A Dramatic Example of Analysis of Covariance

• Activity Number: 50
• Type: Contributed
• Date/Time: Sunday, August 11, 2002 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Education*
• Author(s): Martin Feuerman*+ and Simcha Pollack and John Aloia
• Affiliation(s): Winthrop University Hospital and Winthrop University Hospital and Winthrop University Hospital
• Keywords: Analysis of Covariance ; Adjusted Means ; Covariate ; ANACOVA

Abstract

We present an Analysis of Covariance (ANACOVA) example where the unadjusted means are almost equal (p=0.97); by covariate adjusting there is a statistically significant difference (p < 0.01). We discuss the causes of this dramatic shift, which may be of interest to statistics teachers/students. Our data involves 90 black and 143 white women tested for total body calcium (TBCa) and total body potassium (TBK). We consider the ratio (TBCa/TBK). Mean TBCa/TBK (standard deviation) for blacks and whites are 7.59(0.95) and 7.58(0.87), yielding p=0.97 (unpaired t-test). Weight is well correlated with TBCa/TBK (r = -0.57, p < 0.0001). Further, blacks were heavier than whites (69.0 vs. 64.3 kg, p < 0.001). ANACOVA gives adjusted means for blacks and whites of 7.75 and 7.48 (p < 0.01), about a 4% difference. Thus, the clinical result is not nearly as impressive. In fact, if we rework the data as a multiple linear regression, R**2 = 0.343 (with race component just 0.019). In summary, our significant ANACOVA is due to the weight covariate being well correlated with TBCa/TBK, a large racial difference in the covariate means, and a relatively large sample size detecting a small clinical change.