(b) Conduct the non-parametric test and draw the conclusion.

Question

BlackTom AI · Accepted Answer

(1) Start by restating what is being asked or provided: the prompt is a fill-in-the-blank item that says to conduct the non-parametric test and draw the conclusion, and the given answer text specifies a Mann-Whitney U result and a conclusion about design A vs design B.
(2) Noting the options: there are no explicit answer choices presented in this item, so we cannot evaluate multiple discrete options as in a typical multiple-choice question. We will instead analyze the provided answer content for correctness and clarity.
(3) About the test choice: the Mann-Whitney U test is a non-parametric alternative to the two-sample t-test used to compare distributions of two independent groups when the outcome is ordinal or not normally distributed. The key interpretation hinges on whether the p-value is below the significance threshold (commonly 0.05).
(4) Interpreting the test statistic and p-value: the provided result states U = 5.5 and p = 0.173. A p-value of 0.173 is greater than 0.05, so the standard conclusion is that there is not enough evidence to conclude a statistically significant difference between the two groups at the 0.05 level. The statement also notes medians: Design A median = 19s, Design B median = 22s. Using medians to describe central tendency is consistent with a non-parametric test, which does not assume normality.
(5) Potential issues to consider:
- U being 5.5 is unusual in typical Mann-Whitney reporting because U is often an integer, though adjustments for ties can produce fractional values in some software outputs. If the analysis used a normal approximation with a corrected p-value, the p-value would still reflect non-significance; but the exact fractional U should be checked against how the software reports it.
- The conclusion mentions a specific comparison of medians. While the Mann-Whitney test assesses stochastic dominance between groups, it does not directly test for a difference in medians unless the distributions are similarly shaped. A cautious interpretation would say there is no evidence of a difference in the distributions of task completion times between the two designs, and note medians as a descriptive summary.
- If there were ties or small sample sizes, the exact p-value could differ from asymptotic results. It’s helpful to report both the U statistic and the p-value clearly, and, if possible, the sample sizes for Design A and Design B to contextualize the test.
(6) Addressing the conclusion: the statement ‘There is no statistically significant difference in task completion times between Design A (median = 19s) and Design B (median = 22s) at the conventional 0.05 significance level’ aligns with p = 0.173. The conclusion correctly reflects the failure to reject the null hypothesis at alpha = 0.05, given the p-value. However, it’s good practice to acknowledge that “no statistically significant difference” does not prove equality or absence of practical importance; it merely indicates insufficient evidence to claim a difference given the sample and variability.
(7) If you were to expand or improve the answer text, you might include:
- The sample sizes (n1 and n2) and whether a two-sided or one-sided test was used.
- A note about the effect size or its surrogate (e.g., rank-biserial correlation) to convey practical significance.
- A brief interpretation of the distribution shapes or a plot description to justify the use of Mann-Whitney in this context.
(8) In summary, evaluating the provided result: the test used is appropriate for comparing two independent samples with non-normal data; the p-value of 0.173 indicates no statistically significant difference at the 0.05 threshold, and the medians reported provide descriptive context. The numerical U value being 5.5 should be cross-checked with the software documentation to confirm its calculation with any ties, but the main inferential takeaway (non-significance) stands given p > 0.05.

(b) Conduct the non-parametric test and draw the conclusion. 多项填空题

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