T-Test to check if win/draw/loss results (home results) are independent from country/league where football games take place

Question

I need to verify if win/draw/loss results (home results) are independent from country/league where football games take place. I have the following data table:

League              win draw loss
Premier League      193 96  91
LaLiga              194 95  91
Bundesliga          125 86  95
Serie A             108 65  67

I need to assign alpha of 0.05 significance to verify hypothesis. Do I need to perform Shapiro tests for each vector (win/draw/loss), Kolmogorov-Smirnov test, or some embedded t.test in R?

Answer 1

This looks like a chi-squared test setup to me:

dd <- read.table(header = TRUE, text = "
League              win draw loss
Premier_League      193 96  91
LaLiga              194 95  91
Bundesliga          125 86  95
Serie_A             108 65  67
")


## apply test to data (not including league name):
c1 <- chisq.test(as.matrix(dd[, -1]))
print(c1)

    Pearson's Chi-squared test

data:  as.matrix(dd[, -1])
X-squared = 10.325, df = 6, p-value = 0.1116

(i.e., you can't reject the null hypothesis of equal win/draw/loss proportions across leagues at the $\alpha = 0.05$ level, since $p>0.05$)

To get a slightly better idea of what the test is doing: it's computing the expected number of counts (win/draw/loss) for each league under the assumption of independence, based on the marginal row and column totals:

c1$expected

         win     draw      loss
[1,] 180.3982 99.50995 100.09188
[2,] 180.3982 99.50995 100.09188
[3,] 145.2680 80.13170  80.60031
[4,] 113.9357 62.84839  63.21593

and then comparing these expected counts with the observed values.