Final answer:
The sample size criteria for multinomials typically require that all expected group counts need to be at least 5. This rule ensures the reliability of statistical tests by having a sufficient number of observations in each category. If expected counts are below 5, alternative methods may be needed.
Step-by-step explanation:
When determining the sample size criteria for multinomials, a common rule of thumb is that all expected group counts need to be at least 5. This is to ensure that each category has a sufficient number of observations to provide reliable results when conducting statistical tests such as chi-square tests. This requirement is designed to maintain the validity of the statistical analysis, as having too few observations in any group can distort the test results and lead to incorrect conclusions.
Statistical literature suggests various criteria for different distributions and tests. For example, when dealing with binomial distributions, the rule is that the products np and nq must both be greater than five. In multinomial contexts, the guideline is likewise that expected counts should be 5 or more to apply the chi-square test appropriately. While larger expected counts, like 10 or more, can further improve reliability, the minimum standard most commonly accepted is 5 to minimize sampling error.
In general, these criteria contribute to the reliability of statistical inferences by ensuring that each outcome category is adequately represented in the sample. It's also important to note that if any expected count is less than 5, alternative statistical methods may be required.