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Based on your understanding of null hypothesis testing, diagnose the errors in the researchers' interpretation of their -value.
Case context: A group of researchers conducts a study on the effect of a new cognitive behavioral therapy on anxiety levels. They report a statistically significant result with a -value of .02. In their discussion section, they write, 'Because our -value is .02, there is only a 2% probability that our null hypothesis is true. Furthermore, this means there is a 98% chance that future researchers will replicate our significant findings.'
Question: Based on your understanding of null hypothesis testing, diagnose the errors in the researchers' interpretation of their -value.
Sample answer: The researchers have made two errors in comprehension. First, a -value of .02 does not mean there is a 2% probability that the null hypothesis is true; rather, it means there is a 2% probability of observing their sample data if the null hypothesis were true. Second, it is a misconception to subtract the -value from 1 (1 - .02 = .98) to find the probability of replication. This ignores the crucial role of statistical power in determining whether a study will be successfully replicated.
Key points:
- Explains that a -value of .02 is not the probability that the null hypothesis is true.
- Explains that subtracting the -value from 1 does not yield the probability of replicating a significant result.
- Mentions that the probability of replication also depends on statistical power.
Rubric: The student correctly explains why the researchers' interpretation of the -value as the probability of the null hypothesis being true is flawed, and why using for replication probability is incorrect.
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Research Methods in Psychology - 4th American Edition @ KPU
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