Multiple imputations and ttest

[Alexis Morau]

I am working on multiply imputed dataset abut household wealth portfolios. I would like to check if the difference between participation rates of two groups in differenet assets types is significant. How could I apply the t test for equality of means to multiply impute data?

I am using Stata 15.

[daniel klein]

A ttest is just a linear model regressing outcome on the group indicator variable, that is:

ttest depvar , by(groupvar)

is the same as

regress depvar i.groupvar

regress can be combined with mi.

Best
Daniel

[Alexis Morau]

Thank you for your answer Daniel. Unfortunately I am not sure if I understand you correctly.

I want to check if means of variable (for example Has Financial Assets) in two countries (groups) are equal. If I run your command I get output table with name of one country with insinificant coefficient and constant. Am I right that this means that difference between means of this variable in country A and B are not significant?

[Carlo Lazzaro]

Alexis:
yes, you are.
Look at the following toy-example; both -ttest- and -regress- provide the same result (ie, there's no evidence of a statistically significant difference for the price of foreign and domestic cars):

. sysuse auto.dta
(1978 Automobile Data)

. ttest price, by(foreign) unequal

Two-sample t test with unequal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
Domestic |      52    6072.423    429.4911    3097.104    5210.184    6934.662
 Foreign |      22    6384.682    558.9942    2621.915     5222.19    7547.174
---------+--------------------------------------------------------------------
combined |      74    6165.257    342.8719    2949.496    5481.914      6848.6
---------+--------------------------------------------------------------------
    diff |           -312.2587    704.9376               -1730.856    1106.339
------------------------------------------------------------------------------
    diff = mean(Domestic) - mean(Foreign)                         t =  -0.4430
Ho: diff = 0                     Satterthwaite's degrees of freedom =  46.4471

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.3299         Pr(|T| > |t|) = 0.6599          Pr(T > t) = 0.6701

. regress price i.foreign

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(1, 72)        =      0.17
       Model |  1507382.66         1  1507382.66   Prob > F        =    0.6802
    Residual |   633558013        72  8799416.85   R-squared       =    0.0024
-------------+----------------------------------   Adj R-squared   =   -0.0115
       Total |   635065396        73  8699525.97   Root MSE        =    2966.4

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     foreign |
    Foreign  |   312.2587   754.4488     0.41   0.680    -1191.708    1816.225
       _cons |   6072.423    411.363    14.76   0.000     5252.386     6892.46
------------------------------------------------------------------------------

.

[daniel klein]

To add to Carlo's example: the results are exactly the same when you omit the unequal option from thettest command; the results are very similar when you keep the unequal option in the ttest command and add vce(robust) to the regress command.

Best
Daniel