andrew_gelman_stats andrew_gelman_stats-2013 andrew_gelman_stats-2013-2046 knowledge-graph by maker-knowledge-mining
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Introduction: Milan Valasek writes: Psychology students (and probably students in other disciplines) are often taught that in order to perform ‘parametric’ tests, e.g. independent t-test, the data for each group need to be normally distributed. However, in literature (and various university lecture notes and slides accessible online), I have come across at least 4 different interpretation of what it is that is supposed to be normally distributed when doing a t-test: 1. population 2. sampled data for each group 3. distribution of estimates of means for each group 4. distribution of estimates of the difference between groups I can see how 2 would follow from 1 and 4 from 3 but even then, there are two different sets of interpretations of the normality assumption. Could you please put this issue to rest for me? My quick response is that normality is not so important unless you are focusing on prediction.
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1 Milan Valasek writes: Psychology students (and probably students in other disciplines) are often taught that in order to perform ‘parametric’ tests, e. [sent-1, score-0.788]
2 independent t-test, the data for each group need to be normally distributed. [sent-3, score-0.742]
3 However, in literature (and various university lecture notes and slides accessible online), I have come across at least 4 different interpretation of what it is that is supposed to be normally distributed when doing a t-test: 1. [sent-4, score-1.804]
4 distribution of estimates of means for each group 4. [sent-7, score-0.662]
5 distribution of estimates of the difference between groups I can see how 2 would follow from 1 and 4 from 3 but even then, there are two different sets of interpretations of the normality assumption. [sent-8, score-1.369]
6 My quick response is that normality is not so important unless you are focusing on prediction. [sent-10, score-0.831]
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Introduction: Milan Valasek writes: Psychology students (and probably students in other disciplines) are often taught that in order to perform ‘parametric’ tests, e.g. independent t-test, the data for each group need to be normally distributed. However, in literature (and various university lecture notes and slides accessible online), I have come across at least 4 different interpretation of what it is that is supposed to be normally distributed when doing a t-test: 1. population 2. sampled data for each group 3. distribution of estimates of means for each group 4. distribution of estimates of the difference between groups I can see how 2 would follow from 1 and 4 from 3 but even then, there are two different sets of interpretations of the normality assumption. Could you please put this issue to rest for me? My quick response is that normality is not so important unless you are focusing on prediction.
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Introduction: Andy Cooper writes: A link to an article , “Four Assumptions Of Multiple Regression That Researchers Should Always Test”, has been making the rounds on Twitter. Their first rule is “Variables are Normally distributed.” And they seem to be talking about the independent variables – but then later bring in tests on the residuals (while admitting that the normally-distributed error assumption is a weak assumption). I thought we had long-since moved away from transforming our independent variables to make them normally distributed for statistical reasons (as opposed to standardizing them for interpretability, etc.) Am I missing something? I agree that leverage in a influence is important, but normality of the variables? The article is from 2002, so it might be dated, but given the popularity of the tweet, I thought I’d ask your opinion. My response: There’s some useful advice on that page but overall I think the advice was dated even in 2002. In section 3.6 of my book wit
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Introduction: Jeff Witmer writes: I noticed that you continue the standard practice in statistics of referring to assumptions; e.g. a blog entry on 2/4/11 at 10:54: “Our method, just like any model, relies on assumptions which we have the duty to state and to check.” I’m in the 6th year of a three-year campaign to get statisticians to drop the word “assumptions” and replace it with “conditions.” The problem, as I see it, is that people tend to think that an assumption is something that one assumes, as in “assuming that we have a right triangle…” or “assuming that k is even…” when constructing a mathematical proof. But in statistics we don’t assume things — unless we have to. Instead, we know that, for example, the validity of a t-test depends on normality, which is a condition that can and should be checked. Let’s not call normality an assumption, lest we imply that it is something that can be assumed. Let’s call it a condition. What do you all think?
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Introduction: Steve Peterson writes: I recently submitted a proposal on applying a Bayesian analysis to gender comparisons on motivational constructs. I had an idea on how to improve the model I used and was hoping you could give me some feedback. The data come from a survey based on 5-point Likert scales. Different constructs are measured for each student as scores derived from averaging a student’s responses on particular subsets of survey questions. (I suppose it is not uncontroversial to treat these scores as interval measures and would be interested to hear if you have any objections.) I am comparing genders on each construct. Researchers typically use t-tests to do so. To use a Bayesian approach I applied the programs written in R and JAGS by John Kruschke for estimating the difference of means: http://www.indiana.edu/~kruschke/BEST/ An issue in that analysis is that the distributions of student scores are not normal. There was skewness in some of the distributions and not always in
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Introduction: 19. A survey is taken of students in a metropolitan area. At the first stage a school is sampled at random. The schools are divided into two strata: 20 private schools and 50 public schools are sampled. At the second stage, 5 classes are sampled within each sampled school. At the third stage, 10 students are sampled within each class. What is the probability that any given student is sampled? Express this in terms of the number of students in the class, number of classes in the school, and number of schools in the area. Define appropriate notation as needed. Solution to question 18 From yesterday : 18. A survey is taken of 100 undergraduates, 100 graduate students, and 100 continuing education students at a university. Assume a simple random sample within each group. Each student is asked to rate his or her satisfaction (on a 1–10 scale) with his or her experiences. Write the estimate and standard error of the average satisfaction of all the students at the university. Introd
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Introduction: Milan Valasek writes: Psychology students (and probably students in other disciplines) are often taught that in order to perform ‘parametric’ tests, e.g. independent t-test, the data for each group need to be normally distributed. However, in literature (and various university lecture notes and slides accessible online), I have come across at least 4 different interpretation of what it is that is supposed to be normally distributed when doing a t-test: 1. population 2. sampled data for each group 3. distribution of estimates of means for each group 4. distribution of estimates of the difference between groups I can see how 2 would follow from 1 and 4 from 3 but even then, there are two different sets of interpretations of the normality assumption. Could you please put this issue to rest for me? My quick response is that normality is not so important unless you are focusing on prediction.
