The exact method extends Fisher's logic to tables larger than 2×2; the Monte Carlo option approximates it by simulation when the exact computation is too heavy. Report it the same way: name the method, then give the p-value.

No Exact Tests module? The likelihood-ratio chi-square, printed by default in the same output table, tolerates sparse data somewhat better than Pearson's version, though it is a weaker remedy than a true exact test. And if data collection is still open, the cleanest fix of all is more participants. Our sample size calculator shows how many cases a chi-square design needs before the fieldwork starts.

Which Fix Applies to You

Your situation	Recommended fix	What you report
2×2 table, any expected count < 5	Fisher's exact test (already in output)	Fisher's exact test, p-value only
Larger table, sparse adjacent categories	Combine categories, rerun	χ², df, p, Cramér's V + disclosure of merge
Larger table, categories cannot merge	Exact / Monte Carlo method	Method name + exact p-value
Any cell with expected count < 1	Never report Pearson's chi-square	One of the fixes above, always

How to Report the Fix in APA Format

Whichever route you take, the pattern is the same: state the violation in one clause, name the remedy, then report the result. A complete example for a merged-category solution: Because 3 of 10 cells (30%) had expected counts below 5, the two lowest response categories were combined. The association between study program and satisfaction remained non-significant, χ²(3, N = 88) = 5.91, p = .116, Cramér's V = .26. The structure of the full sentence follows the same rules as any chi-square write-up, covered in our guide to reporting chi-square results in APA format.

Examiners do not penalize assumption violations. They penalize violations that go unmentioned. A footnote-level problem handled openly in two sentences reads as competence, not weakness.

Check It Automatically

If you want the assumption checked without hunting through footnotes, Academic Stats Agent runs the expected-count check on every chi-square analysis, switches to Fisher's exact test when your 2×2 table needs it, and flags larger tables that require a decision from you. The analysis itself is free; you upload your data file and get the full crosstab, test result, and assumption report in about a minute. For the background on when chi-square is the right test in the first place, see our chi-square overview or the step-by-step SPSS walkthrough.