1. When would you use an ANOVA rather than a t test? An ANOVA would be used rather than a t
test when there are more than two levels to the independent variable(s). For example, if an
independent t test was done comparing two different nationalities to see which one scored better on
an exam, one would have to use an ANOVA test if there were three different nationalities being
compared.
2. What are the null and alternative hypotheses for ANOVAs? For ANOVAs, the null hypothesis will
always state that all of the means are equal to each other (Ho: μ=μ=μ). The alternative hypothesis
will always state that there is a difference between at least two of the means.
3. Which of the two estimates of population variance depends on whether the null hypothesis is true?
Why? The betweengroups estimate of the population variance depends on whether the null
hypothesis is true because that is the estimate the focuses on the variation
between
the different
distributions. The withingroups estimate only focuses on the variation within one distribution which
is not mentioned in the null hypothesis.
4. Describe the differences between withingroups estimations of population variance and between
groups estimations of
population variance. As mentioned previously, the withingroups estimations of population variance
describes the variance within each population. It does not depend on the null hypothesis and it gives
no information about the variances between one population and another. The betweengroups
estimations of population variance describe the variance between all of the populations. These do
depend on the null hypothesis and it does give information about the variances between the
populations. For instance, when the null hypothesis is true, remember we said that all of the means
are equal to each other. This means that the variability between the means is no different than the
variability that is normally seen within each population. This also means that in order to determine
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 Fall '09
 Dr.Hall
 Normal Distribution, Variance, Null hypothesis, population variance, ANOVAs

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