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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We stated earlier that a one-way ANOVA test is always right-tailed because the null hypothesis is rejected only when the test statistic, , is too large. Why is the null hypothesis rejected only when is too large?
Breast Milk and IQ. Considerable controversy exists over whether long-term neurodevelopment is affected by nutritional factors in early life. A. Lucas and R. Morley summarized their findings on that question for preterm babies in the publication "Breast Milk and Subsequent Intelligence Quotient in Children Born Preterm (The Lancet, Vol. 339, Issue 8788, Pp, 261-264). The researchers analyzed IQ data on children at age years. The mothers of the children in the study had chosen whether to provide their infants with breast milk within hours of delivery. The researchers used the following designations. Group I: mothers declined to provide breast milk; Group ll a: mothers had chosen but were unable to provide breast milk and Group Il b; mothers had chosen and were able to provide breast milk. Here are the summary statistics on IQ.
At the significance level, do the data provide sufficient evidence to conclude that a difference exists in mean IQ at age years for preterm children among the three groups? Note: For the degrees of freedom in this exercise:
In one-way ANOVA, identify a statistic that measures
a. the variation among the sample means.
b. the variation within the samples.
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
Explain the reason for the word variance in the phrase analysis of variance.
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