Standard Deviations and Standard Errors

Standard Deviations and Standard Errors Standard deviation (computational formula) s=  (x − x) 2 n −1 Interpreting s: 1. Sample standard deviation is roughly how far the sample observations are from the sample mean on average. 2. Sample standard deviation is roughly the average distance between observations and the sample mean. Standard deviation of a sample proportion p(1 − p) n  pˆ = SD( pˆ ) = Interpretation: 1. This standard deviation is roughly how far sample proportion values would be from the true proportion on average for random samples of the same size (i.e. n must be fixed). 2. On average, sample proportion values would be roughly this standard deviation away from the true proportion for random samples of same size. Standard deviation of a sample mean  x = SD( x ) =  n Interpretation: 1. This standard deviation is roughly how far sample mean values would be from the true mean on average for random samples of the same size (i.e. n must be fixed). 2. On average, sample mean values would be roughly this standard deviation away from the true mean for random samples of the same size. Note: Standard error is ESTIMATED standard deviation. Standard error of a sample proportion pˆ (1 − pˆ ) n SE ( pˆ ) = Interpretation: This is the estimated approximate average distance between sample proportion values and the true proportion for random samples of the same size. SD( pˆ ) 0 = Null standard deviation (error) for a sample proportion p0 (1 − p0 ) n This is the estimated approximate average distance between sample proportion values and the true proportion for random samples of the same size assuming the true proportion is p 0 . Standard error of a sample mean SE ( x ) = s n This is the estimated approximate average distance between sample mean values and the true mean value for random samples of the same size. Try to interpret yourself (as we get to them): Standard error of a sample mean difference Standard error of the difference in two sample means Standard error of a difference in two sample proportions