R-如何使用两种不同的调查设计进行两样本 t 检验

Question

I want to perform a two-sample (welch's) t-test on the equality of two means, one of which is obtained using simple random sampling ( srsmean ), and the other which is calculated using survey weighting with the survey package ( mean_weighted ). I also conduct a t-test between mean_weighted and the mean obtained when weighting and stratification are both implemented in the survey design ( mean_strat ).

I know there is a svyttest() function, however, as far as I can tell, this function only tests the means of two samples within one survey design, not means obtained with different survey designs.

I also tried using rnorm to create fictional samples eg c(rnorm(9710, mean = 156958.8, sd = 364368)) , but the problem with this approach is that in complex sampling methods like stratification, the effective n is usually smaller than the nominal n, and so I am unsure what to put as n. Additionally, this method feels a bit contrived, as I would be fitting the data to a particular type of distribution.

Finally, I tried writing out the equation for a t-statistic myself, however, in calculating the "standard error of the difference of means" involving a complex survey design, I also run into problems related to the "effective sample size."

Is there another approach that would work for both the t-test between srsmean, mean_weighted AND the t-test between mean_weighted, mean_strat ?

library(survey)

wel <- c(68008.19, 128504.61,  21347.69,
         33272.95,  61828.96,  32764.44,
         92545.62,  58431.89,  95596.82,
         117734.27)
rmul <- c(16, 16, 16, 16, 16, 16, 16,
          20, 20, 20)
strat <- c(101, 101, 101, 101, 101, 102, 102, 102, 102, 102)


survey.data <- data.frame(wel, rmul, strat)

srsmean <- mean(survey.data$wel)

survey_weighted <- svydesign(data = survey.data,
                             ids = ~wel, 
                             weights = ~rmul, 
                             nest = TRUE)

mean_weighted <- svymean(~wel, survey_weighted)

survey_strat <- survey_strat <- svydesign(data = surveydata, 
                                          ids= ~wel, 
                                          weights = ~rmul, 
                                          strata = ~strat, 
                                          nest = TRUE)
mean_strat <- svymean(~wel, survey_strat)

Answer 1

i'm confused about the purpose of a t-test between your mean_weighted and mean_strat since the difference between those coefficients will always be zero? i might compare the simple random sample against the complex design like this?

library(survey)

wel <- c(68008.19, 128504.61,  21347.69,
         33272.95,  61828.96,  32764.44,
         92545.62,  58431.89,  95596.82,
         117734.27)
rmul <- c(16, 16, 16, 16, 16, 16, 16,
          20, 20, 20)
strat <- c(101, 101, 101, 101, 101, 102, 102, 102, 102, 102)

survey.data <- data.frame(wel, rmul, strat)

survey_unweighted <- svydesign(data = survey.data,
                             ids = ~1)

mean_unweighted <- svymean(~wel, survey_unweighted)

survey_strat <- survey_strat <- svydesign(data = survey.data, 
                                          ids= ~wel, 
                                          weights = ~rmul, 
                                          strata = ~strat, 
                                          nest = TRUE)
mean_strat <- svymean(~wel, survey_strat)


coef_one <- coef( mean_unweighted )
coef_two <- coef( mean_strat )
se_one <- SE( mean_unweighted )
se_two <- SE( mean_strat )

t_statistic <- abs( coef_one - coef_two ) / sqrt ( se_one ^2 + se_two ^2 )
p_value <- ( 1 - pnorm( abs( coef_one - coef_two ) / sqrt( se_one ^2 + se_two ^2 ) ) ) * 2
sig_diff <- ifelse( 1 - pnorm( abs( coef_one - coef_two ) / sqrt( se_one ^2 + se_two ^2 ) ) < 0.025 , "*" , "" )