A one-way classification is used to compare the reaction × of participants under three conditions: stimulus A, stimulus B, and stimulus C. Twenty adults are randomly selected for each of the three conditions, and the three resulting mean reaction × are 354 ms, 418 ms, and 219 ms, respectively. The table shows the differences between the means and the Tukey's confidence intervals for the differences.When comparing the mean reaction time of 354 ms with the mean of 418 ms, the difference between the means is 64 ms, and Tukey's 95% confidence interval for this difference is from 32.0 ms to 96.0 ms. When comparing the mean reaction time of 418 ms with the mean of 219 ms, the difference between the means is 199 ms, and Tukey's 95% confidence interval for this difference is from 167.0 ms to 231.0 ms. When comparing the mean reaction time of 219 ms with the mean of 354 ms, the difference between the means is 135 ms, and Tukey's 95% confidence interval for this difference is from 103.0 ms to 167.0 ms.Which conclusion is appropriate based on Tukey's method?
Every pair of means shows a significant difference.
Tukey's method is used to determine if there are significant differences between the means of multiple groups. In this case, the confidence intervals for the differences between each pair of means do not include zero, indicating that each pair of means is significantly different from one another.
This is correct because the confidence intervals for the differences between the means do not include zero for any of the comparisons. Specifically, the intervals for the differences (64 ms, 199 ms, and 135 ms) confirm significant differences between all pairs of means.
This option suggests that only one mean differs significantly while the others do not, which is incorrect. The analysis shows that all means differ significantly, as indicated by the confidence intervals.
This choice is incorrect because the confidence intervals for all pairs indicate significant differences. If no significant differences existed, the intervals would include zero, which is not the case here.
This statement is misleading because it implies that only the extreme means differ significantly. The analysis shows that all pairs of means have significant differences, not just between the highest and lowest.
In summary, Tukey's method demonstrates that every pair of means (354 ms, 418 ms, and 219 ms) exhibits significant differences, as supported by the confidence intervals for each comparison. This highlights the effectiveness of Tukey's test in identifying significant differences across multiple conditions in reaction time studies.
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