1997 National Household Survey on Drug Abuse
Statistical Significance of Differences
To compare the prevalence of drug use for 1996
versus 1997, one can test the hypothesis of no difference in prevalence
rates using the standard difference in proportions test, expressed as
p1 = 1996 estimated proportion,
var(p1) = variance estimate for p1,
p2 = 1997 estimated proportion,
var(p2) = variance estimate for p2, and
cov(p1,p2) = covariance between p1 and p2.
Under the null hypothesis of no difference in prevalence rates, Z is asymptotically distributed as a normal random variable; calculated values of Z can, therefore, be referred to the unit normal distribution to determine the corresponding probability level (i.e., p value). Because the 1996 and 1997 NHSDAs used a high percentage of overlapping sample segments (see Appendix D), the covariance term in the formula for Z is greater than zero in comparisons of the 1996 and 1997 surveys.
For comparing prevalence estimates within the same survey, the same Z statistic quoted above can be used. The covariance term in the formula for Z is again greater than zero because of the small positive covariance expected between any two nonindependent prevalence estimates.
This page was last updated on December 30, 2008.