I do not see why this should be a
paired t-test. There is no connection between the 100 pairs. Paired would be if you have 100 shoes and each shoe is tested with a different laser...ok, that's not a good example ;):
shoe | laser 1 | laser 2 | Delta
1 34 nm 38 nm 4 nm
2 33 nm 29 nm -4 nm
But maybe I do not understand your description and it is a
paired setting. But I am afraid that you have to clearify it in this case.
Can you specify what difference in
nm (wavelength unit) is considered big enough? Using
R you could use:
polish.1 = c(25,24,36,24,32)
polish.2 = c(22,36,27,28,30)
BigDifference = 2
alternative = "two.sided",
paired = FALSE,
mu = BigDifference
Welch Two Sample t-test
data: polish.1 and polish.2
t = -0.7171, df = 7.951, p-value = 0.4938
alternative hypothesis: true difference in means is not equal to 2
95 percent confidence interval:
mean of x mean of y
Welch means that it is not assumed that the standard deviation of the two data sets is equal.
So the result in the example means that it is not likeley that the wavelength is different (
p-value is about 50 %).
Of course, we can go deeper in the subject of effect size and so on. But I want to wait what you and the others reply/comment.