SBI February 2015

sbi@causeweb.org

21 participants
11 discussions

by Soma Roy

Hello SBI listserv participants and SBI blog readers, Hope you are enjoying your Saturday morning! First, Thank you for your discussions on/contributions to the listserv - it is great to hear about all the things that statistics teachers are doing in their classes! Second, we have several new articles on the Simulation-based Inference blog (https://www.causeweb.org/sbi/) that have been recently posted: 1) We have two new posts on "How to use real data" by Kevin Ross and Nathan Tintle. 2) Erin Blankenship, Karen McGaughey, and Kathryn Dobeck have written about their experiences and what they thought was "The hardest thing about getting started with simulation-based curricula." 3) For readers interested in "How to implement simulation-based methods in high school classrooms/AP Statistics classes" - we have articles from Bob Peterson, Catherine Case, and Josh Tabor, all AP Statistics teachers, writing about their experiences. On behalf of the ISI team, I'd like to thank all our blog contributors for writing these pieces for us. I hope you enjoy reading these articles, and others posted on the blog, as much as I do! Have a nice weekend! - Soma ----------------------- Soma Roy Associate Professor Statistics California Polytechnic State University San Luis Obispo CA 93407 Phone no.: (805)-756-5250 "… for whenever you learn something new, the whole world becomes that much richer." - Norton Juster, The Phantom Tollbooth

8 years, 10 months

A sample item

by Josh Tabor

Hello Everyone- I wanted to share an item I included on my recent AP Statistics test. We had just finished traditional one sample tests for a proportion and one sample tests for a mean. I introduced the chapter with a simulation-based analysis of a test for a proportion, and we had done several similar activities earlier in the year. I like the item because it addresses the logic of inference, but doesn't match up with one of our traditional tests. Also, because it is about baseball! I pasted it below and in the attachment. I also included a brief answer key and comments on my student performance. Feel free to use it with your students if you are interested. Thanks, Josh Tabor In a recent Sports Illustrated article, author Michael Rosenberg addresses "America's Wait Problem." That is, he discusses how fans of some teams have to wait many, many years for their team to win a championship. In Major League Baseball, fans should expect to wait an average of 30 years for a championship-assuming all 30 teams are equally likely to win a championship each season. But is it reasonable to believe that all teams are equally likely to win a championship? In the last 19 seasons, only 10 different teams won a championship. Does this provide convincing evidence that some teams are more likely than others to win a championship? We can find out by testing the following hypotheses: H0: All 30 teams are equally likely to win a championship Ha: Some teams are more likely to win a championship than others. (a) Describe how to use slips of paper to simulate the number of different teams to win a championship in 19 seasons, assuming that each team is equally likely to win the championship each season. Write the name of each team on a slip of paper. Shuffle slips in a hat. Select one team, record, and replace slip. Repeat for a total of 19 champions. Record number of different champions. Repeat many times. Comments on student performance: Many students were able to describe how to prepare the slips. Most of these correctly selected 19 slips with replacement, although some left this out. However, many students did not discuss what they would do after the 19 selections (e.g., record the number of different champs). One hundred trials of a simulation were conducted, assuming that each team is equally likely to win the championship each season. The number of different teams to win a championship in 19 seasons was recorded for each trial on graphed on the dotplot. (b) There is one dot at 10. Explain what this dot represents. Number of difference champions In one simulated 19-year stretch, there were only 10 different champions. Comments: Most students did well on this part. (c) Based on the simulation and the data from the previous 19 seasons, is there convincing evidence that some teams are more likely to win a championship than others? Explain. Because it is very unlikely to get 10 or fewer different winners by chance alone (p-value 1/100), we reject H0. There is convincing evidence that some teams are more likely to win a championship than others. Comments: As expected, this was the hardest part for students. About 10-15% had no idea what to do or tried a traditional z or t test. About 50% focused on the wrong part of the sampling distribution (e.g., said the evidence was convincing because there were no dots at 19, said the evidence was convincing because the distribution was centered at 14-15, which was less than 19 or 30). The remaining students focused on the small probability that there would be 10 or fewer different champions by chance alone. Some even called this a p-value! A few argued that 10 different winners did not provide convincing evidence of Ha because 10 could happen by chance, even though it is would be fairly unusual.

