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Describe the two methods a researcher can use to evaluate a computed statistic in an ANOVA, and explain the decision rules for rejecting or retaining the null hypothesis based on these evaluations.
Question: Describe the two methods a researcher can use to evaluate a computed statistic in an ANOVA, and explain the decision rules for rejecting or retaining the null hypothesis based on these evaluations.
Sample answer: To evaluate a computed statistic, a researcher can either find its corresponding -value or compare it to a predetermined critical value from an table. If the computed ratio is greater than the critical value, the associated -value is less than , and the researcher rejects the null hypothesis to conclude the population means differ. Conversely, if the ratio is less than the critical value, the -value is greater than , and the researcher retains the null hypothesis, concluding there is insufficient evidence that differences exist.
Key points:
- Evaluate the computed statistic by finding its corresponding -value or comparing it against a predetermined critical value from an table.
- Reject the null hypothesis if the computed ratio is greater than the critical value (associated -value is less than ).
- Conclude that population means differ when the null hypothesis is rejected.
- Retain the null hypothesis if the computed ratio is less than the critical value (associated -value is greater than ).
- Conclude there is insufficient statistical evidence of differences when the null hypothesis is retained.
Rubric: Grading should be based on the following: 1) Correctly identifying both evaluation methods (finding the -value and comparing the computed ratio against a critical value from an table). 2) Accurately stating the condition for rejecting the null hypothesis (computed ratio > critical value, ) and its associated conclusion (population means differ). 3) Accurately stating the condition for retaining the null hypothesis (computed ratio < critical value, ) and its associated conclusion (insufficient evidence of differences).
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Research Methods in Psychology - 4th American Edition @ KPU
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