When calculating expected frequencies, which of the following is essential for accurate results?

When calculating expected frequencies, correctly specifying the null hypothesis is crucial because it provides the foundation for determining what the expected frequencies should be under the assumption that the null hypothesis is true. The expected frequencies are derived from the null hypothesis and its associated parameters, such as population proportions or mean differences. If the null hypothesis is incorrectly specified, the expected frequencies will not accurately reflect what is expected in the absence of an effect or difference. This can lead to incorrect conclusions regarding statistical significance and the overall validity of the analysis.

While the other options may play roles in broader aspects of statistical analysis or certain specific tests, the accuracy of expected frequencies directly hinges on a proper understanding and formulation of the null hypothesis. For instance, a large sample size is beneficial for the stability of estimates and the power of the test, and random sampling methods help ensure that the sample represents the population, but these factors do not directly affect how expected frequencies are derived from the null hypothesis. Homogeneity of variance pertains to the assumption needed for certain statistical tests, but it is not a factor in the calculation of expected frequencies themselves.