Appendix C: Random Sample Selection Methodology

Two random samples were constructed for the 1998 National Youth Gang Survey. The first was a random sample of cities and towns with populations between 2,500 and 25,000 (small cities) and the second was of rural counties. These samples were also used for the 1996 and 1997 National Youth Gang Surveys.

In previous surveys, the response rate for cities with populations of more than 150,000 has been as high as 91.3 percent. The response rate for cities with populations between 25,000 and 150,000 was estimated by using a random sample of municipalities in that size range that were surveyed as part of the 1994 National Institute of Justice survey conducted by Curry, Ball, and Decker (1996a, b, c). The response rate of those cities to the 1995 National Youth Gang Survey was estimated to be 74.5 percent. All of the above computations for the proposed sample size assumed a response rate of 75 percent.

The estimated required sample size n was derived by using the formula



  • t is the abscissa of the normal curve that cuts off an area of at the tails.
  • N is the true population size.
  • P is the true proportion of the population with a specific characteristic.
  • Q is the true proportion of the population without a specific characteristic or (1 – P).
  • d is an acceptable error of size that can be incurred at probability .

This computing formula is derived from the formula provided by Cochran’s Sampling Techniques (1977) for sample size n required for producing an error of size d at a specific probability . Cochran uses t, the abscissa of the normal curve that cuts off an area of at the tails, to produce the formula

computing formula

All the terms in the computing formula are presented in a form equivalent to those in Cochran’s formula.

An error rate d was computed as 5 percent. The probability of an estimated error being greater than d used in the computations above is .05. All computations are based on an estimated true population of P = 0.5 and Q = 0.5 because this results in the largest and most conservative estimates for required samples for each stratum.


1998 Youth Gang Survey
OJJDP Summary
November 2000