Final answer:
In the Wilcoxon Signed-Rank Test, a treatment effect that results in consistently larger scores in one treatment would lead to statistically significant results, suggesting the treatment is effective. This applies to medical studies, product effectiveness testing, and comparisons of educational modalities.
Step-by-step explanation:
In the context of the Wilcoxon Signed-Rank Test, a treatment effect that causes scores in one treatment to be consistently larger than scores in the other would produce statistically significant results. Assuming the alternative hypothesis is that there is a decrease in pain after medication, indicating improvement, the differences in scores should be negative. If the null hypothesis is that there is no change, but we observe that post-treatment scores are consistently lower, we would likely reject the null hypothesis in favor of the alternative, suggesting a treatment effect.
When it comes to two independent groups, such as in the evaluation of two different floor waxes, the test of the null hypothesis versus the alternative hypothesis involves determining which wax is more effective, leading to a right-tailed test. A significant result here would mean that one wax is statistically proven to last longer than the other.
The variance in the combined data being larger when the null hypothesis is false can be a result of differing means. In medical studies, such as comparing tumor sizes before and after drug treatment, a statistically significant larger average decrease in the drug-treated group compared to the untreated group may suggest the drug is effective, but this needs further statistical tests to confirm.
Lastly, when measuring effect sizes, values larger than established benchmarks (such as Cohen's 0.8 for a large effect size) indicate significant differences between means, as seen in effect size comparisons between online and face-to-face class final exam scores.