9 years, 2 months

Re: [SBI] Groundhog Day, and a question about simulation methods

by Nathan Tintle

Homer- Sorry I didn't reply sooner, but I wanted to comment on your final paragraph which I've copied here for convenience: "Where does that leave us in teaching? Do we stick with simulation methods that model the role of chance intuitively? In that case we may get rather far into the weeds (after all, three options for simulation in the two-factor is alot for students to handle so early in the course), and we also end up, from time to time, using methods that won't be recommended in data analysis applications down the road. On the other hand if we employ simulation methods without regard to how intuitively they model the presumed role of chance variation in the production of the data, then we are back to using statistical procedures as black boxes that don't convey insight to students at the introductory level. My dilemma may be due in part to a lack of formal statistical training. Has anyone else found themselves puzzled by similar questions?" I'll give a two-pronged response to your questions. First, my personal opinion is to focus in a first course more on the intuitive and conceptual ideas, and less on technical details. Thus, I'm a lot less worried about matching the exact 'best practices' statistical methods with what I teach in Stat 101. For example, using Welch-Sattherwaite to approximate degrees of freedom or a +4 confidence interval or the exactly correct bootstrap, etc. The reality is that best practices (a) change frequently, (b) are extremely technical and (c) are rarely actually agreed upon by everyone (as you point out earlier in your email). So, I'd prefer to stay out of the weeds and focus on simple/intuitive approaches that model the logic of inference, with enough cautions to students that more precise/technical methods are available in practice. Secondly, with specific regards to simulation-based inference, what does this mean for me? It means, I'm actually not as concerned re: precisely matching the data production (e.g., random sampling vs. randomized experiment, etc.) with the simulation 'crank' used (e.g., bootstrap vs. permutation) and am comfortable with keeping students using only a single 'crank' (e.g., permutation test) or maybe two, even though this may present a bit of a disconnect between data production and analysis. In the ISI text, we navigate this by highlighting to students how study design impacts scope of conclusions (Can I generalize? Can I conclude cause-effect?) but don't worry about changing the analysis strategy as well. We find this keeps things more straightforward for students avoiding the 'too many technical details' problem that becomes the focus of a course for many students once you get into it. Finally, I'd point out that for a more advanced group of students, or in a second (third, beyond) course this might be exactly the kind of stuff you *do* want to talk about. But, for my Stat 101 students, this just seems like too much detail to be worth it. All of this being said, it was not an easy decision for our author team, nor one that we all necessarily would have made if we were doing so individually. I'm sure there are lots of other opinions out there and would love to hear from others on the listserv! Perhaps we should have some blog posts on this soon! Nathan On Tue, Feb 3, 2015 at 7:49 PM, Homer White < Homer_White(a)georgetowncollege.edu> wrote: > Hello Everyone, > > > It has been a joy to read about of the great data sets and activities! > I did not have time to respond yesterday, but here goes now. > > > I've got an introductory class with 26 students, and we meet all the > time in a computer classroom. Inspired by the Mosaic Project folks, we > teach with R in the R Studio Server environment. Our approach to > simulation-based inference is about 60% if of the way from traditional > inference towards Locke5/Intro to Statistical Investigations. > > > We do some simulation-based inference very early in the course -- > binomial stuff, on the first day of class, in fact -- and we try again to > work it in early with the chi-square test for the relationship between two > factor variables. We're in that unit now, so students have played a couple > of times with a "slow-simulation" app to get an idea of the null > distribution of the chi-square statistic; subsequently they have been > exposed to the standard chi-square test where the null distribution is > approximated by a chi-square density curve. They are told that it was > quite a godsend for Mr. Pearson to have stumbled on such a family of > approximating curves, because Mr. Pearson had no access whatsoever to > computing machinery. > > > Groundhog Day began with a little come-to-Jesus chat about the first > data analysis report, which the students tackled over the weekend. The > project involved looking at some data from a Current Population Survey and > to investigate the relationship between hourly wages and such factors as > sex, union membership status, race, etc. Apparently there is a rule at my > College that during Greek Rush Week critical thinking is forbidden, > including the act of determining the type of variables involved in your > research question prior to choosing your analytical tools. Accordingly > about a third of the students had attempted to make bar charts and > cross-tables to investigate, for example, whether men or women earn more, > even though wage is a numerical variable. So we cleared that up, I hope. > > > Harrumph. On with the intended show. > > > Today's plan is to revisit simulation one more time, in a situation > where you really need it (rather small number of observations). I bring > up the "ledge-jump" data (#59 in the classic Handbook of Small Data Sets). > a social psychologist studied 21 incidents in Britain involving a person > threatening to leap from the ledge of a building or other high structure. > The idea was to see what factors might affect the behavior of the crowd > that gathers in the street below. > > > To forestall morbid thoughts among students I get up on a nearby table > and assure them through role-play that nobody really gets hurt: the fire > truck comes right away and the firemen teeter back and forth with their big > yellow trampoline, your rabbi, psychiatrist and spouse are phoned and > within minutes they are leaning out of one nearby windows, soothing words > are spoken, sage advice is given, hope is restored. Eventually they talk > you back inside. > > > But in the meantime a crowd has gathered. Sometimes they wait more or > less in silence, appropriately mindful of the seriousness of the situation > playing out above. Sometimes, though, they begin to bait the would-be > jumper (muster up Cockney accent): "Go on, jump will ya?" > > > In the 21 incidents under study, the following was found: > > > weather/crowd Baiting Polite > > > cool 2 7 > > warm 8 4 > > > Discussion, with students ( me still on table): > > > Me: Somebody could say that, for one reason or another, a crowd is more > likely to bait in warm weather. Others might say that the outcome of these > 21 incidents had nothing to do with weather, but is just the result of > random variation in other factors -- above and beyond the weather at each > particular incident. Can you think of any other things besides the weather > that might affect crowd behavior? > > > Student: How many people show up to watch. The more that show up, the > more likely there jerk who will yell "jump' and get the rest of 'em started. > > > Student: How long they have to wait. Maybe if they stand around a long > time they'll get impatient. > > > Student (looking right at me, still on table): What about the dorkiness > of the would-be jumper? > > > Me: Uh, maybe. Gee, thanks, Zach. > > > I get down and we work it out on the blackboard: if weather has nothing > to do with crowd behavior, then our best guess based on the data is that in > each incident, regardless of weather, there is a 10/21 chance for the crowd > to bait. The chi-square test function that the class uses has built-in > provisions for simulation, of three possible types: > > > > - "fixed": the rows sums in the simulated table are constrained to be > the rows sums of the observed table, and you determined the probability of > each outcome in the columns by pooling the data, as we just did to get the > 10/21 figure. > - "double-fixed": both the row and column sums of the simulated table > are constrained to be equal to the row and column sums of the observed > table. > - "random": neither row nor column sums are constrained, and the > probability of a simulated observation landing in a particular cell is the > observed cell count divided by the grand total of the table. > > "random" make sense when the observed data are a random ample a larger > population, and chance comes into play just in the matter of who gets into > the sample. For example, if you randomly sample people and ask their sex > and where they prefer to sit a in classroom (front, middle or back), then > chance is not in how a fixed person will respond but in whether or not that > person gets into the sample. > > > "double-fixed" (corresponding to the way simulation is done in R's > chisq.test(), and probably in many other software systems as well), appears > to be ideally suited for randomized experiment in which the Null hypothesis > imagines that a subject's response is the same regardless of which > treatment group one is placed into. In that case a different random > assignment of subjects to treatment groups might result in a different > table, but the row and column sums would be the same as for the table we > observe in the actual experiment. > > > "fixed" seems to be the right thing for the ledge-jump situation, if we > assume that the 21 incidents weren't sampled randomly out of some larger > population, that they were the only 21 incidents that occurred under the > period of study in the region under study. In that case the weather at the > time of each incident simply was it was, and chance comes into the > production of the observed table through random variation in all other > factors (conditional upon the weather). > > > So we do simulation with the "fixed" option. Everybody's P-value comes > in around 5%, so we decide that don't have overwhelming evidence that > weather and crowd behavior are related. > > > Now I come round to my questions. > > > When we teach inference though simulation, we don't want it to become > another "black box" for students. We want them to see that the simulation > method generates simulated data that reasonably could occur if the > study were to be conducted in a hypothetical world where the Null > hypothesis is definitely true. Hence we the simulation method has to > model, quite transparently, the role that we think chance played -- if the > Null is true -- in giving us the data we actually see. > > > But there appears to be controversy among statisticians as to which > simulation method is best to use for contingency tables. (See e.g., > Agresti, Categorical Data Analysis Third Edition section 3.5.6). I suppose > that sometimes it's possible for a particular simulation method not to > model the role of chance very well, but to possess superior statistical > properties nonetheless, maybe even be the state-of-the art method. (This > situation seems to occur also in bootstrap hypothesis testing, where the > more preferred re-sampling method is rather more difficult to justify > intuitively than is the "naive" re-sampling method.) > > > Where does that leave us in teaching? Do we stick with simulation > methods that model the role of chance intuitively? In that case we may get > rather far into the weeds (after all, three options for simulation in the > two-factor is alot for students to handle so early in the course), and we > also end up, from time to time, using methods that won't be recommended in > data analysis applications down the road. On the other hand if we employ > simulation methods without regard to how intuitively they model the > presumed role of chance variation in the production of the data, then we > are back to using statistical procedures as black boxes that don't convey > insight to students at the introductory level. > > > My dilemma may be due in part to a lack of formal statistical training. > Has anyone else found themselves puzzled by similar questions? > > > Homer S. White > Professor of Mathematics > Georgetown College, KY 40324 > 502-863-8307 > > *Notice*: *This message may contain confidential information and is > intended for the person/entity to whom it was originally addressed. Any > use by others is strictly prohibited. If you received this email in error, > please permanently delete it and disregard.* > -- Nathan Tintle, Ph.D. Associate Professor of Statistics and Dept. Chair Director for Research and Scholarship Dordt College Sioux Center, IA 51250 nathan.tintle(a)dordt.edu Phone: (712) 722-6264 Office: SB1612

