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From |
nick bungy <nickbungystata@hotmail.co.uk> |

To |
"statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu> |

Subject |
st: Standard error of the weighted mean |

Date |
Fri, 3 May 2013 18:03:57 +0100 |

Dear Statalist, I am having issue finding the correct way to calculate the standard error of a probability weighted mean. I can successfully calculate the sample standard deviation, as taken from: http://www.stata.com/support/faqs/statistics/weights-and-summary-statistics/ s2 = {n/[W(n - 1)]} sum wi (xi - xbar)2 The Stata article suggests that the standard error of the weighted mean is then simply: V_srs = s2/n Where V_srs is an ‘estimate of the variance of muhat [mean] assuming a simple random sample of the same number of observations’ However, when I calculate V_srs and compare it to the linearized standard error as taken from the svy: commands, the linearized standard error is significantly larger. Since my calculations and Stata agree on s^2, presumably I must be calculating V_srs (variance of the mean) incorrectly. Can anyone shed some light on where I am going wrong? Here's an example of the disparity between my mata code and the official svy command. sysuse auto gen pweight = trunk^2 + 1 mata st_view(y=. ,. , "mpg") st_view(weight =. ,., "pweight") Weighted_mean = colsum(y:*weight) / colsum(weight) Weighted_var = rows(y)/(colsum(weight)*(rows(y)-1))*colsum(weight:*(y :- Weighted_mean):^2) Weighted_sd = sqrt(Weighted_var) SD_Mean = sqrt(Weighted_var / rows(y)) Weighted_sd SD_Mean end svyset [pweight = pweight] svy: mean mpg estat sd Thanks * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Standard error of the weighted mean***From:*Steve Samuels <sjsamuels@gmail.com>

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