```Date: Thu, 23 Sep 2004 12:38:32 +1000 Reply-To: paulandpen@optusnet.com.au Sender: "SPSSX(r) Discussion" From: Paul Dickson Subject: Re: Odd SPSS Results - Zero Coefficient Comments: To: Hector Maletta Content-Type: text/plain Hector You stated the following: "You reject the null hypothesis that the true value is zero whenever the confidence interval does not include the zero value". That is correct as far as I am concerned. But, I am wondering based on the thread of this discussion whether you meant in cases where the t-test (p-value) of the beta weight is significant, but your confidence intervals overlap with zero. If they are different (CI contains a zero value within the range) but (the P-value is significant) I myself would defer to the t-test, because while both CI and P-values assume probability sampling because they are inferential statistics (most data evaluated is not drawn from individuals with an equal likelihood of being selected) I would think in a case like this that CI's are less robust to violations of this assumption. Correct me if I am wrong here. Would this also not make the p-value a more robust criterion for decision making. What do others do if the confidence interval around the beta weight includes 0, but the p-value for the same beta-weight is significant. Is this possible, since the t-tests in spss are based on a similar decision criteria ideal to the CI where it is assumed that each coefficient = 0 (null hypothesis) when the t-test is run on the beta weight. Regards Paul > Hector Maletta wrote: > > Richard, > In fact I have reread the thread and think I misunderstood the question > and > consequently confused the matter more than clarifying it, and apologize > for > it. > The 95% confidence interval of an estimate of a regression coefficient > is > based on 1.96 times its standard error. If that confidence interval > includes > the zero value, you cannot reject the null hypothesis that the true > value is > zero. Thus, if your estimate is (nearly) zero and nonetheless you > obtain a > very low p value, it means the probability of the true value being zero > is > very low. You should rescale the results and will probably see that the > estimate is not exactly zero. > > However, I have my suspicions about part of Richard Ristow's comments, > namely: > > > At 02:41 PM 9/22/2004, Hector Maletta wrote: > > > > >If there is a population value for the coefficient, and you > > estimate it > > >obtaining a value of zero or any other, the significance > > tells you that > > >the true value is 95% likely to be within two standard > > errors from your > > >estimate. > > > > Is this really true? I thought that the population value > > would fall within two standard-errors-of-estimate of the > > estimated value, in any case. > > "In any case" seems too much for me. You have a probability that it > lies > within a certain interval (usually 2SE corresponding to a 95% > probability) > and a probability (usually 5%) that it lies outside that interval. If > the > probability is larger than 95% the interval is wider, say 3SE or > whatever, > and it is narrower if the probability is less than 95%. You reject the > null > hypothesis that the true value is zero whenever the confidence interval > does > not include the zero value. Suppose the estimate for the coefficient is > 0.25, and the SE is 0.1. A 95% interval means an interval of 2 SE, i.e. > approximately 0.2 to each side of your estimate, ranging from 0.05 to > 0.45. > Since this interval does not include the zero, you have 95% confidence > that > the null hypothesis (which says the true value is zero) is false > (though > there is a 5% probability that it is true). > > Am I so terribly wrong in this? > > Hector ```

Back to: Top of message | Previous page | Main SPSSX-L page