9 years, 2 months

Anyone have access to the data on this study?

by Kevin Rees

Dear all, One of my colleagues passed around this New York Times article on gender roles in the workplace. http://www.nytimes.com/2015/02/08/opinion/sunday/sheryl-sandberg-and-adam-g… In the article they refer to a study in the Journal of Applied Psychology, in the following paragraph: In a study <http://psycnet.apa.org/journals/apl/90/3/431/> led by the New York University <http://topics.nytimes.com/top/reference/timestopics/organizations/n/new_yor…> psychologist Madeline Heilman, participants evaluated the performance of a male or female employee who did or did not stay late to help colleagues prepare for an important meeting. For staying late and helping, a man was rated 14 percent more favorably than a woman. When both declined, a woman was rated 12 percent lower than a man. Over and over, after giving identical help, a man was significantly more likely to be recommended for promotions, important projects, raises and bonuses. A woman had to help just to get the same rating as a man who didn’t help. I was interested in using this data during class, but the only way to access the data is to pay $12 for the article. Does anyone have the data that led to the above values that we could use in a simulation experiment? Thanks for your help, Kevin -- Kevin Rees Math Department Chair Marin Academy www.ma.org 415-482-3260

9 years, 2 months

Re: [SBI] Happy Groundhog Day! What happened in your introductory statistics class today?

