Posts Tagged statistics
Extracting Sunbeams from Cucumbers
Posted by mark in Basic stats & math on January 8, 2012
With this intriguing title Richard Feinberg and Howard Wainer draw readers of Volume 20, Number 4 into what might have been a dry discourse: How contributors to The Journal of Computational and Graphical Statistics rely mainly on tables to display data. Given that “Graphical” is in the title of this publication, it begs the question on whether this method of for presenting statistics really works.
When working on the committee that developed the ASTM 1169-07 Standard Practice for Conducting Ruggedness Tests, I introduced the half-normal plot for selecting effects from two-level factorial experiments. Most of the committee favored this, but one individual – a professor emeritus from a top school of statistics – resisted the introduction of this graphical tool. He believed that only numerical methods, specifically analysis of variance (ANOVA) tables, could support objective decisions for model selection. My comeback was to dodge the issue by simply using graphs and tables – this need not be an either/or choice. Why not do both, or merge them by putting number on to graphs – the best of both worlds?
“A heavy bank of figures is grievously wearisome to the eye, and the popular mind is as incapable of drawing any useful lessons from it as of extracting sunbeams from cucumbers.”
– Economists (brothers) Farquhar and Farquhar (1891)
In their article which can be seen here Feinberg and Wainer take a different tack (path of least resistance?): Make tables look more like graphs. Here are some of their suggestions for doing so:
- Round data to 3 digits or less.
- Line up comparable numbers by column, not row.
- Provide summary statistics, in particular medians.
- Don’t default to alphabetical or some other arbitrary order: Stratify by size or some other meaningful attribute.
- Call out data that demands attention by making it bold and/or bigger and/or boxing it.
- Insert extra space between rows or columns of data where they change greatly (gap).
Check out the remodeled table on arms transfers which makes it clear that, unlike the uptight USA, the laissez faire French will sell to anyone. It would be hard to dig that nugget out of the original data compilation.
Clickers allow students to vote on which answer is right for math questions
Posted by mark in Basic stats & math on October 12, 2011
Yesterday I attended a fun webinar on Interactive Statistics Education by Dale Berger of Claremont Graduate University. Because I was multitasking (aka “continuous partial attention” — ha ha) at work while attending this webinar my report provides just the highlights. However, you can figure out for yourself what they (the stats dept at Claremont) have to offer by going to this web page offering WISE (Web Interface for Statistics Education) tutorials and applets.*
After the presentation a number of educators brainstormed on interactive stats. David Lane of Rice U (author of many stat applets) suggested the use of “interactive clickers” – see this short (< 2 min.) newscast, for example. I wonder what happen when a majority vote for the wrong answer? For some teachers it might be easiest just to declare the most popular response as the correct answer. That would be consistent with the way things seem to be going in politics nowadays. ; )
*Just for fun try the Investigating the Central Limit Theorem (CLT) applet (click the link from the page referenced above or simply click here). This would be a good applet to provide when illustrating CLT using dice (such as is done in this in-class exercise developed by two professors from De Anza College). In this case, pick the uniform Population and sample size 2. Then Draw a Sample repeatedly, and, finally, just Draw 100 samples. Repeat this exercise with sample size 5 a la the game of Yahtzee (a favorite in my youth). Notice how as n goes up the distribution of averages becomes more normal and narrower. That’s the power of averaging.
Mind-reading fish know I am out to catch them
Last week I enjoyed a relaxing sojourn up in the north woods of Wisconsin. The resort encompasses its own pristine pine-ringed lake featuring a 26-foot fishing hole. Just before I headed off for my vacation I read this Scientific American report on The Mind-Reading Salmon: The True Meaning of Statistical Significance
. Although I think they meant to be disrespectful of p-values in this case, my feeling, based on empirical evidence from a large sample size – hundreds of unsuccessful casts of my lure around the shore and over the hole, is that some fish living in isolated areas have developed mental telepathy. How else do they avoid being caught?
PS. Here’s a picture of me in happier days at a different lake last summer. My brother-in-law insisted that the first one to catch a crappie would have to kiss it. Evidently this fish thought it might be fun to try, knowing I’d then release it back into the lake.
An Easter experiment for those who still believe a bunny bears eggs* *(Beware of the green ones!)
