In R how to find the standard error of the mean

Question

Is there any command to find the standard error of the mean in R

User · Answer

y  lt - mean x  na rm TRUE    sd y  for standard deviation var y  for variance   Both derivations use n-1 in the denominator so they are based on sample data

User · Answer

As I m going back to this question every now and then and because this question is old  I m posting a benchmark for the most voted answers   Note  that for  Ian s and  John s answers I created another version  Instead of using length x   I used sum  is na x    to avoid NAs   I used a vector of 10 6  with 1 000 repetitions    library microbenchmark   set seed 123  myVec  lt - rnorm 10 6   IanStd  lt - function x  sd x  sqrt length x    JohnSe  lt - function x  sqrt var x  length x    IanStdisNA  lt - function x  sd x  sqrt sum  is na x     JohnSeisNA  lt - function x  sqrt var x  sum  is na x     AranStderr  lt - function x  na rm FALSE      if  na rm  x  lt - na omit x    sqrt var x  length x      mbm  lt - microbenchmark     plotrix     plotrix  std error myVec       IanStd     IanStd myVec       JohnSe     JohnSe myVec       IanStdisNA     IanStdisNA myVec       JohnSeisNA     JohnSeisNA myVec       AranStderr     AranStderr myVec       times   1000   mbm   Results    Unit  milliseconds        expr     min       lq      mean   median       uq      max neval cld     plotrix 10 3033 10 89360 13 869947 11 36050 15 89165 125 8733  1000   c      IanStd  4 3132  4 41730  4 618690  4 47425  4 63185   8 4388  1000 a        JohnSe  4 3324  4 41875  4 640725  4 48330  4 64935   9 4435  1000 a    IanStdisNA  8 4976  8 99980 11 278352  9 34315 12 62075 120 8937  1000  b   JohnSeisNA  8 5138  8 96600 11 127796  9 35725 12 63630 118 4796  1000  b   AranStderr  4 3324  4 41995  4 634949  4 47440  4 62620  14 3511  1000 a     library ggplot2  autoplot mbm

User · Answer

The standard error  SE  is just the standard deviation of the sampling distribution  The variance of the sampling distribution is the variance of the data divided by N and the SE is the square root of that  Going from that understanding one can see that it is more efficient to use variance in the SE calculation  The sd function in R already does one square root  code for sd is in R and revealed by just typing  sd    Therefore  the following is most efficient   se  lt - function x  sqrt var x  length x     in order to make the function only a bit more complex and handle all of the options that you could pass to var  you could make this modification   se  lt - function x       sqrt var x       length x     Using this syntax one can take advantage of things like how var deals with missing values  Anything that can be passed to var as a named argument can be used in this se call

User · Answer

more generally  for standard errors on any other parameter  you can use the boot package for bootstrap simulations  or write them on your own

User · Answer

Remembering that the mean can also by obtained using a linear model  regressing the variable against a single intercept  you can use also the lm x 1  function for this  Advantages are   You obtain immediately confidence intervals with confint   You can use tests for various hypothesis about the mean  using for example car  linear hypothesis   You can use more sophisticated estimates of the standard deviation  in case you have some heteroskedasticity  clustered-data  spatial-data etc  see package sandwich     generate data x  lt - rnorm 1000      estimate reg reg  lt - lm x 1  coef summary reg     quot Std  Error quot     gt   1  0 03237811     conpare with simple formula all equal sd x  sqrt length x              coef summary reg     quot Std  Error quot      gt   1  TRUE     extract confidence interval confint reg    gt                    2 5      97 5     gt   Intercept  -0 06457031 0 0625035  Created on 2020-10-06 by the reprex package  v0 3 0

User · Answer

You can use the function stat desc from pastec package   library pastec  stat desc x  BASIC  TRUE  NORMAL  TRUE    you can find more about it from here  https   www rdocumentation org packages pastecs versions 1 3 21 topics stat desc

User · Answer

A version of John s answer above that removes the pesky NA s   stderr  lt - function x  na rm FALSE      if  na rm  x  lt - na omit x    sqrt var x  length x

User · Answer

The standard error is just the standard deviation divided by the square root of the sample size  So you can easily make your own function    gt  std  lt - function x  sd x  sqrt length x    gt  std c 1 2 3 4    1  0 6454972

User · Answer

There s the plotrix package with has a built-in function for this  std error

User · Answer

The package sciplot has the built-in function se x

[r] In R, how to find the standard error of the mean?

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