The formula for the Chi-Square test statistic is the following:
$\chi^2 = \sum_{i=1}^{n} \frac{(O_i - E_i)^2}{E_i}$
where O - is observed data, and E - is expected.
I'm curious why it depends on the absolute values? For example, if we change the units we're measuring we'll get a different statistics. Suppose we're performing a test on apple weights. One of the samples weights 165 gram, and we expect it to be 182 gram, then the part of the formula will be:
$\frac{(165 - 182)^2}{182} \sim 1.58791$
http://en.wikipedia.org/wiki/Pearson's_chi-squared_test
Now suppose we're living in a country where the precision is on the top. We use milligrams for everything and we get the same results in different units: 165000 milligrams and 182000, respectively. The statistic:
$\frac{(165000 - 182000)^2}{182000} \sim 1587.91$
So our conclusion will be different based on the units we used. Why? What am I missing and why the values are not normalized in the Chi-squared test?