- The gap test is used to determine the significance of the interval
between recurrence of the same digit.
- A gap of length
*x*occurs between the recurrence of some digit. - See the example on page 313 where the digit 3 is underlined. There
are a total of eighteen 3's in the list. Thus only 17 gaps can occur.
- The probability of a particular gap length can be determined by
a Bernoulli trail.

If we are only concerned with digits between 0 and 9, then

- The theoretical frequency distribution for randomly ordered digits
is given by

- Steps involved in the test.
**Step 1.**- Specify the cdf for the theoretical frequency
distribution given by Equation (8.14) based on the selected class
interval width (See Table 8.6 for an example).
**Step 2.**- Arrange the observed sample of gaps in a cumulative
distribution with these same classes.
**Step 3.**- Find
*D*, the maximum deviation between*F(x)*and as in Equation 8.3 (on page 299). **Step 4.**- Determine the critical value, , from Table
A.8 for the specified value of and the sample size .
**Step 5.**- If the calculated value of
*D*is greater than the tabulated value of , the null hypothesis of independence is rejected.

- See the Example 8.13 on page 314