How to combine 2 unpaired t tests that test the same effect I have am studying an effect that degrades device quality and performed an independent sample test on two batches that had different initial quality.  I would like to make the strongest statement possible about the size effect, but it's tough because of my small unequal sample sizes and significant sample standard deviations.  Since the effect size and sample stds are similar in both tests and it is reasonable that the effect would scale with the starting quality, there should be a way to combine them to get a tighter confidence interval for the size of the effect.  How is this done?

My data are (lower loss is better):
Test 1 (High initial quality devices):
Untreated:  Loss = [7.3e-07, 6.1e-07, 1.0e-06, 7.1e-07, 7.4e-07,  8.6e-07,9.0e-07]
Treated:    Loss = [8.0e-07, 8.1e-07, 1.0e-06, 1.6e-06]
Test 2 (Low initial quality devices):
Untreated:  Loss = [1.0e-06, 1.0e-06, 1.1e-06, 1.6e-06, 1.8e-06, 1.0e-06, 1.4e-06, 9.9e-07]
Treated:    Loss = [1.0e-06, 1.5e-06, 1.4e-06, 2.2e-06]

Thanks.
I posted a follow-up question about P-value interpretation and defending the statistical significance of this result here: How to ascribe and defend statistical significance in linear regression. P-value interpretation and alternatives
I posted another follow-up question whether to include an interaction term in this regression here: 
When to include or reject interaction term in two variable linear regression
 A: I'd combine the two sets of data into a regression (in effect, conduct a two-way main effects ANOVA).
This will combine the two in the way you seem to be suggesting.
The coefficient of the treatment effect in the regression will be an estimate of the common effect.
e.g. in R
deg=read.table(stdin(),header=TRUE) # read in data
Loss      TreatStatus  Quality
7.3e-07   Untreated    High
6.1e-07   Untreated    High
1.0e-06   Untreated    High
7.1e-07   Untreated    High
7.4e-07   Untreated    High
8.6e-07   Untreated    High
9.0e-07   Untreated    High
8.0e-07   Treated      High
8.1e-07   Treated      High
1.0e-06   Treated      High
1.6e-06   Treated      High
1.0e-06   Untreated    Low
1.0e-06   Untreated    Low
1.1e-06   Untreated    Low
1.6e-06   Untreated    Low
1.8e-06   Untreated    Low
1.0e-06   Untreated    Low
1.4e-06   Untreated    Low
9.9e-07   Untreated    Low
1.0e-06   Treated      Low 
1.5e-06   Treated      Low 
1.4e-06   Treated      Low
2.2e-06   Treated      Low
                                      #

--
degfit=lm(Loss~TreatStatus+Quality,deg)  # fit model
summary(degfit)

Call:
lm(formula = Loss ~ TreatStatus + Quality, data = deg)

Coefficients:
                       Estimate Std. Error t value Pr(>|t|)    
(Intercept)           1.062e-06  1.300e-07   8.172 8.38e-08 
TreatStatusUntreated -2.745e-07  1.386e-07  -1.980  0.06158   
QualityLow            4.535e-07  1.322e-07   3.431  0.00264 

Residual standard error: 3.165e-07 on 20 degrees of freedom
Multiple R-squared:  0.4331,    Adjusted R-squared:  0.3764 
F-statistic:  7.64 on 2 and 20 DF,  p-value: 0.003427

There's little suggestion of problems in the diagnostics --

Looking at the first plot, I really don't think changing spread is an issue, but your mileage may vary. If it was a concern, my first instinct would be to think about the fact that the losses should be non-negative and I'd be thinking
about perhaps using a gamma GLM with the same sort of model (this would probably have been one of my first thoughts actually, if I have understood the description of the variables correctly), presumably with an identity link since you're interested in the shift in mean. I don't expect it would make much of a difference, though, to either the estimates or their standard errors.
(The plots seem to support that line of thinking; since there's mild skewness and the spread does seem to perhaps be related to the mean)
