The Economist created interactive visualizations for various polling data related to the 2020 U.S. Presidential election.  While illustrating this data, they used different measures of central tendency and different confidence intervals. Like, it is one thing to say that Candidate A is polling at 47% with a margin of error of 3.2%. I think it is much more useful to illustrate what the CI is telling us about the likely true parameter, based on what we have collected from our imperfect sample. The overlap in confidence intervals when polling is essential to understanding polling.  How to use in class: 1) Electoral college predictions, illustrated with median, 60%, and 95% confidence intervals. Also, I like how this illustrates the trade-off between precision and the size of a confidence interval. The 60% CI is more narrow, but you are only 60% confident that it contains the true number of electoral college votes. Meanwhile, the 95% confidence interval is much wide but also more ...

I usually blog about funny examples for the teaching of statistics, but this example is for teachers teaching statistics. Normile, Bloesch, Davoli, & Scheer's recent publication, "Introducing the new statistics in the classroom" (2019) is very aptly and appropriately titled. It is a rundown on p-values and effect sizes and confidence intervals. Such reviews exist elsewhere, but this one is just so short and precise. Here are a few of the highlights: 1) The article concisely explains what isn't great or what is frequently misunderstood about NHST. 2) Actual guidelines for how to explain it in Psychological Statistics/Introduction to Statistics, including ideas for doing so without completely redesigning your class. 3) It also highlights one of the big reasons that I am so pro-JASP: Easy to locate and use effect sizes.

UPDATE 10/5/22: No paywall article that conveys the same information:  https://www.msn.com/en-us/weather/topstories/cone-of-confusion-why-some-say-iconic-hurricane-map-misled-floridians/ar-AA12Bqyp Did you know that hurricane prediction maps are confidence intervals? This is one of my examples that serves more as a metaphor than a concrete explanation for a statistic, so bear with me. The New York Times created a beautiful, interactive website (it looked exceptionally sharp on my phone). The website attempts to explain what hurricane prediction maps tell us, versus how people interpret hurricane prediction maps. The website is at NYT, so you probably will hit a paywall if you have already viewed three stories on the NYT website in the last month. As such, I've included screenshots here. Here is a map with the projected hurricane path. People think that the white line indicates where the hurricane will go, and the red indicates bad weather. They also think that the broader path...

Josh Katz and Kevin Quealy p ut together a cool interactive website to help users better understand their NYC commute . With the creation of this website, they also are helping statistics instructors illustrate a number of basic statistics lessons. To use the website, select two stations... The website returns a bee swarm plot, where each dot represents one day's commuting time over a 16-month sample.   So, handy for NYC commuters, but also statistics instructors. How to use in class: 1. Conceptual demonstration of the sampling distribution of the sample mean . To be clear, each dot doesn't represent the mean of a sample. However, I think this still does a good job of showing how much variability exists for commute time on a given day. The commute can vary wildly depending on the day when the sample was collected, but every data point is accurate.  2. Variability . Here, students can see the variability in commuting time. I think this example is e...

A tweet straight up solved a problem I encountered while teaching. The problem: How can I explain why the confidence interval area for a regression line is curved when the regression line is straight. This comes up when I use my favorite regression example.  It explains regression AND the power that government funding has over academic research . TL:DR- Relative to the number of Americans who die by gun violence, there is a disproportionately low amount of a) federal funding and b) research publications as to  better understand gun violence death when compared to funding and publishing about other common causes of death in America. Why? Dickey Amendment to a 1996 federal spending bill. See graph below: https://jamanetwork.com/journals/jama/article-abstract/2595514 The gray area here is the confidence interval region for the regression line. And I had a hard time explaining to my students why the regression line, which is straight, doesn't have a perfectly rectangula...

Holy smokes. How am I just learning about this amazing resource (thanks, Amy Hogan, for the lead) now? The folks over at Annenberg, famous for Zimbardo's Discovering Psychology series, also have an amazing video collection about statistics, called "Against All Odds" . Each video couches a statistical lesson in a story. 1) In addition to the videos , there are student and faculty guides to go along with every video/chapter. I think that using these guides, and instructor could go textbook free. 2) The topics listed approximate an Introduction to Statistics course. https://www.learner.org/courses/againstallodds/guides/faculty.html

This NPR story is about a survey conducted by the folks at Sesame Street. And that survey asked parents and teachers about kindness. If kids are kind, if the world is kind, how they define kindness, etc.. The NPR story is a round about way of explaining how we operationalize variables, especially in psychology. And the survey itself provides examples of forced choice research questions and dichotomous responses that could have been Likert-type scales. The NPR Story: The Children's Television Workshop, the folks behind Sesame Street, have employees in charge of research and evaluation (a chance to plug off-the-beat-path stats jobs to your students). And they did a survey to figure out what it means to be kind when you are a kid. They surveyed parents and teachers to do so. The main findings are summarized here . Parents and teachers are worried that the world isn't kind and doesn't emphasize kind. But both groups think that kindness is more important than academic a...

