Compare the variances of the three samples. Is there a noticeable difference? Th

Question

Compare the variances of the three samples. Is there a noticeable difference?

The F statistic is calculated using the formula below. Show that it is correct in this example.

How does the FSTAT compare with the FCRIT value? What does this tell you?

How would you find the F Critical value in the F tables?

What does the output say about the difference in the ant’s attraction to the three sandwiches?

Table: Numbers of ants visiting sandwiches Vegemite Ham & Pickles Anova: Single Factor Groups Count Sum Average Variance 8 246 30.s Bs. 64286 Vegemite Peanut Butter 8 272 34 214 394 49.25 116.5 ANOVA Source of Variation SS P-value 1561 2 780.5 5.626674 0.011048 3.4668 Between Groups 2913 21 138.7143 Within Groups

Explanation / Answer

Compare the variances of the three samples. Is there a noticeable difference?

Yes, the variance for peanut butter is almost twice as much as the variance of Ham & Pickles and it is more than twice as compared to the variance of Vegemite.

F = MSB / MSW = 780.5 / 138.7143 = 5.63

F critical value can be find for checking at 0.05 significance level with 2 numerator degrees of freedom and 21 denominator degrees of freedom.

Since F calculated > F critical, we reject Ho and hence,

There is sufficient evidence to conclude that at least one mean is different from others.

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