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

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?

• It looks like the multiple measures are just that, efforts to get the best measure of a sample, but they are not in themselves independent samples...correct? Only the light#2, dark#3, etc. are samples.
– John
Commented Aug 28, 2013 at 2:49
• You calculation of pooled variance doesn't make sense. Please check that you add variances not standard deviations, and check each term in your calculation carefully (e.g. what's "+(3-1)" for?) Commented Nov 26, 2013 at 5:43

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