<< Firstly, the Z test is inappropriate unless you know the variance of the population you are testing a sample from, not deducing it from the data. >>
Robert, Please refresh my memory. I don't recall the variance of the population being a concern when calculating confidence intervals. What is the reason? Are you talking about the fact that using the sample variance in place of the pop variance is theoretically a crude substitution (although necessary)? The pop variance is rarely known, right? I am only remembering fragments of my MS in stat (actuarial science track). Correct me if I am wrong, but the use of the sample SD in determining a CI is used probably more than 99.99% of the time. If the pop variance is required for a CI, doesn't that imply that using a p-value for hypothesis testing is just as inappropriate? I am just curious... I would like to think that I have a decent comprehension of my stat, and I welcome feedback on my personal knowledge. I look forward to reading your reply. Are you familiar with any of the instructors at Manitoba? My favorite teacher use to work there, Dr. Elias Shue. Thanks! John Weaver PS - I got to learn intro to stat from Dr. Hogg himself! What a comedian! "Robert J. MacG. Dawson" <[EMAIL PROTECTED]> wrote in message news:[EMAIL PROTECTED] Paige Miller wrote: > > [EMAIL PROTECTED] wrote: > > I ran a z test on two sets of scores using the Excel data analysis > > tool to seek to determine whether the difference in the means were > > statistically significant. What I do not understand is how to read > > the results of the z test Excel returns. It give me a "z", "P" one > > tail and "P" two tail. Can anyone explain to me how to interpret > > these results? Thanks. > > If you did the z-test by hand, how would you interpret the z-value? The > results from Excel can be interpreted the exact same way. Paige: The fact that "dbmail" did a z test is almost certainly evidence that he/she has had little background in statistics (or learned it in a day when one didn't "interpret p values" but compared test statistics to a table of 2.5th percentiles); so that comment isn't going to help. Dbmail (should I call you D.B. for short? This isn't Dear Abby, you're allowed to give your real name): Firstly, the Z test is inappropriate unless you know the variance of the population you are testing a sample from, not deducing it from the data. This situation rarely occurs. In particular, if the software did not prompt you to type in the standard deviation, it *was* deducing it from the data. Many years ago people used to use a "Z test" that was just a t test done with the Z tables whenever thay had more than 30 data. This was done because even longer ago t tables hadn't been invented, or because of insecurity about using the "50 degrees of freedom" line when you have 55 degrees of freedom (=56 data). For some reason people have been very concerned about this; most t tables out there have far more rows than needed. There is one (Milton, McTeer,and Corbet) that has 101 different rows, some differing only in the third decimal place(!) However, the common way of dealing with this concern - using the Z test instead, with computed standard deviation - was completely irrational. It was, in fact, equivalent to using the nu=infinity row of the t table! So what these people were saying was really: "I have 55 degrees of freedom and I don't want to round it to 50 or to 60 so I'll round it to infinity instead." Now, this didn't make a huge difference, because above about fifty degrees of freedom not a lot changes in the t table. But it makes no sense. It would be like saying "I'll turn all the sixes in the last decimal place into nines" (and telling students to do the same). It complicates things, makes them a tiny bit wrong, and has no advantages. One possible other contributing factor is the fact that Z tables give many, many probabilities, whereas most easily accessible (="in the back of the text") tables give six to ten probabilities (see my article "A t-table for today") http://www.amstat.org/publications/jse/v5n2/dawson. This does mean that a Z test could be reported as a p value, not as "accept/reject", while a t test could usually not be. With computers, however, that's becoming a non-issue. Anyhow: How you read the results (once you've redone it as a t test): The t statistic is a measure of how many standard errors away from the hypothesized mean the observed mean is. Report it. The 2-tailed p value is a measure of how often you would see a t statistic this large purely due to sampling variation _if_ the null hypothesis were true. If it is very small this is evidence for something other than sampling variation being behind the difference. Report this. Traditionally 5% was considered to be the cutoff between "statistical significance" (p<5%) and "statistical unsignificance" (p>5%) but this is bogus, like saying that any man 6'0" tall or taller is "tall" and any other man is "not tall". It is an artificial dichotomy. It should also be noted that the p-value is (unless the null is exactly true) controlled by sample size - with a bigger sample size your p-value drops. It measures strength of evidence, not truth. The 1-tailed p-value has applications in quality control and safety testing. Basically, it is a measure of how often you would see a t statistic this large _and_in_this_direction_, purely due to sampling variation _if_ the null hypothesis were true. There have been suggestions that it can and should be used in research - I would argue strongly against this. It seems like a great deal - you get to halve your p-value AND you never need to report an effect in the direction opposite to the one you were hoping for - but neither of these is honest. The "value" of reducing the p-value lies only in the hope that the ignorant will compare it with a two-tailed p-value and be impressed. Ignore this number completely in research contexts, and do not report it. You might also consider reporting a t confidence interval for the mean. This is an interval constructed by a method that has the property that 95% of the intervals it constructs contain the true population mean. (It does NOT mean that there is a 95% probability, after the data have been plugged in, that the true mean lies within that interval!) -Robert Dawson . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . ================================================================= . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
