Any difference among the population means in the analysis of variance will inflate the expected values of
Answers
Answer :
In ANOVA, any difference among the population means will inflate the expected values of the test statistic, leading to an increase in the risk of committing a type I error. This is why it's important to check the assumptions of normality and equal variances among the populations before conducting an ANOVA test.
Explanation :
In the analysis of variance (ANOVA), any difference among the population means will inflate the expected values of the test statistic, such as the F-statistic or the t-statistic. This is because the ANOVA test statistic is based on the differences among the sample means, and if the population means are different, it is more likely that the sample means will also be different, resulting in a larger test statistic.
This inflation of the expected values can lead to an increase in the risk of committing a type I error, also known as a false positive. This means that there is a higher chance of rejecting the null hypothesis (i.e. that there is no difference among the population means) when it is actually true.
This is why it is important to check the assumptions of normality and equal variances among the populations before conducting an ANOVA test. If these assumptions are not met, alternative tests such as the Kruskal-Wallis test or the Welch's ANOVA test should be used.
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