ODA vs. Undocumented Chi-Square: Clarity vs. Confusion

Paul R. Yarnold

Optimal Data Analysis, LLC

A longitudinal smoking cessation study followed three patient groups: group 1=40 patients attending at least one group session; group 2=62 interviewed patients who did not attend group sessions; group 3=group 1+group 2. Data were collected four times: at the interview, and two- weeks and one- and two-months post-discharge. Each time patients rated their smoking behavior using a six-point scale: 1=quit smoking; 2=reduced smoking >50%; 3=reduced smoking <50%; 4=switched to pipe; 5=no change; 6=smoking increased. The scale is linear—assessing monotonically decreasing smoking—except for response option 4 (with N<3 at all four testings). Option 4 made the response scale nonlinear so the author used chi-square analysis to compare groups within and across testings (the latter test is a violation of the chi-square assumption that all observations appear once in the design matrix). Nevertheless, N<3 for Option 4 causes violation of the minimum expectation assumption. Furthermore, were an omnibus effect to be identified then the pairwise comparisons needed to identify the differences that produced the effect would also violate the minimum expectation assumption. The author offered two general statements regarding undocumented chi-square-based findings that violated two crucial underlying assumptions, and offered qualitative discussion. This is a surprisingly common practice in studies involving multicategorical variables that are analyzed using chi-square analysis: ODA clarifies the findings in such applications.

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