by michelle_sisto

Hi Everyone, It has been a pleasure reading this thread all week. Unfortunately I'm not teaching Intro Stats right now. However, I am teaching VBA programming in Excel to Master of Finance students and we use an awful lot of simulation and statistics. The class consists of 3 hour sessions in a computer lab, once a week over 6 weeks. Yesterday in class (week 4) the students worked with 10 years of monthly adjusted closing prices from two stocks. They had to write a program to find monthly returns of the stocks, the means and variances of each, and then generate portfolios of the two stocks by varying weights to each in increments of 10% or an increment input by use. Lastly, they found the minimum variance portfolio. After getting the programming down and recalling the basic gist of a two asset portfolio, they created histograms of each stock's returns to see if modeling the returns as a normal distribution may be reasonable. After which, they simulated new stock return data by generating random returns from a normal distribution and a t-dist with same mean and variance of original sample returns. They examined how the efficiency frontier and minimum variance portfolio varied with new data. Homework for next time is to expand the exercise further by introducing investment in two stocks and a "risk free" asset. Here we'll play around a good bit with how varying the interest rate of the risk free asset impacts the portfolio composition. While it isn't quite on topic - thought I'd share. Also would love to have Robin's data set on population of countries to predict land area. I'm quite sure Monaco is an outlier on this one! Michelle Sisto EDHEC Business School Nice, France From: sbi-bounces(a)causeweb.org To: sbi(a)causeweb.org Cc: Date: Mon, 02 Feb 2015 21:50:45 -0500 Subject: Re: [SBI] Happy Groundhog Day! What happened in your introductory statistics class today?  Allan, et al - Nice idea! Saw your message right after I came out of class and should have responded then when it was fresh. This was day 9 of a 42 class semester and we're finishing up the chapter on descriptive statistics/graphics (after initial classes on data production, sampling, experiments). First exam is later this week and first project (describing their own dataset) is also due at the end of the week. Today's topic was least squares regression (after doing scatterplots and correlation last class). Started with a Fathom demo where students put a movable line on a scatterplot to show the trend (we meet full time in a computer classroom), had Fathom show the "squares" and find SSE to see whose line was best. Then let them move their lines around to try to lower SSE until they found essentially the least squares line. Once they saw how to find the fit automatically in Fathom we looked at several situations: Hgt to predict Wgt (interpreting the slope), population of countries to predict land area (showing influential points/outliers), presidential approval rating as a predictor of election margin, page number in Consumer Report Guide to predict fuel capacity of a car (no relationship). They then did another Fathom demo, dragging a point around to see the effect on the least squares line, especially when the the point became very influential. We finished up by introducing r^2 as the proportion of variability in response explained by the predictor. This involved one more Fathom demo where they made the movable line horizontal to see that the "best" constant is the mean, giving the total variability as its sum of squared errors, then found the "improvement" with the least squares line to measure the variability explained by the predictor. Lots of Fathom today, but that changes next class (Wednesday) when we switch to StatKey and start in on simulations to lead to bootstrap confidence intervals - a topic more relevant to this list. Robin Lock St. Lawrence University On 2/2/2015 12:34 AM, Allan Rossman wrote: Happy Groundhog Day! I continue to find it inexplicable that neither private colleges nor public universities see fit to cancel classes out of respect for this august occasion. But this year I've decided to try to make the best of this lamentable oversight, and I need your help! I think it might be fun to ask introductory statistics teachers to compare notes on what's happening in their classes on one particular day. What better day than Groundhog Day for revisiting the same question over and over, and over and over, and over and over, from multiple perspectives? I'm writing this after Groundhog Day has officially begun in Punxsutawney, Pennsylvania, but it's shortly after 9pm on Super Bowl Sunday here in California. So, to get the ball rolling on this whimsical idea (I strongly prefer the word "whimsical" to "silly" in this context), I'll use future tense to anticipate what will happen in my class on Monday. I plan to be sound asleep when Punxsutawney Phil makes his celebrated prognostication. (Too much information: Thirty years ago I did indeed make the trek to Gobbler's Knob with my future bride before sunrise on February 2, but I won't be up so early or anywhere near Punxsutawney this year!) My introductory students and I in STAT 217-09 at Cal Poly will begin the fifth week of our ten week term on February 2 by finishing up a discussion of principles of well-designed experiments. We’ll discuss a study conducted at Harvard about whether students spend $50 differently depending on whether they’re told that it’s a “tuition rebate” or “bonus income.” Then we’ll consider one of the first studies of the drug AZT for reducing mother-to-child transmission of HIV. We’ll culminate this discussion by collecting some in-class data on a very simple randomized experiment investigating whether grouping of letters can affect memory. All students will receive the same 30 letters in the same order, but some will find convenient, recognizable three-letter groupings and others will see more irregular groupings of letters. Then I expect to have time to introduce a study about whether swimming with dolphins is beneficial to patients who suffer from clinical depression. We'll discuss the design of the study and do a quick exploration of the 2x2 table of results, setting the stage for simulating a randomization test to assess whether the difference between success proportions in two treatment groups is statistically significant. Carrying out this simulation in class, using cards and then an applet, will have to wait until February 3 when the excitement of the momentous day has passed. (Or who knows, perhaps my students and I will find when we awake on Tuesday that we are destined to magically relive Monday again and again...) Please indulge me in this fanciful exercise by replying to this Simulation-Based Inference listserv with a description of what happened, or will happen, in your introductory statistics class on Groundhog Day 2015. Maybe we statistics teachers will learn something interesting by exchanging this information and reflecting on the variety of responses. Even if not, we can honor the grand tradition of Groundhog Day by engaging in a substantially less grand but only marginally more silly (oops, I mean whimsical) one. With best wishes for the special day and for an early spring (to those of you who must endure winter), Allan Rossman -- Allan J. Rossman Professor and Chair Statistics Department Cal Poly San Luis Obispo, CA 93407 arossman(a)calpoly.edu http://statweb.calpoly.edu/arossman/ _______________________________________________ SBI mailing list SBI(a)causeweb.org https://www.causeweb.org/mailman/listinfo/sbi -- Robin Lock Burry Professor of Statistics St. Lawrence University

