6. A researcher used a one-way classification to compare the reaction × of participants based on three conditions: stimulus A, stimulus B, and stimulus C. The researcher randomly selected 12 adults for each of the three conditions and then compared the resulting mean reaction ×. A one-way ANOVA provided an F-statistic of 0.185 and a critical F-value of 0.206.Which conclusion is appropriate for these results?
Answer: C
None of the mean reaction × are significantly different.
The one-way ANOVA results indicate that the F-statistic of 0.185 is less than the critical F-value of 0.206. This suggests that there is no significant difference among the mean reaction × across the three conditions.
A) At least one pairing of mean reaction × has a significant difference.
This option is incorrect because the F-statistic of 0.185 does not exceed the critical F-value of 0.206, indicating that there is no evidence to support that at least one mean is significantly different from the others.
B) There is a significant difference between all pairs of mean reaction ×.
This statement is not valid as it implies that all pairs have significant differences, which contradicts the findings of the ANOVA. The F-statistic suggests there are no significant differences between any of the mean reactions.
C) None of the mean reaction × are significantly different.
This option is correct as the F-statistic of 0.185 is lower than the critical F-value of 0.206, indicating that there are no significant differences among the mean reaction × for the three conditions.
D) Exactly one pair of mean reaction × has a significant difference.
This choice is incorrect because the analysis does not support the existence of any significant differences between the means, let alone the assertion of exactly one significant pair.
Conclusion
The analysis clearly shows that none of the mean reaction × are significantly different, as indicated by the F-statistic being below the critical value. All other options incorrectly suggest varying degrees of significance that are not supported by the data. Therefore, option C is the only appropriate conclusion based on the ANOVA results.