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Introduction: I use just-in-time teaching assignments in all my classes now. Vince helpfully sent along these instructions for setting these up on Google. See below. I think Jitts are just wonderful, and they’re so easy to set up, you should definitely be doing them in your classes too. I’ve had more difficulty with Peer Instruction (the companion tool to just-in-time teaching) as it requires questions at just the right level for the class. I do have students frequently work in pairs, though, so I think I get some of the benefit of that. P.S. I’d love to share all the Jitts with you for Bayesian Data Analysis, but I’m afraid this would poison the well and future students would not have the opportunity to be surprised by them. Yes, I know, I should just come up with new ones every year—but I’m not quite ready to do that! Perhaps soon I will. In the meantime, a commenter asked for some Jitts, so here are the ones for the first and last weeks of class: Jitt questions for Bayesian Data
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Introduction: Now that September has arrived, it’s time for us to think teaching. Here’s something from Andrew Heckler and Eleanor Sayre. Heckler writes: The article describes a project studying the performance of university level students taking an intro physics course. Every week for ten weeks we took 1/10th of the students (randomly selected only once) and gave them the same set of questions relevant to the course. This allowed us to plot the evolution of average performance in the class during the quarter. We can then determine when learning occurs: For example, do they learn the material in a relevant lecture or lab or homework? Since we had about 350 students taking the course, we could get some reasonable stats. In particular, you might be interested in Figure 10 (page 774) which shows student performance day-by-day on a particular question. The performance does not change directly after lecture, but rather only when the homework was due. [emphasis added] We could not find any oth
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Introduction: Just in time for Halloween, here’s a horror story for you . . . Howard Wainer writes: In my book “Uneducated Guesses” in the chapter on value-added models, I discuss how the treatment of missing data can have a profound effect on the estimates of teacher scores. I made up how a principal might send the best students on a field trip at the beginning of the year when the ‘pre-test’ was given (and their scores would be imputed from the students who showed up) and that the bottom half of the class would have a matching field trip on the day of the post test. Everyone laughed. But apparently someone decided to take it seriously. http://www.amren.com/news/2012/10/el-paso-schools-confront-scandal-of-students-who-disappeared-at-test-time/ http://www.elpasotimes.com/episd/ci_20848628/former-episd-superintendent-lorenzo-garcia-enter-plea-aggreement You can’t make this stuff up. This sort of thing is not surprising but it’s worth keeping in mind. That a measurement system c
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Introduction: Milan Valasek writes: Psychology students (and probably students in other disciplines) are often taught that in order to perform ‘parametric’ tests, e.g. independent t-test, the data for each group need to be normally distributed. However, in literature (and various university lecture notes and slides accessible online), I have come across at least 4 different interpretation of what it is that is supposed to be normally distributed when doing a t-test: 1. population 2. sampled data for each group 3. distribution of estimates of means for each group 4. distribution of estimates of the difference between groups I can see how 2 would follow from 1 and 4 from 3 but even then, there are two different sets of interpretations of the normality assumption. Could you please put this issue to rest for me? My quick response is that normality is not so important unless you are focusing on prediction.
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Introduction: Sally Murray from Giving What We Can writes: We are an organisation that assesses different charitable (/fundable) interventions, to estimate which are the most cost-effective (measured in terms of the improvement of life for people in developing countries gained for every dollar invested). Our research guides and encourages greater donations to the most cost-effective charities we thus identify, and our members have so far pledged a total of $14m to these causes, with many hundreds more relying on our advice in a less formal way. I am specifically researching the cost-effectiveness of political lobbying organisations. We are initially focusing on organisations that lobby for ‘big win’ outcomes such as increased funding of the most cost-effective NTD treatments/ vaccine research, changes to global trade rules (potentially) and more obscure lobbies such as “Keep Antibiotics Working”. We’ve a great deal of respect for your work and the superbly rational way you go about it, and
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Introduction: Thomas Basbøll [yes, I've learned how to smoothly do this using alt-o] gives some writing advice : What gives a text presence is our commitment to asserting facts. We have to face the possibility that we may be wrong about them resolutely, and we do this by writing about them as though we are right. This and an earlier remark by Basbøll are closely related in my mind to predictive model checking and to Bayesian statistics : we make strong assumptions and then engage the data and the assumptions in a dialogue: assumptions + data -> inference, and we can then compare the inference to the data which can reveal problems with our model (or problems with the data, but that’s really problems with the model too, in this case problems with the model for the data). I like the idea that a condition for a story to be useful is that we put some belief into it. (One doesn’t put belief into a joke.) And also the converse, that thnking hard about a story and believing it can be the pre
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Introduction: Joshua Vogelstein writes: I know you’ve discussed this on your blog in the past, but I don’t know exactly how you’d answer the following query: Suppose you run an analysis and obtain a p-value of 10^-300. What would you actually report? I’m fairly confident that I’m not that confident :) I’m guessing: “p-value \approx 0.” One possibility is to determine the accuracy with this one *could* in theory know, by virtue of the sample size, and say that p-value is less than or equal to that? For example, if I used a Monte Carlo approach to generate the null distribution with 10,000 samples, and I found that the observed value was more extreme than all of the sample values, then I might say that p is less than or equal to 1/10,000. My reply: Mosteller and Wallace talked a bit about this in their book, the idea that there are various other 1-in-a-million possibilities (for example, the data were faked somewhere before they got to you) so p-values such as 10^-6 don’t really mean an
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