I have shared Kristoffer Magnusson's fantastic visualizations of statistical concepts here previously ( correlation , Cohen's d ). Here is another one that helps to explain confidence intervals , and how the likelihood of an interval containing true mu varies based on interval size as well as the size of the underlying sample. The site is interactive in two ways. 1) The sliding bar at the top of the page allows you to adjust the size of the confidence interval, which you can read in the portion of the page labeled "CI coverage %" or directly above the CI ticker. See below. 2) You can also change the n-size for the samples the simulation is pulling. The site also reports back the number of samples that include mu and the number of samples that miss mu (wee little example for Type I/Type II error). How to use it in class: Students will see how intervals increase and decrease in size as you reset the CI percentage. As the sample size increases, the range ...

This syllabus for  PSY 607: Everything is Fucked ,  made the rounds last week. The syllabus is for a course that  purports  that science is fucked. The course readings are a list of articles and books that hit on the limitations of statistics and research psychology ( p -values, shortcomings of meta-analysis, misuse of mediation, replication crisis, etc.). PSY 607 isn't an actual class ( as author/psychologist/blogger Srivastava explains in this piece from The Chronicle ) but it does provide a fine reading list for understanding some of the current debates and changes in statistics and psychology.  Most of articles are probably too advanced for undergraduates but perfectly appropriate for teaching graduat e students about our field and staying up to date as instructors of statistics. Here is a link to the original blog post/syllabus. 

Good data should inform our decisions. Even a really stressful decision. This site demonstrates this beautifully by providing UK pediatric hospital survival rates to aid the parents of children undergoing heart surgery. The information is translated for laypeople. They present statistical ideas that you and your students have heard of but without a lot of statistical jargon. The data is also explained very clearly. For example, they  present detailed hospital survival rates , which include survival ranges: So, it contains data from a given period. It includes the actual mortality rate and a range likely to have a valid mortality rate. So, essentially, they are confidence intervals but not precisely confidence intervals. In addition to this more traditional presentation of the data, the survival ranges are explained in greater detail in a video . I think this video is helpful because it describes the distribution of the sample mean and how to use them to estimate ac...

This headline is a good example of a) journalists misrepresenting statistics as well as b) confidence intervals/margin of error more broadly. See the headline below: In actuality, Bernie didn't exactly take the lead over Hillary Clinton. Instead, a Quinnipiac poll showed that 41% of likely Democratic primary voters in Iowa indicated that they would vote for Sanders, while 40% reported that they would vote for Clinton. If you go to the original Quinnipiac poll , you can read that the actual data has a margin of error of +/- 3.4%, which means that the candidates are running neck and neck. Which, I think, would have still been a compelling headline.  I used this as an example just last week to explain applied confidence intervals. I also used this as a round-about way of explaining how confidence intervals are now being used as an alternative/compliment to p -values. 

Geoff Cumming Geoff Cumming gave a talk at APS 2014 about the " new statistics " (reduced emphasis on p-value, greater emphasis on confidence intervals and effect sizes, for starters). This workshop is now available, online and free, from APS . The three hour talk has been divided into five sections, and each sections comes with a "Table of Contents" to help you quickly navigate all of the information contained in the talk. While some of this talk is too advanced for undergraduates, I think that there are portions, like his explanation of why p-values are so popular, p-hacking, confidence intervals can be nice additions to an Introduction to Statistics class.

Two prominent psychology journals are changing their standards for publication in order to address several long-standing debates in statistics (p-values v. effect sizes and point estimates of the mean v. confidence intervals). Here are the details for changes that the Association for Psychological Science is creating for their gold-standard publication, Psychological Science, in order to improve the transparency in data reporting. Some of the big changes include mandatory reporting of effect sizes, confidence intervals, and inclusion of any scales or measures that were non-significant. This might be useful in class when describing why p-values and means are imperfect, the old p-value v. effect size debate, and how one can bend the truth with statistics via research methodology (and glossing over/completely neglecting N.S. findings). These examples are also useful in demonstrating to your students that these issues we discuss in class have real world ramifications and aren't be...

One way of teaching about margin of error/confidence intervals is via political polling data. From  mvbarer.blogspot.com Here is a good site that has a break down of polling data taken in September 2012 for the 2012 US presidential election. I like this example because it draws on data from several well-reputed polling sites, includes their point estimates of the mean and their margin of errors. This allows for several good examples: a) the point estimates for the various polling organization all differ slightly (illustrating sampling error), b) the margin of errors  are provided, and c) it can be used to demonstrate how CIs can overlap, hence, muddying our ability to predict outcomes from point estimates of the mean. I tend to follow the previous example with this gorgeous polling data from Mullenberg College : This is how sampling is done, son! While stats teachers frequently discuss error reduction via big n , Mullenberg takes it a step further by o...

from http://hello-jessica.tumblr.com Who knew that Zoidberg was an ad hoc reviewer?