8.1 Variances of Two Proportions

Var(p̂1 - p̂2) = (p1q1)/n1 + (p2q2)/n2

the formula for the variance of the difference in proportions - pay close attention to the subscripts: all subscripts with a 1 refer to the first proportion, and all subscripts with a 2 refer to the second

SD(p̂1 - p̂2) = √( (p1q1)/n1 + (p2q2)/n2 )

the formula for the standard deviation of the difference in proportions

SE(p̂1 - p̂2) = √( (p1q1)/n1 + (p2q2)/n2 )

the formula for the standard error of the difference in proportions

the pythagorean theorem of statistics

a theorem that states that when adding or subtracting two random variables, the resulting standard deviation is equal to the square root of the sum of the individual variances if the random variables are independent

Var(X ± Y) = Var(X) + Var(Y)

the mathematical formula for the addition rule for variances of random variables

SD(p̂) = √(pq/n)

the formula for the standard deviation of a sample proportion

SD(X ± Y) = √Var(X) + Var(Y)

the mathematical formula for the pythagorean theorem of statistics

addition rule for variances of random variables

a rule that states that when adding or subtracting two random variables together, the resulting variance is always the sum of the individual variances if the random variables are independent