Final answer:
The independence assumption refers to the condition where each score on a variable does not affect any other, typically required for valid statistical testing. It is separate from, but often mentioned alongside, the assumptions of normality and equal variances required for tests such as ANOVA.
Step-by-step explanation:
The independence assumption in statistics refers to the condition where the scores on the variable are independent of each other, which means that the presence or value of one outcome does not affect the presence or value of another. This is crucial for many statistical tests to ensure the validity of the results. The independence assumption is not related to the normality of the variable in each of the populations nor directly to whether two group variances are equal, though these may be separate assumptions needed for specific tests, such as the one-way ANOVA.
In the context of one-way ANOVA and similar statistical tests, the assumptions typically include that each sample is drawn from a normally distributed population, all samples are independent and randomly selected, and the populations from which the samples are drawn have equal standard deviations (or variances), which is known as homoscedasticity.
Variance equality and random selection of samples are also essential assumptions for accurately performing hypothesis testing on means and proportions using the analysis of variance (ANOVA). However, when the assumption of equal variances is violated, further statistical tests may be necessary to confirm this before proceeding with the analysis.