Bob, I would also say that "it depends". Part of the beauty of academia is the diversity of views.
If your goal is to teach a formulaic approach then they don't need to see the relationships. Personally, I teach an introductory graduate course in a medical school over 2 quarters. I try to emphasize the relationship between many of the distributions. For example, square the t to get an F with 1 df. Take a large sample and the t approaches a "z". Square the z to get a chi-square. The F approaches a chi-square with the numerator df in large samples. The F and the t need denominator degrees of freedom because there is uncertainty in estimating the variance but we are assuming a really good estimate of the variance in large samples. I try to sneak it in with examples. And a good stats package that does probabilities helps. The t and z statistics are great pedagogically for introducing concepts since they are easily understood. Most students have had at least some exposure to the bell curve. And most textbooks never get far past the t-test...waste lots of pages on when to use a t and when to use a z and even give some dumb rules about >30 or some such nonsense. I realize I'm dealing with a different student, but most students generalize easily enough. I'm not sure if they retain it, but hope they learn something out of it other than how to plug and chug. I feel a lot of things make more sense if everything isn't presented in isolation as a "see one of these and do this to it" approach you see in a lot of introductory texts. For example, you can get a lot across by showing that a t-test, one-way ANOVA with 2 factor levels and a regression with indicator variables give exactly the same results. In addition, the nonparametric ranking procedures are just "ANOVA" type models assuming large samples and replacing data with ranks. Kruskal-Wallis and Friedman are easier to present without getting bogged down in the computations and post-hoc analyses, not discussed by most authors, are easy to develop. The chi-square in a 2x2 table is analogous to the t-test assuming equal variance. In fact, its useful to show that pq/n is just the usual s.e. formula. Other kx2 contingency table analyses are analogous to the ANOVA or maybe a regression for testing trend. In other words, it's all related. As for the typical chi-square contingency table stuff, I feel it's easy enough to skip that and talk about logistic regression after discussing ANOVA and multiple regression. You can mention that the simple chi-square in some cases is the score statistic of the logistic regression. Warren May University of Mississippi Medical Center "Neil W. Henry" <[EMAIL PROTECTED]> wrote in message news:<[EMAIL PROTECTED]>... > Bob Johnson wrote: > > > > The chi-square distribution with df = 1 is the z-distribution squared. I’ve >heard it said that it is good for students in introductory statistics courses to see >this. How important do you feel it is to include this concept in an introductory >statistics course? > > > If chisquare is used at all in the introductory course then it is > important to make this point. > > CONTEXT: Most courses test the hypothesis of equal proportions in > independent samples from two populations using z, and later introduce > chi-square for the k-population situation. Some (I think more should) > introduce chisquare as a goodness of fit procedure when there are more > than 2 response alternatives ("is the die fair?"), after having used z > for the 2 response case ("is the coin fair?"). > > OBJECTIVE: In these situations it is a good idea to explain why, when > both procedures are applicable, they give the same result. I would not > want students to agonize over the question "should I use z or should I > use chi-square when k = 2?" > > If the course never deals with more than 2 populations, or with more > than two categories of response, chi-square might not be mentioned at > all. > > Neil Henry > > > If the answer to the first is, “it is important”, follow-up questions: > > What is the objective? > > In what context should it be introduced? > > > > Thank you, > > > > ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ > > Robert R. & Barbara S. Johnson > > E-mail: [EMAIL PROTECTED] > > Voice / Fax (call 1st): 315.595.2844 > > Post: 84 West Lake Rd BranchportNY 14418 > > > > . > > . > > ================================================================= > > 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/ . =================================================================
