Graduate Data Analysis: consistency of e.g. two measurements

[niteOwl]

How do we check consistency of measured data, e.g.

x1 = 1 ± 0.1
x2 = 1.4 ± 0.3

I can do this for two different samples to check for significance in terms of different means, but how to check internal consistency of a single set. How can we do this using:
a) standard normal probability table
b) a least squares method

 

[mathman]

http://www.ats.ucla.edu/stat/mult_pkg/whatstat/

The above may help. As you can see, there is no simple answer.

 

[gleem]

You really want to determine if the two values are from the same parent distribution. Basically you want to determine from the data if the hypothesis that they are from the same distribution is statistically significant. You can check to see if the difference is significant . This distribution will have an uncertainty of 0.32 = ( .3²+.1²)^1/2.. If the two measurements are from the same population then their difference should be on average zero. Since the uncertainty is 0.32 the difference of 0.4 is about 1.25 standard deviation from the difference (0.4) and the probability of the difference being larger is about 0.22. So this is saying that the hypothesis is not false and that there is about 1 in 5 chance that the two measurements will be at least this far apart.