Imagine experiment in which we show three cars: red, black and violet to responders and ask them which one is 'the coolest'. Question is: is their choice affected by their age?
Now we have two strategies:
- Multinomial logit with age as independent and choice of color as dependent variable.
- ANOVA (compare ages in red, black and violet groups) essentially linear model with choice of color as independent and age as dependent variable
I know that these two answer very different questions. And I know that first one is better choice. But suppose, I for some reason, used ANOVA and it showed significant differences among groups (assume that ANOVA assumptions were met).
Can I still conclude that age affects choice?
- I know that, technically, ANOVA showed me that distribution of ages is different in different groups
- I don't want to cut age into intervals and run chi-squared-like test
- I won't be using it for predictions, I just need yes/no answer if age affects choice