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Case Study

Based on standard practices in psychological research methods, diagnose the errors in the researcher's conclusions regarding the threshold for good internal consistency and their conceptual definition of what Cronbach's α\alpha represents for this 10-item scale.

Case context: A psychologist drafts a paper describing a new 10-item survey designed to measure test anxiety. In the methodology section, the researcher reports that the scale achieved a Cronbach's α\alpha of +0.78+0.78. They conclude that this value meets the standard threshold for good internal consistency, and they state that this coefficient represents the correlation between one specific split-half division of the items.

Question: Based on standard practices in psychological research methods, diagnose the errors in the researcher's conclusions regarding the threshold for good internal consistency and their conceptual definition of what Cronbach's α\alpha represents for this 10-item scale.

Sample answer: The researcher made two errors. First, a Cronbach's α\alpha of +0.78+0.78 falls below the standard statistical threshold of +0.80+0.80 or greater required to indicate good internal consistency. Second, Cronbach's α\alpha does not represent a single split-half correlation; conceptually, it represents the mean of all possible split-half correlations for the set of items. For their 10-item scale, there are actually 252252 ways to split the items, and Cronbach's α\alpha represents the mean of all 252252 split-half correlations.

Key points:

  • The standard threshold for good internal consistency is +0.80+0.80 or greater, meaning +0.78+0.78 is insufficient
  • Cronbach's α\alpha represents the mean of all possible split-half correlations, not a single one
  • A 10-item measure has 252252 possible split-half ways to be split into two halves

Rubric: Grading Criteria: - Correctly identifies that +0.78+0.78 is below the accepted threshold of +0.80+0.80 for good internal consistency (1 point). - Explains that Cronbach's alpha represents the mean of all possible split-half correlations, not just a single split (1 point). - Mentions that there are 252252 possible split-half correlations for a 10-item measure (1 point).

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Updated 2026-05-26

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Research Methods in Psychology - 4th American Edition @ KPU

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