Contingency table test

Question

I have dataset about my chess results and I would like to test, if I have advantage when I start with white pieces (or if result depends on starting color).

         W      L
White   525    474
Black   496    503 

I would like to use e.g. Chisq.test or Odds ratio test, but I don't know, if there is not problem with dependence of variable (because all observations are measured on me). What do you think? Thank you for answers.

Answer 1

Cool question. What you're concerned about is the assumption of independence that tests for contingency tables rely on (as well as a wide range of other statistical models).

You're right that the fact that all of the measures are on the same subject (you) makes them related, but in this case it isn't actually a problem because the scope of the problem is only that one subject --- you're trying to determine whether you have an advantage when you start with white vs. black. The whole universe you're considering is just chess games you play. Within that universe, the assumption that each game is an independent observation may be completely reasonable.

Here are some other factors that could actually cause a violation of the independence assumption in this scenario:

1. Your opponent. Are some of the games with one player and others with another?

2. Game circumstance. Perhaps some games are played at home on your computer and others are played in a busy park, or some are played casually and some are at a competitive tournament. Perhaps some games are played in the morning and others at night (and you might be more alert at one time vs. the other).

3. Time / expertise. Has your game been improving over the course of this data collection?

4. Lots of other possible factors --- use your imagination.

If anything like the above situations are active, that could be violating the assumption of independence in your data within the universe of your design, i.e. games you play. To the extent that these things are associated with the factors you're testing (color and game outcome), they will bias your results. For example, if you don't really have an advantage when you play with one color over another, but you are more likely to win under the competitive pressure of a tournament and you get assigned white more often than black at tournaments, that will make it look like you have an advantage when you play with white.