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?
None of the mean reaction × are significantly different.
The F-statistic of 0.185 is less than the critical F-value of 0.206, indicating that there is no statistically significant difference between the mean reaction × across the three conditions. Therefore, we conclude that the means are similar enough that we fail to reject the null hypothesis.
This statement suggests that there is a significant difference among at least one of the mean comparisons. However, since the calculated F-statistic (0.185) is lower than the critical F-value (0.206), this implies that no significant differences exist among the groups, making this conclusion incorrect.
This option asserts that every pair of means is significantly different from each other, which is not supported by the statistical findings. The F-statistic indicates a lack of significant variation among the groups, so this conclusion overstates the evidence and is therefore incorrect.
As established, the F-statistic of 0.185 is below the critical value of 0.206, leading to the conclusion that there are no significant differences between the means of the reaction × for the different stimuli. Thus, this choice accurately reflects the outcome of the analysis.
This conclusion implies that only one comparison among the means shows significance. Given the F-statistic does not exceed the critical value, we cannot claim even a single pair is significantly different, making this statement incorrect.
In a one-way ANOVA, when the calculated F-statistic is lower than the critical F-value, it indicates that there are no significant differences among the group means. In this case, the F-statistic of 0.185 being less than 0.206 confirms that none of the mean reaction × for the three stimuli conditions differ significantly, supporting the conclusion that all means are statistically equivalent.
Related Questions
View allA researcher needs a sample of students at a university. The researche...
The birth weights of 50,000 babies were recorded and analyzed. The dis...
How can a researcher decrease the width of a confidence interval?
What is an example of a discrete variable?
A researcher wants to collect data to create a confidence interval. Wh...
Related Quizzes
View all0PC1 Planning Instructional Strategies for Meaningful Learning Version 1
AP01 Elementary Literacy Curriculum Version 1
AQ01 Applied Healthcare Statistics C784 Version 1
BJ01 Introduction to Business Finance Version 1
C172 Network and Security Foundations Version 1
C180 Introduction to Psychology Version 1
C180 Introduction to Psychology Version 2
CKC1 Introduction to Humanities Version 1
DZ01 Mathematics for Elementary Educators III MATH 1330 Version 1
FF01 Human Growth and Development Version 1
- ✓ 500+ Practice Questions
- ✓ Detailed Explanations
- ✓ Progress Analytics
- ✓ Exam Simulations