Globalisation and Efficiency in the Fixed-odds Soccer Betting ... - Istituti

andom process). Estimating the regression equation once only would therefore be misleading
because of the unreliability of the standard errors.
Accordingly, we estimate each equation twenty times using twenty different
randomisations. The statistical significance of the coefficients can then be examined using a
procedure outlined in Snedecor and Cochran (1967). We count the number of cases in the
twenty trials where a particular coefficient is significant at the 5% level. A normal
approximation can be used to test the null hypothesis that the “true” proportion of cases where
the coefficient is not equal to zero is 5%. If the null is true, the observed proportion of
rejections, R1 is distributed approximately normally with mean r and standard deviation
s = (r (1-r)/n) ½ , where n is the sample size, here 20. The normal deviate, with a correction for
continuity, is z = (|R – r| - (2n) -1 )/s. The critical value for this test statistic is 2.33 at a
conservative 1% significance level. If there are four significant (at 5%) coefficients out of
twenty in our trials, the value of z is 2.57 which exceeds our 1% critical value, so where there are
four or more significant coefficients amongst twenty trials, we conclude that the particular
coefficient is significantly different from zero (or one as appropriate).
6. Results
Table 1A reports our results for the whole sample in each of our four seasons. The values shown
are mean coefficient estimates across twenty trials. The figures in parentheses indicate in how
many trials the particular coefficient estimate was significantly different from the value specified
by the null (zero or one). Where this number is four or more, we can reject the null hypothesis.
19