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Showing posts with the label normal distributions

NYT's "What's going on in this graph?"

The New York Time's maintains The Learning Network, which contains news content that fits well into a variety of classrooms teaching a variety of topics.  Recently, they shared a good stats example. They created curves illustrating global climate change over time. The top graph illustrates a normal curve, with normal temperature as the modal value. But as we shift forward in time, hot days become modal and the curves no longer overlap. Sort of like the classic illustration of what a small to medium effect size looks like in terms of distribution overlap.  This graph is part of the NYT's "What's going on in this graph?" series , which are created and shared in partnership with the American Statistical Association.

Annenberg Learner's "Against All Odds"

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

Pew Research's "Growing Ideological Consistency"

This interactive tool from Pew research illustrates left and right skew as well as median and longitudinal data. The x-axis indicates how politically consistent (as determined by a survey of political issues) self-identified republicans and democrats are across time. Press the button and you can animate data, or cut up the data so you only see one party or only the most politically active Americans. http://www.people-press.org/2014/06/12/section-1-growing-ideological-consistency/#interactive The data for both political part goes from being normally distributed in 1994 to skewed by 2014. And you can watch what happens to the median as the political winds change (and perhaps remind your students as to why mean would be the less desirable measure of central tendency for this example). I think it is interesting to see the relative unity in political thought (as demonstrated by more Republicans and Democrats indicating mixed political opinions) in the wake of 9/11 but more politicall...

If your students get the joke, they get statistics.

Gleaned from multiple sources (FB, Pinterest, Twitter, none of these belong to me, etc.). Remember, if your students can explain why a stats funny is funny, they are demonstrating statistical knowledge. I like to ask students to explain the humor in such examples for extra credit points (see below for an example from my FA14 final exam). Using xkcd.com for bonus points/assessing if students understand that correlation =/= causation What are the numerical thresholds for probability?  How does this refer to alpha? What type of error is being described, Type I or Type II? What measure of central tendency is being described? Dilbert: http://search.dilbert.com/comic/Kill%20Anyone Sampling, CLT http://foulmouthedbaker.com/2013/10/03/graphs-belong-on-cakes/ Because control vs. sample, standard deviations, normal curves. Also,"skewed" pun. If you go to the original website , the story behind this cakes has to do w...

Cheng's "Okcupid Scraper – Who is pickier? Who is lying? Men or Women?"

People don't always tell the whole truth on dating websites, embellishing the truth to make themselves more desirable. This example of how OK Cupid users lie about their heights is a good example for conceptually explaining null hypothesis testing, t -tests, and normal distributions. So, Cheng, article author and data enthusiast, looked through OK Cupid data. In this article, she describes a few different findings, but I'm going to focus on just one of them: She looked at users' reported heights. And she found a funny trend. Both men and women seem to report that they are taller than they actually are. How do we know this? Well, the CDC collects information on human heights so we have a pretty good idea of what average heights are for men and women in the US. And then the author compared the normal curve representing human height to the reported height data from OK Cupid Users. See below... From http://nycdatascience.com/okcupid-scraper/, by Fangzhou Cheng  ...

Kristopher Magnusson's "Understanding the t-distribution and its normal approximation"

Once again, Kristopher Magnusson has combined is computer programming and statistical knowledge to help illustrate statistical concepts . His latest  interactive tool allows students to view the t-curve for different degrees for freedom. Additionally, students can view error rates associated with different degrees of freedom. Note that the critical region is one-tailed with alpha set at .05. If you cursor around the critical region, you can set the alpha to .025 to better illustrate a two-tailed test (in terms of the critical region at which we declare significance).  Error rates when n < 30 Error rates when n > 30 This isn't the first time Kristopher's interactive tools have been featured on this blog! He has also created websites dedicated to explaining effect size , correlation , and other statistical concepts .

minimaxir's "Distribution of Yelp ratings for businesses, by business category"

Yelp distribution visualization, posted by redditor minimaxir This data distribution example comes from the subreddit r/dataisbeautiful  (more on what a reddit is  here ). This specific posting (started by minimaxir) was prompted by several  histograms illustrating  customer ratings for various Yelp (customer review website) business categories as well as the lively reddit discussion in which users attempt to explain why different categories of services have such different distribution shapes  and means. At a basic level, you can use this data to illustrate skew, histograms, and normal distribution. As a more advanced critical thinking activity, you could challenge your students to think of reasons that some data, like auto repair, is skewed. From a psychometric or industrial/organizational psychology perspective, you could describe how customers use rating scales and whether or not people really understand what average is when providing customer feedba...

mathisfun.com's Standard Normal Distribution Table

Now, I am immediately suspicious of a website entitled "MathIsFun" (I prefer the soft sell...like promising teaching aids for statistics that are, say, not awful and boring). That being said, t his app. from mathisfun.com  may be an alternative to going cross-eyed while reading z-tables in order to better understand the normal distribution. mathisfun.com With this little Flash app., you can select z-scores and immediately view the corresponding portion of the normal curve (either from z = 0 to your z, up to a selected z, or to the right of that z). Above, I've selected z = 1.96, and the outlying 2.5% of the curve is highlighted.  Now, this wouldn't work for a paper and pencil exam (so you would probably still need to teach students to read the paper table) but I think this is useful in that it allows students to IMMEDIATELY see how z-scores and portions of the of the curve co-vary.