What does the expected frequency represent in statistical analysis?

The expected frequency is a crucial concept in statistical analysis, particularly in hypothesis testing and the Chi-square test. It represents the number of observations we would anticipate in a particular category or cell if the null hypothesis is true. This is essentially a theoretical or calculated value derived from the assumed distribution of data under the null hypothesis, assuming no effect or relationship exists.

In practice, expected frequencies allow researchers to compare the observed frequencies—actual counts from a study—to what would be expected if there were no differences or associations in the population being studied. For example, if you're testing whether a die is fair, the expected frequency would indicate how many times you would expect each face to show up based on the assumption that all faces occur equally often over a large number of rolls.

The other provided options describe different statistical terms or concepts, but they do not align with the specific meaning of expected frequency. The second option refers to observed data rather than theoretical expectations. The third option speaks to probability, which, while related to expectations, is not specifically about counting expected outcomes based on hypothesis testing. The fourth option defines the mean of a dataset, which measures central tendency rather than representing anticipated counts in categorical data.