# Two games with collected statistics, how accurate is the data?

Suppose one wants to test how many players still play the day after receiving the game, and two days after receiving it.

And that the results would be:

Game 1:

• Total numbers of players = 120
• Players playing the next day = 21,7%
• Players playing two days after = 18,3%

Game 2:

• Total numbers of players = 62
• Players playing the next day = 16,1%
• Players playing two days after = 8,1%

Is it possible to calculate how accurate the result is, particularly in game 2. What is the +- percentage?

Could game 2 in fact be better than game 1?

• If players decide to play independently of each other, the answer is here. – Scortchi Jul 2 '13 at 9:50
• @Scortchi The question also appears to be asking (in the final sentence) about the standard error of the difference of two such percentages – Glen_b Jul 2 '13 at 10:21
• @Glen Good point: there's an answer for that here. – Scortchi Jul 2 '13 at 12:24

Here, under the same assumptions (in particular that the players in each group are not the same and decide to continue to play independently of each other), you could use a $\chi^2$ test for independence. If the test allows you to reject the null hypothesis of independence, it means that the difference you observe is unlikely to have come about by chance. Since game 1 is better than game 2 in the sample, you would then conclude that it is indeed better than game 2 and, conversely, that game 2 is unlikely to be in fact better than game 1.