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  • #16
    Sidra:
    I would stick with Satterthwaite’s approximation, as it is default when unequal variances are assumed.
    That said, the difference between the two options is pretty negligible, as you can see from the following toy-example:
    Code:
    use "C:\Program Files (x86)\Stata15\ado\base\a\auto.dta"
    *Results using Satterthwaite’s approximation*
    . 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
    
     *Results using Welch’s formula*
    . ttest price, by(foreign) unequal welch
    
    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               -1729.232    1104.714
    ------------------------------------------------------------------------------
        diff = mean(Domestic) - mean(Foreign)                         t =  -0.4430
    Ho: diff = 0                             Welch's degrees of freedom =  48.5288
    
        Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
     Pr(T < t) = 0.3299         Pr(|T| > |t|) = 0.6598          Pr(T > t) = 0.6701
    
    .
    Kind regards,
    Carlo
    (Stata 18.0 SE)

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    • #17
      In general, the two specifications should give similar results. When in doubt, you will generally do well using Stata's default settings.

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      • #18
        Thanks a lot Carlo and Phil.

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