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:
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 .
Comment