9 years, 2 months

Re: [SBI] Groundhog Day, and a question about simulation methods

by Homer White

Hello Everyone, It has been a joy to read about of the great data sets and activities! I did not have time to respond yesterday, but here goes now. I've got an introductory class with 26 students, and we meet all the time in a computer classroom. Inspired by the Mosaic Project folks, we teach with R in the R Studio Server environment. Our approach to simulation-based inference is about 60% if of the way from traditional inference towards Locke5/Intro to Statistical Investigations. We do some simulation-based inference very early in the course -- binomial stuff, on the first day of class, in fact -- and we try again to work it in early with the chi-square test for the relationship between two factor variables. We're in that unit now, so students have played a couple of times with a "slow-simulation" app to get an idea of the null distribution of the chi-square statistic; subsequently they have been exposed to the standard chi-square test where the null distribution is approximated by a chi-square density curve. They are told that it was quite a godsend for Mr. Pearson to have stumbled on such a family of approximating curves, because Mr. Pearson had no access whatsoever to computing machinery. Groundhog Day began with a little come-to-Jesus chat about the first data analysis report, which the students tackled over the weekend. The project involved looking at some data from a Current Population Survey and to investigate the relationship between hourly wages and such factors as sex, union membership status, race, etc. Apparently there is a rule at my College that during Greek Rush Week critical thinking is forbidden, including the act of determining the type of variables involved in your research question prior to choosing your analytical tools. Accordingly about a third of the students had attempted to make bar charts and cross-tables to investigate, for example, whether men or women earn more, even though wage is a numerical variable. So we cleared that up, I hope. Harrumph. On with the intended show. Today's plan is to revisit simulation one more time, in a situation where you really need it (rather small number of observations). I bring up the "ledge-jump" data (#59 in the classic Handbook of Small Data Sets). a social psychologist studied 21 incidents in Britain involving a person threatening to leap from the ledge of a building or other high structure. The idea was to see what factors might affect the behavior of the crowd that gathers in the street below. To forestall morbid thoughts among students I get up on a nearby table and assure them through role-play that nobody really gets hurt: the fire truck comes right away and the firemen teeter back and forth with their big yellow trampoline, your rabbi, psychiatrist and spouse are phoned and within minutes they are leaning out of one nearby windows, soothing words are spoken, sage advice is given, hope is restored. Eventually they talk you back inside. But in the meantime a crowd has gathered. Sometimes they wait more or less in silence, appropriately mindful of the seriousness of the situation playing out above. Sometimes, though, they begin to bait the would-be jumper (muster up Cockney accent): "Go on, jump will ya?" In the 21 incidents under study, the following was found: weather/crowd Baiting Polite cool 2 7 warm 8 4 Discussion, with students ( me still on table): Me: Somebody could say that, for one reason or another, a crowd is more likely to bait in warm weather. Others might say that the outcome of these 21 incidents had nothing to do with weather, but is just the result of random variation in other factors -- above and beyond the weather at each particular incident. Can you think of any other things besides the weather that might affect crowd behavior? Student: How many people show up to watch. The more that show up, the more likely there jerk who will yell "jump' and get the rest of 'em started. Student: How long they have to wait. Maybe if they stand around a long time they'll get impatient. Student (looking right at me, still on table): What about the dorkiness of the would-be jumper? Me: Uh, maybe. Gee, thanks, Zach. I get down and we work it out on the blackboard: if weather has nothing to do with crowd behavior, then our best guess based on the data is that in each incident, regardless of weather, there is a 10/21 chance for the crowd to bait. The chi-square test function that the class uses has built-in provisions for simulation, of three possible types: * "fixed": the rows sums in the simulated table are constrained to be the rows sums of the observed table, and you determined the probability of each outcome in the columns by pooling the data, as we just did to get the 10/21 figure. * "double-fixed": both the row and column sums of the simulated table are constrained to be equal to the row and column sums of the observed table. * "random": neither row nor column sums are constrained, and the probability of a simulated observation landing in a particular cell is the observed cell count divided by the grand total of the table. "random" make sense when the observed data are a random ample a larger population, and chance comes into play just in the matter of who gets into the sample. For example, if you randomly sample people and ask their sex and where they prefer to sit a in classroom (front, middle or back), then chance is not in how a fixed person will respond but in whether or not that person gets into the sample. "double-fixed" (corresponding to the way simulation is done in R's chisq.test(), and probably in many other software systems as well), appears to be ideally suited for randomized experiment in which the Null hypothesis imagines that a subject's response is the same regardless of which treatment group one is placed into. In that case a different random assignment of subjects to treatment groups might result in a different table, but the row and column sums would be the same as for the table we observe in the actual experiment. "fixed" seems to be the right thing for the ledge-jump situation, if we assume that the 21 incidents weren't sampled randomly out of some larger population, that they were the only 21 incidents that occurred under the period of study in the region under study. In that case the weather at the time of each incident simply was it was, and chance comes into the production of the observed table through random variation in all other factors (conditional upon the weather). So we do simulation with the "fixed" option. Everybody's P-value comes in around 5%, so we decide that don't have overwhelming evidence that weather and crowd behavior are related. Now I come round to my questions. When we teach inference though simulation, we don't want it to become another "black box" for students. We want them to see that the simulation method generates simulated data that reasonably could occur if the study were to be conducted in a hypothetical world where the Null hypothesis is definitely true. Hence we the simulation method has to model, quite transparently, the role that we think chance played -- if the Null is true -- in giving us the data we actually see. But there appears to be controversy among statisticians as to which simulation method is best to use for contingency tables. (See e.g., Agresti, Categorical Data Analysis Third Edition section 3.5.6). I suppose that sometimes it's possible for a particular simulation method not to model the role of chance very well, but to possess superior statistical properties nonetheless, maybe even be the state-of-the art method. (This situation seems to occur also in bootstrap hypothesis testing, where the more preferred re-sampling method is rather more difficult to justify intuitively than is the "naive" re-sampling method.) Where does that leave us in teaching? Do we stick with simulation methods that model the role of chance intuitively? In that case we may get rather far into the weeds (after all, three options for simulation in the two-factor is alot for students to handle so early in the course), and we also end up, from time to time, using methods that won't be recommended in data analysis applications down the road. On the other hand if we employ simulation methods without regard to how intuitively they model the presumed role of chance variation in the production of the data, then we are back to using statistical procedures as black boxes that don't convey insight to students at the introductory level. My dilemma may be due in part to a lack of formal statistical training. Has anyone else found themselves puzzled by similar questions? Homer S. White Professor of Mathematics Georgetown College, KY 40324 502-863-8307 Notice: This message may contain confidential information and is intended for the person/entity to whom it was originally addressed. Any use by others is strictly prohibited. If you received this email in error, please permanently delete it and disregard.

