Re: Definition of Relationship Between Variables (was Re: Eight
What Don's post lacks in speed in certainly makes up in thoroughness. This posts concerns Jan De Leeuw's definition, in which two variables were not independent if the expected variance changed. Maybe a good example is IQ scores, in which the expected mean does not vary with gender, but the standard deviation does. Does IQ depend on gender? Don, if I understand him correctly, is saying that we can define independence any way we want. While technically correct, I think it odd (after reading Jan's post) to define independence completely on the average. Why not variance, or why not median, or even mode? In light of Jan's comment, I think my intuitive understanding of the phrase Variable A is independent of Variable B is that the probability distribution of A does not change with the value of B. If one wanted to talk about the expected average of A being independent of B, one could say that directly. So, I conclude that the average IQ is independent of gender, but IQ is not. Bob = Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at http://jse.stat.ncsu.edu/ =
Re: Definition of Relationship Between Variables (was Re: Eight
Or maybe I didn't understand Don's response to Jan. Pressing ever onward, though I had suggested using DEFINITION: There is a *relationship* between the vari- ables x and y if for at least one pair of values x' and x of x E(y|x') ~= E(y|x). as opposed to Don's DEFINITION: There is a *relationship* between the vari- ables x and y if for at least one value x' of x E(y|x') ~= E(y) We agree that the two are mathematically equivalent. But I think mines better, psychologically. I think in terms of my definition and I actually had to translate Don's definition to mine in order to understand why his definition was true. Don suggests that mine works well for the case when variable X can take only two values. But that is not how I meant it, nor how I stated it. My definition captures the continuous case too. Now let's talk examples. Don offers the following: For example, after several visits to a new bank a person may observe, The earlier in the morning I go to the bank, the less time I have to wait to be served. (Duration of waiting time is the response variable and bank arrival time is the predictor variable.) Don concludes that his definition better suits this example. But I disagree. Or I just think of things differently. The key is this. When the person concludes that they have to wait less time in the morning, what are they comparing that to? . . . . . . Your supposed to be answering this question . . . . . . . . . . . If they are comparing that to when they go at a time other than the morning, the example follows my definition. x' versus x'' -- morning versus not morning -- 10:00 versus 2:00. To fit Don's definition, they would have to be comparing that to the average time they wait, overall, including morning. Now, to me, it makes more sense to compare morning to not-morning; the comparison from morning to overall is not how I think. Or maybe I didn't understand this either. It's just my thought. But I think this is an important topic -- how basic ideas of statistics are defined, and how to define them in terms of how people think. I like Don's work a lot, because he addresses these issues, has useful things to say, and makes me think. Bob Frick = Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at http://jse.stat.ncsu.edu/ =
Re: teaching statistical methods by rules?
Alan McLean wrote, among other things: On the other hand, a body of knowledge can be thought of as a set of 'rules'. I think you are concentrating on the information in what is learned and ignoring the format. This works for computers, which learn in only one format (memory), but not for people, for which memory is just one format. My argument: For the sake of example, suppose I want to teach students how to tie their shoes. I could observe what I do and create a verbal description. I could teach students this verbal description, and they could memorize it. I could test them on their ability to remember this information. A student who could remember it probably could tie their shoes. My students might end up knowledge roughly the same information as me, but their knowledge wouldnt be stored in their brains the same way it is stored in mine. I have a connected series of motor movements built into my brain as a habit. And these different storage formats have different implications. My students would be good at verbal descriptions, but probably not so fast at actually tying their shoes. Now to reality. Research on implicit learning has suggested that people can learn something without being able to report what they have learned. Presumably, they have no conscious knowledge of what they have learned. In my published opinion, there are three types of implicit knowledge, with habits being just one. Combined with conscious knowledge, that makes four different types of learning. The format in which something is learned has implications. One is for memory. Research suggests that implicit learning is retained much longer than explicit learning. Another is for usage. Obviously, for verbal report, conscious knowledge is far superior than any other type of knowledge. But the other types of learning probably are probably better for other types of performance. For example, in one study, we either gave subjects implicit knowledge of a rule or explicitly taught them a collection of rules. The subjects with implicit knowledge could use the information in an identification task better than they could report it. The subjects with conscious knowledge could report the rules better than they could use them. The hardest type of learning to describe or define is what I call mental models, and what often corresponds to what people call understanding. For example, you have a mental model of your spouse (or friend). You can use this mental model to predict what your spouse or friend will do. You can also try to use this mental model to verbally describe your spouse or friend, but that isn't a natural use of the mental model and that format of learning isn't that good for verbal report. Someone adept at statistics would have a mental model of standard deviation, the t-test, statistical testing, etc. Teaching students rules or formulas does not develop mental models. Bob F.
Re: teaching statistical methods by rules?
Jerry Dallal wrote: Robert Frick wrote: I know it is hard to make statistics fun, but FOLLOWING RULES IS NEVER FUN. Not in math, not in games, nowhere. In math and in games, following rules isn't just fun, IT'S THE LAW. In fact, you can't have fun unless you follow them. :-) Well, technically, most real rules tell you what not to do -- they usually don't tell you what to do, because that isn't fun. In bridge, the language of the bidding is very prescribed, but you almost always have choices as to what you can bid. On the other hand, the prescription to bid 1NT with a balanced hand and 15-17 points tells you what to do, but is not a real rule of the game. Instead, it is a rule the experts constructed so that the game wouldn't be fun. Ha ha, they really constructed the rule so that people could play better bridge. Destroying the game is an unintended byproduct. In math, aren't students often taught algorithms for solving problems? Again, no fun. Bob F.
Re: teaching statistical methods by rules?
I happened to have a vehement and probably radical opinion on this. One of my sayings: "Ironically, our educational system is ideally suited to teaching computers and ill-suited to teaching human beings." If you are going to program a computer to do statistics, tell the computer rules to follow. If you give students rules to memorize, they will surely forget them. If you had a student who learned and applied the rules, people would say that the student was mindlessly following rules and couldn't think for him/herself. But your best student will just remember half the rules -- and by that, I mean half of each rule. I know it is hard to make statistics fun, but FOLLOWING RULES IS NEVER FUN. Not in math, not in games, nowhere. There are advantages to teaching rules. Most students like it. They certainly understand that method of teaching. They just won't learn anything. Bob F. EAKIN MARK E wrote: I just received a review which stated that statistics should not be taught by the use of rules. For example a rule might be: "if you wish to infer about the central tendency of a non-normal but continuous population using a small random sample, then use nonparametrics methods." I see why rules might not be appropriate in mathematical statistics classes where everything is developed by theory and proof. However I teach statistical methods classes to business students. It is my belief that if faculty do not give rules in methods classes, then students will infer the rules from the presentation. These student-developed rules may or may not be valid. I would be intested in reading what other faculty say about rule-based teaching depending on whether you teach theory or methods classes. Mark Eakin Associate Professor Information Systems and Management Sciences Department University of Texas at Arlington [EMAIL PROTECTED] or [EMAIL PROTECTED]
