To compare the population mean for population i with the population mean for pop
ID: 3361699 • Letter: T
Question
To compare the population mean for population i with the population mean for population j in the one way means model, what are your two hypotheses? What is the appropriate test statistic here and its distribution (and degrees of freedom)?
How is a L level confidence interval for the difference in population means constructed in the one way means model?
What is the problem that arises in k = 3 populations when computing 3 individual confidence intervals comparing each pair of means?
If the sample sizes are equal, do we use the Tukey or Bonferroni method? For unequal sample sizes, do we use Tukey or Bonferroni?
State the form of the one way effects model. Describe each term and your assumptions.
Explanation / Answer
unequal sample sizes can lead to unequal variance between samples, which affects the assumption of equal varainces in tests like ANOVA.
Having both unequal sample sizes and variances affeects statistical power and type 1 error rates.
if the confidence interval for difference does not contain zero, we can conclude that there is statistically significant difference in the two population values at the given level of confidence.
the boneferroni procedure is a good all around tool, but for all pairwise comparisons the tukey studntized range procedure, is the distribution of the difference between the maximum and a minimum over the standard error of the mean.
Bonferroni has more powerful when the number of compairson is small, whereas tukey is more powerful when testing large numbers of means.
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