Expected count

An expected count is how many observations a category would get if the null hypothesis were exactly true; it is the baseline in a chi-square test.

Expected counts are the tallies a chi-square model predicts for each cell when the null hypothesis holds, and the test measures how far the observed counts drift from them. For a two-way table, each cell's expected count is E=(row total)×(column total)grand totalE = \frac{(\text{row total}) \times (\text{column total})}{\text{grand total}}. For example, in a 200-person table a cell whose row totals 80 and column totals 50 has E=80×50200=20E = \frac{80 \times 50}{200} = 20. Every expected count should be at least 5 for the chi-square approximation to be trustworthy.

More hypothesis testing terms, or browse the full statistics glossary.