Stats t-test for soccer data I am new to stats and had the following question
I am studying if the total number of fouls in a soccer game increases/decreases if a particular team is winning at half time. This is what I did (one sample t-test). 


*

*Took 5 years of data and found its mean and std. dev of fouls in a game (includes matches where the result was a draw or either team was wining at HT i.e. all possible combination of results)

*Now, I took 100 random results (these are 100 from the above data set itself) but here I took only results where either team was winning.
I found the std.dev, mean and t-value.


I have few questions here:
1. I am assuming point two above as the treated population. Here the treatment is; if a team is losing there is a psychological effect on the person/team which probably increases the chances of committing a foul. Does this make sense?
2. The random points(100) that I selected above are points from the same 5 years data. Is that OK? or the data points should be from a different season/matches which are not included in the 5 year data sample I have.
Any help is greatly appreciated!
Thanks,
Ace
 A: 
I am studying if the total number of fouls in a soccer game increases/decreases if a particular team is winning at half time. This is what I did (one sample t-test).

"number of fouls" is count data. It's not suitable for a one-sample t-test. The distribution will tend to have variance that changes with mean and also somewhat skew. The number of fouls per match may be high enough that the discreteness doesn't matter much, but you may want to worry about different variances.

Now, I took 100 random results

Why only 100?

I have few questions here: 1. I am assuming point two above as the treated population. Here the treatment is; if a team is losing there is a psychological effect on the person/team which probably increases the chances of committing a foul. Does this make sense? 

You should probably be comparing losing vs winning (or perhaps losing vs not-losing; or winning vs not-winning); you should avoid having the same matches in both. 
You presumably want to make inference about a population other than just the data you have, so don't treat the data you have as a population.
A: Firstly, I want to second what Glen_B said.
In terms of the causal pathway you're suggesting, don't you need to focus on second half fouls? Fouls in the first half can't be due to a psychological reaction to the half time score.
Preferably those second half fouls should be compared to an appropriate baseline that takes some account of team/opponent/referee; even comparison vs first half fouls would be better than nothing.
Remember that "losing at half time" is basically a proxy for "being the weaker team". If you do find teams losing at half time tend to foul more, to some extent that's telling you that weaker teams foul more (not unexpected if that's part of a game plan to stop more skillful players) rather than what you're interested in. So you do need to do something that controls for team (and opposition) quality.
And it will be essentially impossible to identify a specifically psychological effect. You have no way of telling if the effect is purely tactical for instance - also plausible, since fouls are often the product of defensive desperation. A team that is behind in a match is likely under more defensive pressure anyway, and if they are attempting to get a goal back then it's reasonable to think defenders may be more likely to be left without adequate cover and so forced into committing a foul. I'm not saying that is the correct interpretation of any pattern in fouling, just that you can't jump to the conclusion of it being psychological unless you have some way to distinguish this from other effects with the data you have available. Underlying issues of causation are more subtle than you're giving credit for.
