Week 4 theoretical questions Flashcards
How can paired or matched samples help in the statistical inference?
Using matched or paired samples can help control for a prominent nuisance factor’s impact on the outcome variable, so that the focal difference on outcome variable due to the factor of interest is less likely to be masked or hidden due to the noise introduced by the nuisance factor (i.e., reducing the probability to make a Type II error).
Explain the essential rationale underlying one-way ANOVA.
In essence, in one-way ANOVA, we compare the variation in the outcome variable caused by the treatment against the variation in the outcome variable caused by other nuisance factors (error) while controlling for the impacts of the experiment design (e.g., number of treatment groups, sample sizes).
Why do we reject Ho in ANOVA
In essence, in one-way ANOVA, we compare the variation in the outcome variable caused by the treatment against the variation in the outcome variable caused by other nuisance factors (error) while controlling for the impacts of the experiment design (e.g., number of treatment groups, sample sizes).
If the former variation is sufficiently larger than the later variation, we view it as evidence against the null hypothesis and conclude at least two group means differ from each other; if the former variation is not sufficiently larger than the later variation, we view it as evidence consistent with the null hypothesis and conclude all group means are not different from each other.
On the conceptual level, how are those post-hoc comparison tests (e.g., LSD with Bonferroni adjustment, Tukey method) different from multiple pairwise T-tests in comparing group means?
In essence, the difference is that those post-hoc comparison tests take the overall experiment-wise error into consideration and have explicit control over the probability of making at least one Type I error among all the pairwise comparison tests, whereas simple multiple pairwise T-tests cannot do so.
In these campaigns, “20% off” coupons are widely distributed. These coupons are only valid for one week.
Which test is most appropriate to infer whether sales increase during the promotional campaign? Why?
Paired/matched T-test is most appropriate. The daily gross sales during vs. after campaign are naturally paired by the day of the week, which is supposed to have a large effect on the gross sales (e.g., gross sales are usually higher on weekends). Using paired/matched T-test allows one to control for the impact of day of the week (nuisance factor) on daily sales while studying the impact of the promotion campaign on sales.
