What is the relationship between expected frequency and the Chi Square statistic?

The Chi Square statistic fundamentally measures how much the observed frequencies of a categorical variable differ from the expected frequencies. It quantifies the discrepancies between what we would expect to find (the expected frequency) based on a specific hypothesis and what we actually observe (the observed frequency).

When calculating the Chi Square statistic, the formula involves comparing the squared differences between these two frequencies, normalized by the expected frequency. A larger discrepancy—indicating that the observed values deviate significantly from what was expected—results in a higher Chi Square value, suggesting that the data do not fit the expected distribution well.

The relationship described by the correct option highlights that the Chi Square statistic is intrinsically tied to the notion of expected frequency, as it directly assesses how far the observed data diverges from those expected counts. This connection is crucial for interpreting Chi Square tests in the context of categorical data analysis and hypothesis testing.