# How to find statistical significance?

I'm reading a book called soccernomics. There is data for Home/Away wins in case a penalty is awarded or not awarded in football (soccer) games. Data is as follows:

| Result    | Pen. Not Awarded  | Pen. awarded  |  Total    |
|---------- |-----------------  |-------------  |-------    |
| Home Win  | 557               | 142           | 719       |
| Away Win  | 336               | 80            | 416       |
| Tie       | 321               | 64            | 385       |
|-----------|-------------------|---------------|-----------|
| Total     | 1234              | 286           | 1520      |


The author is trying to argue that the observation that "penalty favors the home team", i.e. a team playing at home is more likely to win with an awarded penalty as compared to a team playing away from home; is not statistically significant. How does one conclude that using the given data?

Most likely whoever it was did a chi-squared test of homogeneity of proportions on the 3x2 table.

There are other possibilities (G test, Fisher exact test, etc etc), or maybe they did the chisquare on the 2x2 subtable ignoring ties, etc.

The result of the chisq test I mentioned first is not significant (that is, the proportions are consistent with the underlying proportions with and without penalties being the same for each category):

> chisq.test(m)

Pearson's Chi-squared test

data:  m
X-squared = 2.2022, df = 2, p-value = 0.3325

• Could you please point me to somewhere I can read about which test to use in which situation? Apr 28, 2017 at 6:05
• Across which collection of situations? There's literally thousands of hypothesis tests (and unfortunately many of the guides to what tests to use seem to think the form of the data determines what test you do - as if the particular hypotheses you wanted to look at and your assumptions had nothing to do with it. They also tend to completely ignore large classes of possible tests for no readily apparent reason. Often they're worse than nothing. Nevertheless Wikipedia has a list of commonly used ones here.) Apr 28, 2017 at 6:30
• Wikipedia's list is probably not substantially worse than most of the other such tables. There's another here. Some of the information is literally wrong; some of what's not literally wrong is still poor advice. (As an example of what's wrong at the second link, the last column heading implies those nonparametric tests compare medians. None of them are actually comparing medians in general.) Apr 28, 2017 at 6:34
• Here's a third one. It could be worse, but there's still plenty I'm not happy about with it. Apr 28, 2017 at 6:54