Note that TSS, SSB, and SSW are all measures of variation. a. If SSB is approxim

Question

Note that TSS, SSB, and SSW are all measures of variation.  

a. If SSB is approximately equal to TSS, what does this imply about the sample variances for the treatments?

b. If SSW is approximately equal to TSS, what does this imply about the relation between the treatment means?

c. If SSB is approximately equal to TSS, then SSB/TSS is approximately 1. How is this related to the coefficient of determination from linear regression? Explain.

d. True or false: SSB, SSW, and TSS are always nonnegative.

e. True or false: SSB < TSS, always.

f. True or false: SSW < TSS, always.

g. True or false: SSB/TSS is always between 0 and 1.

h. True or false: SSB/TSS + SSB/SSW = 1, always.

Explanation / Answer

Result:

Note that TSS, SSB, and SSW are all measures of variation.  

a. If SSB is approximately equal to TSS, what does this imply about the sample variances for the treatments?

Between sample variance are larger than within sample variances.

Treatment means are significantly different.

b. If SSW is approximately equal to TSS, what does this imply about the relation between the treatment means?

Treatment means are not significantly different.

c. If SSB is approximately equal to TSS, then SSB/TSS is approximately 1. How is this related to the coefficient of determination from linear regression? Explain.

Coefficient of determination is approximately 1. Most of the variance in y is explained by x.

d. True or false: SSB, SSW, and TSS are always nonnegative. True

e. True or false: SSB < TSS, always. True

f. True or false: SSW < TSS, always. True

g. True or false: SSB/TSS is always between 0 and 1. True

h. True or false: SSB/TSS + SSB/SSW = 1, always. False

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