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Explain how the software's output and the hand-calculation method are conceptually aligned to lead to the identical statistical conclusion of retaining the null hypothesis.
Case context: A health psychologist is investigating the correlation between people's calorie estimates and their weight. Having no directional expectation, she conducts a two-tailed test. For a sample of students, she computes Pearson's as . She analyzes the data using two different methods: first using statistical software which outputs a -value of , and second by hand, finding a critical value of for degrees of freedom.
Question: Explain how the software's output and the hand-calculation method are conceptually aligned to lead to the identical statistical conclusion of retaining the null hypothesis.
Sample answer: The software and hand-calculation methods are conceptually aligned because they use equivalent decision rules to assess statistical significance. The software calculates a -value () and compares it to the standard alpha level of . Because the -value is greater than , the null hypothesis is retained. The hand-calculation compares the calculated Pearson's () to the critical value (). Since the calculated correlation is less extreme than the critical value, it mathematically confirms that the probability of obtaining this result under the null hypothesis is greater than . Both rules indicate that the relationship is not statistically significant, resulting in retaining the null hypothesis.
Key points:
- Software method retains the null hypothesis because the -value () is greater than the alpha level ().
- Hand-calculation method retains the null hypothesis because the absolute value of Pearson's () is less extreme than the critical value ().
- The comparison of a calculated value to a critical value is mathematically aligned with comparing a -value to an alpha level, leading to the same decision.
Rubric: The response must explain the decision rule for the software approach (comparing to alpha = ) and the hand-calculation approach (comparing calculated to critical value = ). It must show comprehension that a correlation less extreme than the critical value corresponds to a -value greater than alpha, leading to the same conclusion.
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Research Methods in Psychology - 4th American Edition @ KPU
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In a psychological study with a sample size of 22 participants, a researcher calculates a Pearson's correlation coefficient of -0.21. To determine if this relationship is statistically significant using a hand-calculation method, a critical value of 0.444 is used. Arrange the following steps to reflect the logical sequence of analysis required to derive the statistical conclusion for this study.
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In the health psychologist's example study investigating calorie estimates and weight, the statistical software provides a -value of , which leads the researcher to reject the null hypothesis.
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A health psychologist investigating the correlation between calorie estimates and weight for a sample of students () calculates a Pearson's of . Upon evaluating this result against a critical value of , the researcher concludes that the correlation is not extreme enough to exceed the threshold for significance. To finalize this statistical judgment, the researcher must _____ the null hypothesis.
In the health psychologist's study, the degrees of freedom equal (computed as ). The subtraction of accounts for the number of _____ that must be estimated from the sample data in order to compute Pearson's .
A peer reviewer is critically evaluating the health psychologist's null hypothesis test of the correlation between calorie estimates and weight. Arrange the following evaluative checks in the correct logical order for conducting a rigorous methodological critique.
In the health psychologist's study investigating calorie estimates and weight, describe the manual steps and values required to test the correlation coefficient by hand, including how degrees of freedom are calculated and how the final decision is reached.
Explain how the software's output and the hand-calculation method are conceptually aligned to lead to the identical statistical conclusion of retaining the null hypothesis.
If a researcher replicates the calorie estimate and weight study with the same sample size of () and critical value of , but calculates a Pearson's of , apply the hand-calculation decision rule to determine and justify whether they should reject or retain the null hypothesis.