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I have 3 categorical variables (CVa, CVb, CVc) all 0 or 1. Two continuous variables (IV1, IV2) are confounding my observational study. The multiple regression

lm(DV ~ CVa + CVb + CVc + CVa:CVb + CVa:CVc + IV1 + IV2)

is showing great significance for CVa

              Estimate   Std. Error t value Pr(>|t|)
(Intercept)  -1.414684   1.498886  -0.944  0.35233
CVa1         -0.841076   0.256946  -3.273  0.00255 **
CVb1         -0.413594   0.168753  -2.451  0.01990 * 
CVc1         -0.328669   0.183652  -1.790  0.08298 . 
IV1          -0.011768   0.006519  -1.805  0.08049 . 
IV2           0.487658   0.211015   2.311  0.02743 * 
CVa1:CVb1     0.321766   0.238869   1.347  0.18743   
CVa1:CVc1     0.741290   0.259402   2.858  0.00744 **

I thought that ANCOVA (between factor CVa) must also show significance, but

summary(aov(DV ~ CVa + CVb + CVc + CVa:CVb + CVa:CVc + IV1 + IV2))

is not showing any significance for CVa

          Df Sum Sq Mean Sq F value  Pr(>F)   
CVa        1  0.368  0.3681   3.093 0.08817 . 
CVb        1  0.427  0.4275   3.593 0.06709 . 
CVc        1  0.015  0.0148   0.125 0.72629   
IV1        1  0.585  0.5849   4.916 0.03384 * 
IV2        1  0.693  0.6935   5.828 0.02166 * 
CVa:CVb    1  0.126  0.1262   1.061 0.31069   
CVa:CVc    1  0.972  0.9716   8.166 0.00744 **
Residuals 32  3.807  0.1190

Am I doing ANOVA instead of ANCOVA? If yes, how do I control for IV1, IV2 to get that F-value they usually report in papers?

Just in case, lsmeans(m2,pairwise ~ CVa * CVb) reports that main effect of CVa is significant when controlled for IV1, IV2

$`CVa:CVb pairwise differences`
               estimate        SE df  t.ratio p.value
0, 0 - 1, 0  0.47043119 0.1725208 32  2.72681 0.04807
gung - Reinstate Monica
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Daniil
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1 Answers1

4

summary(lm(...)) reports tests based on Type 3 SS
summary(aov(...)) reports based on Type 1 SS

T1 tests the variables in the order they are entered in the model, eg/
CVa
CVb|CVa
CVc|CVa,CVb
etc

T3 tests the variables effectively conditional on all other variables in the model, eg/
CVa|Cvb,CVc,etc
CVb|Cva,CVc,etc

This is why you are getting different test results. More information on partitioning sum of squares can be found in this answer, and how to get T3 out of aov() here

Affine
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