Efficiency as a dependent variable

Question

I have a dataset, consisting of two independent variables each with two levels.

The independent variables are individuals (1 vs. 2) and light (day vs. night) The dependent variable is the efficiency to detect an object (in other words the proportion of objects detected in a known population of objects). I want to find out whether there is a difference between individuals and between amount of light.

I wonder which statistical test is should use for the analysis, is it possible to use a two-way ANOVA?

Answer 1

In short: Yes.

I find this table very useful in determining which statistical analysis to apply.

You have 1 dependent variable, 2 or more independent variables (independent groups), the nature of your depentant variable can probably be assumed to be normal, at least marginally, so the correct statistical analysis would indeed be factorial (or two-way) ANOVA.

The linked page also contains instructions on how to perform this test in STATA or SAS.

PS: Welcome to the site!

Answer 2

Regarding normality @mzuba may be correct but there are problems with this approach if the dependent variable has non-constant variance in the groups (which is the case for proportions where the variance depends on the mean).

What you could do though is to extend the two-way ANOVA to a two-way Analysis of Deviance for the appropriate generalized linear model. Since it reads as if you know the number of trials and the number of successes a binomial might be fine, else a beta or count data model should do the trick.