Expected frequency
= Expected frequency
{title2=$E_j=np_j$}
= Expected count
{synonym}
The <expected value> of the number of observations in a category under a specified <statistical model>. For $n$ observations with common category <probability> $p_j$, <linearity of expectation> gives $E_j=np_j$; the calculation does not itself require <independence>. In a <contingency table>, fitting <independence> gives $E_{ij}=n_{i+}n_{+j}/n$. These are model-based counts, which may be fractional, rather than an additional set of observed responses. <Pearson's chi-squared test> compares observed counts with their corresponding <expected frequencies>.