I think Bill is right about the implications of Karl's observation. While I expressed it here imperfectly, what I do is what Michael suggests. I am explicit that there are two ways to skin the cat and either gives the identically decision in the end.
But, if the decision process is being upset by students not dealing with leading zeros well, and related issues, then it is no surprise that students have difficulty with these decisions. Paul On Sep 29, 2012, at 8:30 AM, William Scott wrote: I think the prediction from Karl's observation is that if the obtained t is 1.0999783 and the critical t is 1.11100003, then many students would make a mistake in choosing which was larger. I am gob-smacked. Karl's observation, if true, might explain many things that until now have been mysterious to me. Bill Scott >>> Michael Palij <m...@nyu.edu<mailto:m...@nyu.edu>> 09/29/12 7:08 AM >>> When I teach statistical inference, say with t-tests, I emphasize that there are two rules that they can follow and that both lead to the same conclusion: (1) Rule 1 for two-tailed t-tests: If | obtained t-value | is greater than | critical t-value |, then reject the null hypothesis (else fail to reject). NOTE #1: the use of "| |" is for absolute value, so the obtained t-value, regardless of sign has to be larger than the critical t-value (which might be obtained from a table or, say, Excel's t-test output which provides both crit t and prob(obt t-value). NOTE #2: the same rule holds for two-tailed tests for the Pearson r/correlation coefficients. NOTE #3: for one-tailed t-text or Pearson r or F-values or Chi-square, the rule become "if obtained statistic is greater than critical statistic, then reject null hypothesis". NOTE #4. I make sure that students understand the word form of the rule before focusing on the more abstract formula representation. (2) Rule 2 for tow-tailed t-tests If Probability(obtained statistic) is less than alpha (= .05), then reject the null hypothesis (else fail to reject). NOTE #1: I emphasize that the numbers for the two rules go in opposite directions: you want small probabilities and large test statistic values. NOTE #2: I show a figure of the t-test distribution or from Glass & Hopkins 3ed, Table Fig6-5-Normal Curve, which shows the area under the curve. It's a page long figure with a graphic for the standard normal curve at the top of the page and several x-axes below, including the SAT, GRE, and the Wechsler and Stanford-Binet intellligence scales. I point out that the y-axis represents relative frequency and as you go further from the mean, the relative frequency or probability of a value decreases. So, I can ask "Which percentage of values of z, T-score, SAT, GRE, Weschler, or Standford fall above one standard deviation above the mean." What values cut off the top 5% or 10% (a table is used for this). I emphasize that the more "extreme" the measurement, the less likely values that larger or larger will occur. NOTE #3: I show that in Excel that the t-test procedure provides both the critical t value (for use with rule #1) and the probability of the obtained t-value which should be compared against alpha. I also show that in SPSS, only the probability of the obtained t-value is given, so one has to use rule. I point out that if one calculates the t-value by hand, they have to use rule #1. I think somewhere along the way they learn: As the obtained statistic increases in absolute value, its probability decreases. We can then ask either (a) is the value of the obtained statistic *greater than* some threshold (critical value) or (b) is its frequency of occurrence (p-value) *less than" some threshold value represented by alpha. The choice of one rule over the other depends upon how the values are obtained (i.e., by hand, by Excel, by SPSS, etc.) and we should apply the appropriate rule for the information we have at hand. -Mike Palij New York University m...@nyu.edu<mailto:m...@nyu.edu> On Sep 28, 2012, at 7:16 PM, Wuensch, Karl L wrote: Nope -- my TA would put two numbers up on the board, like .05 and .032, and ask them, in words, which is lower – or he would put one number up, like .046, and ask whether it was less than or more than .05. Cheers, ----------------------- Original Message -------------------- On Friday, September 28, 2012 6:11 PM. Beth Benoit wrote: Karl, Is it possible they're having trouble with the < vs. the >? I'd be willing to bet that most Americans - no, slash that - most people struggle with what those two signs represent. I know, it "ain't rocket science," but I suspect a lot of people never had that explained to them. Please say that's what it really is. ;-) On Fri, Sep 28, 2012 at 5:43 PM, Wuensch, Karl L <wuens...@ecu.edu<mailto:wuens...@ecu.edu>> wrote: I am not the greatest fan of NHST, but do my duty to teach it. For a good while now I have been disturbed that a substantial proportion of my undergraduate students never figure out how to decide whether or not a test is significant. I tried stressing that p is a measure of the goodness of fit between the data and the null, that p is like the strength of evidence in support of the accused null defendant in statistical court, and so on. Nothing seemed to help much. Now one of my teaching assistants has discovered why. Given two numbers, these students are unable to identify which is smaller. No, I am not kidding. Yes, this involves numbers between 0 and 1. My TA spend half an hour trying to teach them how to tell which is the smaller of two numbers, without great success. --- You are currently subscribed to tips as: wsc...@wooster.edu. 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