Should I be using "pooled variance" in this situation?

Question

Two variables were known to me: dark sample and light sample

To see if measured distance of sample components affected the shade of samples, I measured component distance of three dark samples and three light samples.

• I measured each sample three times - for repeatability -
• took the mean of the measurements for each sample.
• Then I took the Std Dev of the 6 means
• and then took the pooled variance of the 6 samples.

soooo.....

light#1 - 4.56mm, 4.57mm, 4.56mm = mean 4.56  
light#2 - 4.47mm, 4.45mm, 4.43mm = mean 4.45    
light#3 - 4.37mm, 4.36mm, 4.37mm = mean 4.37   
dark#1  - 4.47mm, 4.45mm, 4.42mm = mean 4.45   
dark#2  - 4.40mm, 4.41mm, 4.42mm = mean 4.41   
dark#3  - 4.41mm, 4.44mm, 4.41mm = mean 4.42

• Then I took Std Dev of Light means = 0.04 and Std Dev of Dark means = 0.02
• Then I took the pooled variance of the samples:

$$(3-1)(0.04) + (3-1)(0.02) / (3-1) + (3-1) = 0.03$$

Is that the correct use of pooled variance?

Answer 1

I'm assuming the multiple measures are just that, efforts to get the best measure of a sample, but they are not in themselves independent samples

Based on your claim, you're pooling standard deviations, not variances. So, you have to start with the variance. Once you do that, what you have is correct for a pooling if the values you entered are correct and you do the adds before the divide. If you look carefully at the equations, and understand the one for variance, there's an even simpler pooling equation when number of samples in each group are equal.

(var(light) + var(dark)) / 2

But I can't figure where you're getting those SD's from. They don't arise from the 3 samples in each group.