Adding variables. There is a difference between assessing the statistical significance of a variable acting alone and a variable being added to a model.

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Presentation transcript:

Adding variables. There is a difference between assessing the statistical significance of a variable acting alone and a variable being added to a model.

Summary Test 1 by itself is statistically significant. t=2.97, P-value=0.0074 Test 2 by itself is not statistically significant. t=2.05, P-value=0.0530

Summary Test 1 adds significantly to the model that already contains Test 2. t=2.52, P-value=0.0205 Test 2 does not add significantly to the model that already contains Test 1. t=1.51, P-value=0.1469

Adding another variable Model with Test 1, Test 2, and Test 3. Can think about this as adding Test 3 to the model that already has Test 1 and Test 2 in it.

Change in R2 Model with Test 1, Test 2, and Test 3 – R2=0.526 Model with Test 1 and Test 2 – R2=0.367 Difference=0.526–0.367=0.159

Statistical Significance Is the change in R2 statistically significant? Parameter Estimate for Test 3. t=–2.52, P-value=0.0209 Effect Test for Test 3. F=6.343, P-value=0.0209

Statistical Significance Because the P-value (0.0209) is small (< 0.05) we would reject the null hypothesis that the slope parameter is zero. Test 3 adds significantly to the model with Test 1 and Test 2.

Other Tests Does Test 1 add significantly to the model with Test 2 and Test 3? t=3.52, P-value=0.0023 F=12.424, P-value=0.0023

Statistical Significance Because the P-value (0.0023) is so small (< 0.05) we would reject the null hypothesis that the slope parameter is zero. Test 1 adds significantly to the model with Test 2 and Test 3.

Other Tests Does Test 2 add significantly to the model with Test 1 and Test 3? t=1.36, P-value=0.1909 F=1.840, P-value=0.1909

Statistical Significance Because the P-value (0.1909) is not small (> 0.05) we would fail to reject the null hypothesis that the slope parameter is zero. Test 2 does not add significantly to the model with Test 1 and Test 3.

Unanswered Questions Is Test 3, by itself, statistically significant? Does Test 3 add significantly to the model with Test 1? Does Test 3 add significantly to the model with Test 2?

Test 1, Test 2 and Test 3 Source df Sum of Squares Model 3 67628.99 Error 19 61018.75 C. Total 22 128647.74

Test 1 and Test 2 Source df Sum of Squares Model 2 47259.34 Error 20 81388.40 C. Total 22 128647.74

Test 1 and Test 3 Source df Sum of Squares Model 2 61721.24 Error 20 66926.50 C. Total 22 128647.74

Test 2 and Test 3 Source df Sum of Squares Model 2 27729.65 Error 20 100918.09 C. Total 22 128647.74