Expected Frequency: Definition, Formula, Calculation

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Contingency Tables > Expected Frequency

What is Expected Frequency?

The expected frequency is a probability count that appears in contingency table calculations including the chi-square test. Expected frequencies also used to calculate standardized residuals, where the expected count is subtracted from the observed count in the numerator.

  • Observed Frequencies are counts made from experimental data. In other words, you actually observe the data happening and take measurements. For example, you roll a die ten times and then count how many times each number is rolled. The count is made after the experiment.
  • Expected Frequencies are counts calculated using probability theory. For example, before you roll a six-sided die, you calculate the probability of any one number being rolled as 1/6.

How to Calculate Expected Frequency by Hand

Expected frequencies are calculated for each cell in a contingency table. So if you have, say, 16 cells, you’ll need to perform the steps 16 times (one for each cell). The formula to calculate expected frequency is: expected-cell-frequency-formula

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