Mean difference of two normally distributed populations

Paired comparisons test
In a paired-comparisons test, the two populations have some degree of correlation or co-movement, and the calculation of test statistic takes account of this correlation.

Use t-test based on the variable being the difference between pairs of sample values. {Look up df=n-1, p=significance}.

H0=Ud-Udo

Sample mean difference, denoted by d:

d = (1/n)(d1 + d2 + d3 …. + dn)

where:
n is the number of paired observations
di is the difference between ith observation in the sample.

Sample variance = (sum of all deviations from d )²/(n – 1)

Standard deviation (sd) = (Sample variance)^1/2 = [(sum of all deviations from d )²/(n – 1)]^1/2
Standard error = sd/(n)^1/2.