Hi all,

I'm currently doing a quick study into a material where grain size could potentially affect a desired property Y, but I'm uncertain about the statistical methodology and inference.

I have had 6 specimens under the microscope.
For each, I obtain an average grain size, a SE for grain size and a SE for the average.
The grain size for each of the six specimen is nicely normally distributed.

Now I want to use the average grain size (with appropriate standard error of the average) as explanatory variable in a regression. At this point my first questions arises:

Should I incorporate the known SE of the means in the regression analysis and how? They're not treated the same way as measurement errors, which cause attenuation.

After plotting the material property Y against the average grain size (so 6 data points), I observe 2 clusters. 3 data points for the perfect product and 3 data points for specimens taken out of production, because the material property did not meet standards.

Looking at this, it seems more intuitive to make clusters and compare the mean of property Y for both clusters. However, both dependent and independent variable are continuous.

Given the description above, I like the opinion of someone with a broader knowledge of the different statistical approaches.

Thank you in advance!