DSRT 734: Testing Hospital Rank Against Physician Count

DSRT 734 Question

A researcher is interested in testing if the rank of a hospital
according to US News Best Hospital Rankings is related to the number
of physicians they employ. What is the correct test for the researcher
to run?

Option A

Pearson's correlation


Option B

Pearson's chi-square


Option C

Independent samples t-test


Option D

Spearman's rho correlation rs

What this question assesses

This prompt assesses method selection when one variable is an ordinal rank and the other is a count, with emphasis on the distinction between monotonic association, linear association, categorical tables, and group means.

How to approach this type of question

Classify hospital rank as ordered information: adjacent rank numbers do not necessarily represent equal-sized differences in hospital performance. Physician count is numeric, but its distribution may be skewed and tied values may occur. The research question concerns whether the variables move together across hospitals rather than whether predefined groups have different means. In actual data, draw a scatterplot, inspect monotonic direction, nonlinear form, influential hospitals, and ties, and check that hospitals are independent observational units. Then compare which candidate respects ordinal information and summarizes a monotonic relationship, which assumes a linear quantitative relationship, and which requires a contingency table or group contrast. Also remember that a relationship between rank and staffing would not show which variable causes the other. This framework supports a choice without disclosing one.

A rank of 1 represents an ordering, not a measured distance from rank 2, and its numerical direction may invert intuitive “better” performance. Record that direction before interpreting the sign of any coefficient. Examine ties in ranking and physician counts and follow the selected method’s treatment of them. A quality report would include sample size, coefficient, p-value, and uncertainty while avoiding a staffing-causation claim from an observational relationship.

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Related DSRT 734 resources

• University of the Cumberlands course resources
• DSRT 734 Inferential Statistics in Decision-Making
• DSRT 734 Questions: Inferential Statistics in Decision-Making
• How to Choose an Inferential Statistical Test