1.CS2 CMP-CH10-page 37 "This is because any problems resulting from undergraduation will usually already have been picked up by either the smoothness test (if adhering too closely to the crude rates has led to an erratic pattern of rates) or by the chi-squared test (if adhering too closely to the crude rates over one part of the age range has led to large discrepancies in another part)." the smoothness test How the smoothness test led to an erratic pattern of rates? All we can get from this test is the difference in crude rate. Why is there "an erratic pattern of rates"? chi-squared test Why it led to large discrepancies in another part? The observations are all independent of each other, aren't they?
I want to chech that if low value of chi-square test value = undergraduated? I can understand that the smoothness test can test over- or undergraduated, but why only undergraduation be solved by this test?
Hello Smoothness test Imagine the extreme where we just take the crude rates as the graduated rates (this is undergraduated). Say that the crude rates are not particularly smooth (as we wouldn't really expect them to be). For example, consider the graph on page 7 of Chapter 10. If we take the crude rates as the graduated rates, then we can visualise the graduation by simply drawing lines from point to point. This does not vary smoothly with age but rather jumps around from age to age, up and down by both large and small amounts. This is not what we would expect the true underlying rates to look like. This issue should appear when we consider the third differences in the smoothness test. Hence, this test can identify issues with undergraduation. Chi-squared test The chi-squared test is a test for overall bias in the graduated rates (ie it looks at the differences between the observed and expected rates). Too large of a difference may be an indication of overgraduation (ie rates that are too 'smoothed' and don't adhere well to the actual data). So, it doesn't really test for undergraduation. The point being made on page 37 is about the situation where, depending on how the graduated as been performed, it's possible that part of the graduation may appear to be undergraduated (where it adheres to the data really well) and another part may be overgraduated (where it doesn't adhere to the data well). If the test fails, this will be because of the overgraduated section (ie where there is a large discrepancy between the crude and graduated rates). Hope this helps! Andy
