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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.
The first is variation between samples, while the second is variation within sample components.
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An -curve has df . What is the number of degrees of freedom for the
a. numerator?
b. denominator?
Regarding one-way , fill in the blanks in each of Exercises
13.15 A measure of variation among the sample means is called the ------ The mathematical abbreviation for it is--------
13.19 What does the term one-way signify in the phrase one-way?
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.l 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 thesignificance 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.
many species of cuckoos are brood parasites. The females lay their eggs in the nests if similar bird species that then raise the young cuckoos at the expense of their own young. The question might be asked, "Do the cuckoos lay the same size eggs regardless of the size of the bird whose nest they use"? Data on the lengths, in millimeters of cuckoo eggs found in the nests of six bird species- Meadow Pipit, Tree pipit, Hedge Sparrow, Robin, Pied Wagtail and wren are provided on the WeissStats site. These data are collected by the late O. Latter in \(1902\) and used by L. Tippett in his text The Methods of Statistics.
a. Obtain individual normal probability plots and the standard deviations of the sample.
b. Perform a residual analysis
c. use your results from part (a) and (b) to decide whether conducting a one-way ANOVA test on the data is reasonable. If so, also do parts (d) and (e).
d. use a one-way ANOVA test to decide, at the\(5%\) significance level whether, the data provide sufficient evidence to conclude that a difference exists among the means of the populations from which the samples were taken.
e. Interpret your results from part (d).
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