Statistical Techniques I EXST7005 Exam 2 Review

Exam Coverage n There will be problems requiring the use of F and Chi square tables. Probabilities from statements and tabular values from probabilities. Plan on at least one page of these types of problems, maybe two. n Some of the problems on the internet are somewhat obtuse. Most of the exam will be pretty straight forward.

Exam Coverage (continued) n The t-test! Will definitely be on the exam, probably in several forms. è Possibly, will have intermediate statistics, mean and variance and d.f., maybe SS. Be able to determine if variances are equal and complete calculations for two-sample t-test. Put necessary equations on 8.5 by 11 inch paper. è Also be able to use SAS output to complete two sample t-test.

Exam Coverage (continued) n Confidence intervals. è Yes it will definitely be there, probably in several forms. è Major pitfall - carefully note if we are placing an interval on INDIVIDUALS or on MEANS! This is true of t-tests in general, but on this exam mostly applicable to confidence intervals. è Also, be able to use the Chi square to place intervals on variances.

Exam Coverage (continued) n True-false and multiple choice questions. è KNOW central limit theorem and power definitions. They apply to every type of test and if not on this exam, they will be on one of the others. These are key concepts in statistics.  One new related concept with confidence intervals. Confidence is 1- .

Exam Coverage (continued) n Know the assumptions for each test. They are basically the same, though we have a new one for the two-sample t-test ONLY IF variances are pooled. Know the expected value of all distributions (0, 0,  and 1, respectively).

Exam Coverage (continued) n Know linear combination concepts and application to calculations. We saw linear combinations applied to the t-test. The coefficients were 1 and -1, simple. Could you test H0:   2 = 0? I expect that you could, it is a simple extension of what I did.

Exam Coverage (continued) If you see a problem like this - H0:   2=0. è 1) Don't panic. It's a two-sample t-test like any other. So, first test the variances and decide if you can pool.  2) Instead of calculating the difference  Y1-  Y2, calculate, just calculate  Y1-0.9*  Y2 è 3) Instead of calculating the variance S21/n1+S22/n2, get S21/n1+(0.9)2S22/n2.  4) Simplify if the variances can be pooled (i. e. S2  Y = S2p(1/n1+(0.81)/n2). è 5) Do test (7 steps, +7 for variance).

Exam Coverage (continued) If you see a problem like this - H0:   2=0. è If I gave you a SAS output with a two-sample t-test, could you complete this test? è Suppose the variances were not significantly different, could you still do the test? Is there enough information on SAS output to pool the variances?

Exam Coverage (continued) Remember, we can place confidence intervals on differences. Just get difference (estimating  =  1-  2) and then find appropriate t-value (  /2) and then add and subtract t*(std error) from estimate of the difference.  Now, could you do that for   2? è

Exam Coverage (continued) n Finally, problem recognition! n I have a belief that if you set out to do an analysis, and you cannot recognize the type of analysis that you are supposed to do, then it is just as bad as not knowing how to do the analysis in the first place, actually it is worse. è If I describe a problem, can you pick the appropriate analysis. è Or, can you tell me when to use one type of analysis and when to use another?

Exam Coverage (continued) n Problem recognition! n Options for problems are:  Z test (  2 known)  t-test - one-sample (  2 not known)  t-test - two-sample (  2 not known, compare two means)  Chi square test (test  2 against  2)  F test (test  2 against  2) è Paired t-test (compare two means, observations paired).

Exam Coverage (continued) n Problem recognition! n For the described problem, plan on stating not only the type of problem, but also the degrees of freedom for the test and perhaps providing a critical value for the test.

Web page n The web page has been updated with questions asked recently. I will update this with any new questions that come in over the next day or so.