# Ranking candidates based on their accuracy and efficiency

I have a dataset of 1000 candidates whom I have assessed for a skill. I have calculated accuracy of correct answers of each user as well as efficiency of each user based on number of attempts taken by a user to solve a problem. Both these metrics are in percentage form. Now I want to give rank to each user based on their accuracy and efficiency. Both the metrics are equally important.

What statistical methods are best suited to do this ranking?

Did you have a look at this? If you'd like to be conservative in your ranks for either of the metrics then computing the conservative skill estimate for that metric for each candidate of say about $\mu-3\sigma$ and then sorting by that should be fine.

One method that seems apparent immediately to me would be the product of those two columns.

Suppose your data looked like this:

accuracy    efficiency
0.85        0.87
0.75        0.95
0.8         0.9
0.6         0.5
0.6         0.7
0.7         0.8
0.95        0.9
0.98        0.6
0.45        0.6
0.85        0.79


If both columns are equally weighted, why not try accuracy * efficiency for your metric? This would sort of give you the "best" candidate by this particular metric.

You'd end up with this column:

product
0.7395
0.7125
0.72
0.3
0.42
0.56
0.855
0.588
0.27
0.6715


Then you can use Excel's RANK function on product to order your candidates. Or just sort descendingly on product.

Maybe there are more sophisticated ways, but this is a quick win in my book.