# Quantify influence in ANOVA

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