In the second paragraph under "Rationale": "If the graduated rates are overgraduated, the standardised deviations will not swap from negative to positive very often and there will be fewer runs than expected." Is this sentence right? I would have thought that there will be frequent sways between + and - if there was overgraduation (ie the graduated curve is an extreme straight line running across the data points). Anyone care to elaborate this plus the point on "fewer runs"? Cheers.
If the ungraduated points roughly followed a curve, and you drew a straight line through them, you wouldn't get many switches from positive to negative - you've over-graduated, because the pattern is more complex than a straight line. An alternative curve graduation through these points might give you a switch nearly every point, so it would be making a pretty good stab (so graduating well), or not smoothing enough (so under-graduating): either way, not over-graduating. So if your straight line gives you lots of switches, that's probably a good piece of graduating: following the ungraduated points any more closely will give you a bumpy curve, and you would be under-graduating.
Thanks didster and alpha09 Any of you have any problems with the examples and solutions in this chapter? I have tons (please see my other postings) and they don't make sense to me.
I still cant get hold of this concept. If my rates are undergraduated, wouldn't I hardly have switches cause my graduated line is running through all possible points?
I agree with your line of questioning. The signs test is saying that if errors are normally distributed, then they are equally +ve and -ve. If you have a lot more positive than negative, or vice versa, then your estimation procedure may be biased. The runs test is a slightly more complex test of the same idea. It might be helpful to check the definitions of over- and under-graduation - I don't have the Core Reading definitions in front of me and there is room for misinterpretation here which will confuse things.