9 years, 2 months

Happy Groundhog Day! What happened in your introductory statistics class today?

by Allan Rossman

Happy Groundhog Day! I continue to find it inexplicable that neither private colleges nor public universities see fit to cancel classes out of respect for this august occasion. But this year I've decided to try to make the best of this lamentable oversight, and I need your help! I think it might be fun to ask introductory statistics teachers to compare notes on what's happening in their classes on one particular day. What better day than Groundhog Day for revisiting the same question over and over, and over and over, and over and over, from multiple perspectives? I'm writing this after Groundhog Day has officially begun in Punxsutawney, Pennsylvania, but it's shortly after 9pm on Super Bowl Sunday here in California. So, to get the ball rolling on this whimsical idea (I strongly prefer the word "whimsical" to "silly" in this context), I'll use future tense to anticipate what will happen in my class on Monday. I plan to be sound asleep when Punxsutawney Phil makes his celebrated prognostication. (Too much information: Thirty years ago I did indeed make the trek to Gobbler's Knob with my future bride before sunrise on February 2, but I won't be up so early or anywhere near Punxsutawney this year!) My introductory students and I in STAT 217-09 at Cal Poly will begin the fifth week of our ten week term on February 2 by finishing up a discussion of principles of well-designed experiments.We’ll discuss a study conducted at Harvard about whether students spend $50 differently depending on whether they’re told that it’s a “tuition rebate” or “bonus income.”Then we’ll consider one of the first studies of the drug AZT for reducing mother-to-child transmission of HIV.We’ll culminate this discussion by collecting some in-class data on a very simple randomized experiment investigating whether grouping of letters can affect memory. All students will receive the same 30 letters in the same order, but some will find convenient, recognizable three-letter groupings and others will see more irregular groupings of letters. Then I expect to have time to introduce a study about whether swimming with dolphins is beneficial to patients who suffer from clinical depression. We'll discuss the design of the study and do a quick exploration of the 2x2 table of results, setting the stage for simulating a randomization test to assess whether the difference between success proportions in two treatment groups is statistically significant. Carrying out this simulation in class, using cards and then an applet, will have to wait until February 3 when the excitement of the momentous day has passed. (Or who knows, perhaps my students and I will find when we awake on Tuesday that we are destined to magically relive Monday again and again...) Please indulge me in this fanciful exercise by replying to this Simulation-Based Inference listserv with a description of what happened, or will happen, in your introductory statistics class on Groundhog Day 2015. Maybe we statistics teachers will learn something interesting by exchanging this information and reflecting on the variety of responses.Even if not, we can honor the grand tradition of Groundhog Day by engaging in a substantially less grand but only marginally more silly (oops, I mean whimsical) one. With best wishes for the special day and for an early spring (to those of you who must endure winter), Allan Rossman -- Allan J. Rossman Professor and Chair Statistics Department Cal Poly San Luis Obispo, CA 93407 arossman(a)calpoly.edu http://statweb.calpoly.edu/arossman/

