Testing �_d

We routinely test to see whether the sample mean difference is significantly different from 0 ("no expected difference"). A formal 4 step procedure is recommened. Steps are:

(A) Statement of the null and alternative

The two sided null and alternative are H₀: � = 0 vs. H₁: � not = 0

(B) Set alpha level

Alpha = something (usually .05 by convention)

(C) Calculate test statistics

Paired t-statistic = (sample mean dif) / (sem), df = n - 1, the two-sided p value corresponds to the tail probabilities beyond the absolute value of the t-statistic on Students t with df degrees of freedom

These statistics are calculated automatically when Epi Info one-variable MEANS command is properly directed toward the DELTA variable

There are also several Web calculators that can be used to "crunch" the numbers

(D) State conclusion

The null hypothesis is rejected if p < alpha. Otherwise, the null hypothesis is retained for want of evidence.