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Based on the properties of the ordinal level of measurement, diagnose the flaw in the student's reasoning. Explain why the mean is not the appropriate measure of central tendency for these data and state what should be used instead.
Case context: A clinical psychology student is conducting a study on generalized anxiety disorder. They ask patients to rate their anxiety levels from 'least severe' to 'most severe.' After collecting the data, the student decides to calculate the mean to describe the central tendency of the data, arguing that the numerical ratings assigned to the severity levels allow for this calculation.
Question: Based on the properties of the ordinal level of measurement, diagnose the flaw in the student's reasoning. Explain why the mean is not the appropriate measure of central tendency for these data and state what should be used instead.
Sample answer: The student's data is at the ordinal level of measurement because anxiety is rated in order of severity from least to most. The flaw in the student's reasoning is that calculating a mean assumes equal intervals between points on the scale, but ordinal scales do not assume equal differences between adjacent scale values. Because ordinal data only provide a sequence or order, the student should use the median or mode as indicators of central tendency instead of the mean.
Key points:
- The anxiety ratings represent a rank order, making it an ordinal level of measurement.
- Ordinal scales do not assume equal differences between adjacent scale values.
- Calculating a mean is inappropriate because it requires the assumption of equal differences.
- The median or mode should be used as indicators of central tendency for ordinal data.
Rubric: Full credit for correctly identifying that the anxiety scale is ordinal, explaining that ordinal scales lack equal intervals between adjacent values (which makes the mean inappropriate), and stating that the median or mode should be used instead.
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Research Methods in Psychology - 4th American Edition @ KPU
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