9 years, 2 months

Groundhog Day

by Sean Bradley

It's not exactly what you asked for, Allan, but still in the Punxsutawney spirit -- from the Washington Post: http://www.washingtonpost.com/blogs/wonkblog/wp/2015/01/31/40-years-of-grou… Cheers, Sean Bradley Clarke University Dubuque Iowa

9 years, 2 months

Re: [SBI] Happy Groundhog Day! What happened in your introductory statistics class today?

by Nathan Tintle

SBI members, I'm teaching an 8-week 'accelerated' intro stat course this semester for students who've had calculus or AP statistics and am in week 4, which means I'm about halfway. The course is entirely online this semester so we don't have class 'today' per se, but are working this week on comparing two group proportions---seeing, for the first time, a permutation test as a way to simulate the null hypothesis (we've done one-sample inference since week one). Like Allan, I'll be doing the swimming with dolphins activity among others. Other highlights this week include (1) A two-proportion Z test (as a convenient mathematical approximation to the permutation test---with some extra data conditions needed), (2) Introducing R (we've been using web applets all semester so far but students will be introduced to R use on their projects if they wish) and (3) Reading and writing on the difference between mathematics (primarily deductive reasoning) and statistics (primarily inductive reasoning), and how this relates to what we can and can't learn from statistics, etc. etc (we can do this already because we've been doing statistical inference for 4 weeks already!) Great to hear from others of you about the innovative/interesting things you're doing in the class! On Sun, Feb 1, 2015 at 11:34 PM, Allan Rossman <arossman(a)calpoly.edu> wrote: > Happy Groundhog Day! > > I continue to find it inexplicable that neither private colleges nor > public universities see fit to cancel classes out of respect for this > august occasion. But this year I've decided to try to make the best of > this lamentable oversight, and I need your help! > > I think it might be fun to ask introductory statistics teachers to compare > notes on what's happening in their classes on one particular day. What > better day than Groundhog Day for revisiting the same question over and > over, and over and over, and over and over, from multiple perspectives? > > I'm writing this after Groundhog Day has officially begun in Punxsutawney, > Pennsylvania, but it's shortly after 9pm on Super Bowl Sunday here in > California. So, to get the ball rolling on this whimsical idea (I strongly > prefer the word "whimsical" to "silly" in this context), I'll use future > tense to anticipate what will happen in my class on Monday. I plan to be > sound asleep when Punxsutawney Phil makes his celebrated prognostication. > (Too much information: Thirty years ago I did indeed make the trek to > Gobbler's Knob with my future bride before sunrise on February 2, but I > won't be up so early or anywhere near Punxsutawney this year!) > > My introductory students and I in STAT 217-09 at Cal Poly will begin the > fifth week of our ten week term on February 2 by finishing up a discussion > of principles of well-designed experiments. We’ll discuss a study > conducted at Harvard about whether students spend $50 differently depending > on whether they’re told that it’s a “tuition rebate” or “bonus income.” Then > we’ll consider one of the first studies of the drug AZT for reducing > mother-to-child transmission of HIV. We’ll culminate this discussion by > collecting some in-class data on a very simple randomized experiment > investigating whether grouping of letters can affect memory. All students > will receive the same 30 letters in the same order, but some will find > convenient, recognizable three-letter groupings and others will see more > irregular groupings of letters. > > > > Then I expect to have time to introduce a study about whether swimming > with dolphins is beneficial to patients who suffer from clinical > depression. We'll discuss the design of the study and do a quick > exploration of the 2x2 table of results, setting the stage for simulating a > randomization test to assess whether the difference between success > proportions in two treatment groups is statistically significant. Carrying > out this simulation in class, using cards and then an applet, will have to > wait until February 3 when the excitement of the momentous day has passed. > (Or who knows, perhaps my students and I will find when we awake on Tuesday > that we are destined to magically relive Monday again and again...) > > Please indulge me in this fanciful exercise by replying to this > Simulation-Based Inference listserv with a description of what happened, or > will happen, in your introductory statistics class on Groundhog Day 2015. > Maybe we statistics teachers will learn something interesting by exchanging > this information and reflecting on the variety of responses. Even if > not, we can honor the grand tradition of Groundhog Day by engaging in a > substantially less grand but only marginally more silly (oops, I mean > whimsical) one. > > With best wishes for the special day and for an early spring (to those of > you who must endure winter), > > Allan Rossman > > > -- > Allan J. Rossman > Professor and Chair > Statistics Department > Cal Poly > San Luis Obispo, CA 93407arossman@calpoly.eduhttp://statweb.calpoly.edu/arossman/ > > -- Nathan Tintle, Ph.D. Associate Professor of Statistics and Dept. Chair Director for Research and Scholarship Dordt College Sioux Center, IA 51250 nathan.tintle(a)dordt.edu Phone: (712) 722-6264 Office: SB1612

