When the between-groups variance is a lot larger than the within-groups variance, the F-value is ____ and the likelihood of such a result occurring because of sampling error is _____

a. large; low
b. large; high
c. small; low
d. small; high

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Answer:

a. large; low.

Step-by-step explanation: The between group variance is usually used in ANOVA(ANALYSIS OF VARIANCE) to show how two or more parties or groups differ from each other. While the within group variance is usually used to describe how members of factors in a given group differ from eachother when conducting a research. The within group variance is also known to show the difference among a particular population and the mean of that population.

When the between-groups variance is a lot larger than the within-groups variance, the F-value is large and the likelihood of such a result occurring because of sampling error is low

From the question, we understand that the F value changes as the difference between the variances change.

The between-groups variance illustrates the difference between two or more groups while the within-group variance illustrates the difference among a population and the population mean .

As the difference between the variances increases, the F-value also increases, while the likelihood reduces.

Hence, the correct option is (a) large; low

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