I have done the following measurements:
- Independent Variables IV1 and IV2 with a ordinal scale
- Dependent Variable 'DV' with an ordinal scale
- Tested 8 different values for IV1 and 6 different values for IV2 in a full factorial design with 5 repetition each and recorded the dependent variable. So in total 240 measurements were done.
Now an ANOVA test on these measurements show that with a very high probability (> 1 - 2e-16) both independent variables contribute to the variance of 'DV'. Thats what I expected, so everything OK until here.
> aov(DV~IV1+IV2, data=d) Terms: IV1 IV2 Residuals Sum of Squares 1721.6289 918.6018 198.5668 Deg. of Freedom 7 5 227 Residual standard error: 0.9352772 Estimated effects may be unbalanced > summary(aov(DV~IV1+IV2, data=d)) Df Sum Sq Mean Sq F value Pr(>F) IV1 7 1721.6 245.95 281.2 <2e-16 *** IV2 5 918.6 183.72 210.0 <2e-16 *** Residuals 227 198.6 0.87 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
I now want to quantify how much influence a change in IV1 and a change in IV2 has on the dependent variable DV. How can I do this?
I'm not sure whether I'm asking the right question at all.
A solution which came to my mind was fitting a linear model to
DV~IV1+IV2 (R syntax) an taking the coefficients as the influence. I'm not sure if this is the right way of looking at the data because I can't be sure that there is a linear dependency between DV and IV1, IV2.
> lm(DV~IV1+IV2, data=d) Coefficients: (Intercept) IV1 IV2 6.2580969 0.0002853 -0.0703225