Hi - here we go!
Note this is Q4.29 in my 2008 version!
Chi-square - It's basically just referring to the fact that the expected value of a variable that has a chi-squared distribution is equal to the number of degrees of freedom - refer back to your CT3 notes or any stats text book for this.
Std devs - It is using the binomial - but is using an approximation to the variance in the denominator - should be Eqp but assumes that p is very close to 1 so ignore it.
Table of values - expected values are the number of ages multiplied by the expected (Unit Normal proportions) - this is explained in the notes Ch 12 Section 7.2 Step 3 - and for the observed just count them up - eg (-2,-1) group - the 2nd, 4th and last values in the list of calculated std devs are in this range, ie 3 in all.
Cum devs - the observed value is simply the total actual deaths minus the total expected deaths = 10710 - 10734 = -24. Divide by the standard deviation of this (ie sqaure root of 10734 = 103.6), giving a standardised value (test statistic) of -24/103.6 = -0.23. This is within the acceptable 2-tailed range of -1.96 to +1.96. To be honest, I don't see how this differs from the way it is done in the course. As to why this in unit-normal - the approach I've just described is shown in Section 7.4 of Chap 12. Whenever you take a Normal variable (-24 here), take off its mean (zero) and divide by its standard deviation (103.6 here), then a standard normal variable is the result. Go back to CT3 again if you're not sure!
As for the serial correlations test - I have no idea why this isn't in, to be honest. If this was an exam question then it would be a perfectly viable test to choose. One thing in the exam though, if a question just says "test adequately", or similar, then you don't have to do every test. Eg cum devs and signs tests are broadly equivalent, and serial correlations and grouping of signs are broadly equivalent. (However, this argument doesn't apply to this Q because the solution includes both the signs and cum dev tests but only the grouping of signs test!) Comments from others very welcome here!
Last edited by a moderator: Feb 16, 2008