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3E How Numbers Deceive

# 3E How Numbers Deceive - How Numbers Deceive...

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How Numbers Deceive Friday January 21, 2011 (continued) Better in Each Case, bur Worse Overall Example 1. A pharmaceutical company creates a new treatment for acne. To compare the new treatment to an old treatment, the company conducts a test. The old treatment is give to 90 patients and the new treatment is given to 110 patients. The results after four weeks of treatment are as follows: Mild Acne Among patients with mild acne, 10 received the old treatment and 90 received the new treatment. Of the 10 receiving the old treatment , 2 were cured for a 20% cure rate. Among the 90 receiving the new treatment, 30 were cured for a 33% cure rate. The new treatment had a higher cure rate for those with mild acne. Severe Acne Among patients with severe acne, 80 received the old treatment and 20 received the new treatment. Of the 80 receiving the old treatment, 40 were cured for a %50 cure rate. Of the 20 patients receiving the new treatment, 12 were cured for a 60% cure rate. The new treatment had a higher cure rate among patients with severe acne. Mild Acne Severe Acne Cured Not Cured Cured Not Cured Old Treatment 2 8 40 40 New Treatment 30 60 12 8 The new treatment had a higher cure rate for both patients with mild acne and for patients with sever acne. Lets look at the overall result. Old Treatment Of the 90 patients receiving the old treatment, 42 were cured, 2 of 10 with mild acne and 40 of 80 with severe acne. Therefore the overall cure rate for the old treatment was 42/90 = 46.7% New Treatment Of the 110 patients receiving the new treatment, 42 were cured (30 of 90 with mild acne and 12 of 20 with severe acne) The overall cure rate for the new treatment was 42/110 = 38.2% Example 1 is an illustration of Simpson’s Paradox . It is possible for a set of data to give different results in each of several groups than it does when the groups are taken together.

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3E How Numbers Deceive - How Numbers Deceive...

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