9 years, 2 months

Re: [SBI] SBI Digest, Vol 3, Issue 1

by Todd Swanson

“Okay, campers, rise and shine, and don't forget your booties 'cause it's cooooold out there today.” Similar to Bill Murray’s Groundhog Day, we had a winter storm blow through Michigan the day before Groundhog Day. It was bad enough for all the schools in the area to close, except, of course, Hope College. So we met and discussed the benefits of random assignment in well run experiments. At the beginning of class, I had all the students flip a coin. I then passed out a sheet of paper and they wrote down whether they got heads or tails, their height, and their sex. I lectured for a short bit about the benefits of random assignment, mostly in the context of the Physician’s Health Study and briefly talked about blocking. Then I put the data collected in class into an applet so we could compare the distribution of heights and the distribution of sex between the heads and the tails group. It worked very well since each pair of distributions were quite similar. We then opened up an applet that simulated the same thing we just did, but could look at a distribution of the outcomes of many such random assignments. Finally we worked on a short exploration discussing how students that write in cursive on the SAT essay scored significantly higher than those that print. The exploration also discussed an experiment where identical essays, one printed and one written in cursive, were given randomly assigned to graders. The graders tended to grade the one’s written in cursive higher. So far this semester we have focused on a single proportion and looked at tests of significance, confidence intervals, generalizing to a population (random sampling), and now causation with random assignment. We are now ready to start inference involving two variables. Also, like Bill Murray’s Groundhog Day, once I did this with one section of my introductory statistics course, I did in all over again with my second. “They say we’re young and we don’t know …” Todd On Mon, Feb 2, 2015 at 6:55 AM, <sbi-request(a)causeweb.org> wrote: > Send SBI mailing list submissions to > sbi(a)causeweb.org > > To subscribe or unsubscribe via the World Wide Web, visit > https://www.causeweb.org/mailman/listinfo/sbi > or, via email, send a message with subject or body 'help' to > sbi-request(a)causeweb.org > > You can reach the person managing the list at > sbi-owner(a)causeweb.org > > When replying, please edit your Subject line so it is more specific > than "Re: Contents of SBI digest..." > > > Today's Topics: > > 1. Happy Groundhog Day! What happened in your introductory > statistics class today? (Allan Rossman) > > > ---------------------------------------------------------------------- > > Message: 1 > Date: Sun, 01 Feb 2015 21:34:10 -0800 > From: Allan Rossman <arossman(a)calpoly.edu> > To: Simulation-Based Inference <sbi(a)causeweb.org> > Subject: [SBI] Happy Groundhog Day! What happened in your introductory > statistics class today? > Message-ID: <54CF0C52.3010905(a)calpoly.edu> > Content-Type: text/plain; charset="utf-8"; Format="flowed" > > Happy Groundhog Day! > > I continue to find it inexplicable that neither private colleges nor > public universities see fit to cancel classes out of respect for this > august occasion. But this year I've decided to try to make the best of > this lamentable oversight, and I need your help! > > I think it might be fun to ask introductory statistics teachers to > compare notes on what's happening in their classes on one particular > day. What better day than Groundhog Day for revisiting the same > question over and over, and over and over, and over and over, from > multiple perspectives? > > I'm writing this after Groundhog Day has officially begun in > Punxsutawney, Pennsylvania, but it's shortly after 9pm on Super Bowl > Sunday here in California. So, to get the ball rolling on this > whimsical idea (I strongly prefer the word "whimsical" to "silly" in > this context), I'll use future tense to anticipate what will happen in > my class on Monday. I plan to be sound asleep when Punxsutawney Phil > makes his celebrated prognostication. (Too much information: Thirty > years ago I did indeed make the trek to Gobbler's Knob with my future > bride before sunrise on February 2, but I won't be up so early or > anywhere near Punxsutawney this year!) > > My introductory students and I in STAT 217-09 at Cal Poly will begin the > fifth week of our ten week term on February 2 by finishing up a > discussion of principles of well-designed experiments.We?ll discuss a > study conducted at Harvard about whether students spend $50 differently > depending on whether they?re told that it?s a ?tuition rebate? or ?bonus > income.?Then we?ll consider one of the first studies of the drug AZT for > reducing mother-to-child transmission of HIV.We?ll culminate this > discussion by collecting some in-class data on a very simple randomized > experiment investigating whether grouping of letters can affect memory. > All students will receive the same 30 letters in the same order, but > some will find convenient, recognizable three-letter groupings and > others will see more irregular groupings of letters. > > Then I expect to have time to introduce a study about whether swimming > with dolphins is beneficial to patients who suffer from clinical > depression. We'll discuss the design of the study and do a quick > exploration of the 2x2 table of results, setting the stage for > simulating a randomization test to assess whether the difference between > success proportions in two treatment groups is statistically > significant. Carrying out this simulation in class, using cards and > then an applet, will have to wait until February 3 when the excitement > of the momentous day has passed. (Or who knows, perhaps my students and > I will find when we awake on Tuesday that we are destined to magically > relive Monday again and again...) > > Please indulge me in this fanciful exercise by replying to this > Simulation-Based Inference listserv with a description of what happened, > or will happen, in your introductory statistics class on Groundhog Day > 2015. Maybe we statistics teachers will learn something interesting by > exchanging this information and reflecting on the variety of > responses.Even if not, we can honor the grand tradition of Groundhog Day > by engaging in a substantially less grand but only marginally more silly > (oops, I mean whimsical) one. > > With best wishes for the special day and for an early spring (to those > of you who must endure winter), > > Allan Rossman > > > -- > Allan J. Rossman > Professor and Chair > Statistics Department > Cal Poly > San Luis Obispo, CA 93407 > arossman(a)calpoly.edu > http://statweb.calpoly.edu/arossman/ > >

9 years, 2 months

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