Western Governors University (WGU) BUS3100 C723 Quantitative Analysis for Business Practice Exam

The assumption that is not a criterion for ANOVA (Analysis of Variance) is random sampling without replacement. ANOVA requires that the observations be independent, meaning that the measurement of one sample does not affect the measurement of another. This is crucial for the validity of the results.

Additionally, ANOVA assumes that the populations from which the samples are drawn are normally distributed. This assumption helps to ensure that the test statistics follow a known distribution under the null hypothesis. Furthermore, ANOVA assumes that the variances among the different groups being compared are equal, often referred to as homogeneity of variance. This is important because unequal variances can lead to inaccurate F-ratios and p-values, affecting the conclusions drawn from the analysis.

While random sampling is generally a best practice for various statistical analyses, the critical aspect for ANOVA is the independence of observations and the assumptions related to distribution and variance, rather than the specific method of sampling (with or without replacement). Therefore, the option regarding random sampling without replacement is not a core assumption of ANOVA.