Goodness of Fit

Benford’s law states that in listings, tables of statistics, etc., the digit 1 tends to occur with probability , much greater than the expected 11.1% (i.e., one digit out of 9). More specifically, the empirical distribution of probabilities is

Using the suggested categories, we have the following table:

We want to test the following:

So we have now the table with the expected values (under the null hypothesis):

We compute now the Chi-Square statistics:

The critical value for 2 df and is 5.991. The test statistics is way beyond the critical value, so we reject the null hypothesis. This supports the claim the check amounts are the result of fraud.