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Chapter 13: Q.13.35 (page 542)

State the one-way ANOVA identity, and interpret its meaning with regard to partitioning the total variation in the data.

Short Answer

Expert verified

The first is variation between samples, while the second is variation within sample components.

Step by step solution

01

Given Information

Consider identity in a one-way ANOVA.

02

Explanation

The total sum of the squares equals the addition of the treatment sum and the error sum of the squares is the one-way ANOVA identity.

SST=SSTR+SSE

The above relation demonstrates that the entire variation among all observations is split into two parts.

Variance across samples is one factor, and variation within sample components is another.

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Most popular questions from this chapter

We have provided data from independent simple random samples from several populations. In each case, determine the following items.

a. SSTR

b. MSTR

c. SSE

d. MSE

e. F

Refer to Exercise \(13.5\).

a. Find and interpret a \(95%\) confidence interval for the mean monthly rent of newly completed apartments in the Midwest.

b. Find and interpret a \(95%\) confidence interval for the difference between the mean monthly rents of newly completed apartments in the Northwest and South.

c. What assumptions are you making in solving parts (a) and (b)?

In Exercise \(13.42-13.47\) we provide data from independent simple random samples from several populations. In each case,

a. compute SST, SSTR and SSE by using the computing formulas given in Formula \(13.1\) on page \(535\).

b. compare your results in part (a) for SSTR and SSE with those you obtained in Exercises \(13.24-13.29\) where you employed the defining formulas.

c. construct a one-way ANOVA table.

d. decide at the \(5%\) significance level, whether the data provide sufficient evidence to conclude that the means of the populations from which the samples were drawn are not all the same.

In one-way ANOVA,

a. list and interpret the three sums of squares.

b. state the one-way ANOVA identity and interpret its meaning with regard to partitioning the total variation among all the data.

Fill in the missing entries in the partially completed one-way ANOVA tables.
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