${\chi}^2$

Fill table with difference of real and expected frequencies.

Deviations from expectation

$$\neg {\tt holmes}$$ holmes Total

sherlock 7 - 0.05 0 - 6.95 -

$$\neg {\tt sherlock}$$ 39 - 45.95 7023 - 7016.05 -

Total - - -

and there is a statistic called ${\chi}^2$ which is made from these differences.

$${\chi}^2 = \sum \frac{(f_o - f_e)^2}{f_e}$$

This will be big when we are not dealing with word confetti.

Contributions to ${\chi}^2$

$$\neg {\tt holmes}$$ holmes Total

$$\frac{(7 - 0.05)^2}{0.05} \frac{(0 - 6.95)^2}{6.95}$$ sherlock -

$$\neg {\tt sherlock} \frac{(39 - 45.95)^2}{45.95} \frac{(7023 - 7016.05)^2}{7016.05}$$ -

Total - - -

Summing these

which you can look up in the table and find to be unlikely by chance.