Final answer:
In one-way ANOVA, variances used to test for differences between group means include the variance within groups and the variance between groups, culminating in the calculation of the F statistic to assess statistical significance.
Step-by-step explanation:
When you conduct an analysis of variances, which is known as ANOVA (analysis of variance), the variances used to test for differences between means are those calculated within the ANOVA framework. In the case of one-way ANOVA, you are testing whether there are statistically significant differences among several group means. To test these differences, ANOVA uses the variability within the groups and between the groups to calculate the F statistic, which is then compared to an F distribution to determine significance.
The one-way ANOVA test has several key assumptions including: normality of populations, randomly selected and independent samples, equal standard deviations (or variances) across populations, the factor as a categorical variable, and the response as a numerical variable. When testing for differences among means, ANOVA compares the variations between the means of different groups to the variation within each of these groups.