Describe the difference between the variance between samples M...

Question

Describe the difference between the variance between samples MSB and the variance within samples MSW.

Accepted Answer

Hello there. Today we want to solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. If the mean square between groups, MSB is much larger than the mean square within groups, MSW. What does this indicate in a ANOVA test? Awesome. So it appears for this particular prom, we're given the statement that if the mean square between groups, which is denoted as MSB, is much larger than the mean square within groups, which is denoted as MSW, So if once again if MSB is much larger is much larger than MSW, what does this indicate in an analysis of variance test? That's what ANOVA stands for, analysis of variance. So if MSB once again is much larger than MSW, what will this indicate in an ANOVA test, and that is our final answer that we're ultimately trying to solve for. So with that said, Let's read off our multiple choice answers to see what our final answer might be. A is there is no evidence of differences among the group means. B is the sample sizes are too small for meaningful analysis. C is at least one group mean is significantly different from the others, and D is all group means must be equal. Awesome. So what we need to do first is we need to recall that MSB, so MSB measures the variation between group means, and it reflects how far each group's average is from the overall mean. Whereas MSW measures the variation within each group, meaning how spread out the values are inside of each group. And for when we state that MSB is much larger than MSW, this means, as we should recall, that the group averages are very different compared to the variability inside the groups. This means that in conclusion, this suggests that at least one group mean. will be significantly different from the others, and that the null hypothesis. That all group means are equal may be rejected. So with that in mind, our final answer without a doubt will have to be multiple choice answer letter C, which once again states at least one group mean is significantly different from the others, and that's it. We've officially solved for this problem. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Describe the difference between the variance between samples MSB and the variance within samples MSW.

Key Concepts

Variance Between Samples (MSB)

Variance Within Samples (MSW)

Analysis of Variance (ANOVA)

Watch next