Standard Error for sample Variance S 2 is: S 2 /[(n-1)/2] ½

Standard Error for the Multiplication of Two Independent Means 1 ´ 2 is: { 1 S 2 2 /n 2 + 2 S 1 2 /n 1 } ½ .

Standard Error for Two Dependent Means 1 ± 2 is: {S 1 2 /n 1 + S 2 2 /n 2 + 2 r ´ [(S 1 2 /n 1 )(S 2 2 /n 2 )] ½ } ½ .

Standard Error for the Proportion P is: [P(1-P)/n] ½

Standard Error for P 1 ± P 2 , Two Dependent Proportions is: {[P 1 + P 2 - (P 1 -P 2 ) 2 ] / n} ½ .

Standard Error of the Proportion (P) from a finite population is: [P(1-P)(N -n)/(nN)] ½ . The last two formulas for finite population are frequently used when we wish to compare a sub-sample of size n with a larger sample of size N, which contains the sub-sample. In such a comparison, it would be wrong to treat the two samples"as if" there were two independent samples. For example, in comparing the two means one may use the t-statistic but with the standard error: S N [(N -n)/(nN)] ½
as its denominator. Similar treatment is needed for proportions.