Today’s Saint Paul Pioneer Press “Bulletin Board” provides an idea on how to provide some added delight for any children who still believe in the Easter Bunny: Have them plant one of their jelly beans, then watch for it to grow into a lollipop. Doesn’t that sound like a fun experiment!
By the way, be careful with the green jelly beans – they cause acne (p<0.05) according to this exhaustive statistical-study of every available color.
Armed and dangerous – switchblades and statistics
Posted by mark in Basic stats & math on April 11, 2011
(Warning: Quirky material ahead =>)
Seeing this CBS News about Maine legalizing switchblades for one-armed people reminded me of a riddle about limbs that’s posed by some statisticians for educational purposes. Here it is: “The great majority of people in [fill in your country here] have more than the average number of [choose either arms or legs here].”
For an answer {UK, legs}, see this posting on averages by Kevin McConway, Professor of Applied Statistics in the Department of Mathematics and Statistics at The Open University. I heard this riddle also from Hans Rosling in his BBC TV program on “The Joy of Statistics.”* He spoke of his home country of Sweden, whose inhabitants on average have 1.999 legs.
I’m quitting while I’m ahead. Oops, this makes me wonder if I have an average number of heads – a scary thought, my hunch being that I’m below average for this. I never imagined that averages could be so creepy!
*See this StatsMadeEasy blog on Rosling
Supreme Court overturns tyranny of statistical significance
In today’s Wall Street Journal, The Numbers Guy (Carl Bialik) reports on a unanimous ruling by the Supreme Court that companies cannot hide behind statistical significance (lack thereof in this case) as an excuse for nondisclosure of adverse research. He passes along this practical advice:
“A bigger effect produced in a study with a big margin of error is more impressive than a smaller effect that was measured more precisely.”
– Stephen Ziliak, economics professor
However, this legal analysis of the ruling cautions that statistical significance remains relevant for assessing materiality of an adverse event.
Given all this, we can be certain of only one thing – more lawsuits.
Fun graphs and charts on names: How popular is yours and where is it populated?
My latest issue of National Geographic came with this fascinating mapping of population by surname. Seeing “Anderson” looming large over Minnesota did not surprise me, but I didn’t realize how many of us “snow birds” had permanently escaped to California. Take a look and see if you can locate any of you long-lost wander-kin around the USA.
The Junk Charts blog, one of my favorites, gave a generally favorable review of the “Nat-Geo” name chart, but they recommended an even-better one – the Baby Name Wizard, which plots the popularity of first names over the last 130 years.
I am expecting my first grandchild this summer, so there’s been lots of talks about names lately, thus this statistical chart caught my eye. You, too, may find it interesting. I suggest you start by hovering mouse over the widest streams (blue for boy, pink for girl) at the left (John, Mary, etc)* and then see how their popularity changes over the past 130 years. A tip: Click the graph to see trends for any given name, or enter it directly. Press “x” to get out of any specific name field (or type in another). I typed in my name and saw an explosion of popularity in mid-20th century, but now it’s fading away. The same holds true for my sister Nancy and my wife Karen – we all get tagged as baby-boomers straight away.
If you think there’s any chance of your name ranking in the top 1,000 for popularity in the USA at any time since 1880, type it in. How do you do, _______ (<= name here)?
Yankees leverage wins by throwing money at their players
Posted by mark in sports, Uncategorized on September 26, 2010
Today’s New York Times sports section provided this intriguing graphic on “putting a price tag on winning”. Their hometown Yankees stand out as the big spenders by far. It paid off in wins over the last decade – the period studied. However, if you cover up the point depicting the Yanks, the graph becomes far less compelling that salary buys wins – mainly due to counteractive results enjoyed by two low-payroll teams: The Minnesota Twins and the Oakland Athletics.
I found similar patterns and, more importantly, data to reproduce these, in this study of MLB Payroll Efficiency, 2006-2008 by Baseball Analyst Rich Lederer.
No offense to Rich or the NY Times – it is the damn Yankees (sorry but I am weary of them defeating the Twins every post-season) who are the blame for this flaw in drawing conclusions from this data: One point exerts undue leverage on the fit, which you can see on this diagnostic graph generated by Design-Expert® software.
However, after doing the obvious thing – yanking the Yanks from the data, the conclusion remains the same: Higher payroll translates to more wins in Major League baseball. Here are the stats with/without the Yankees:
- R-squared: 0.41/0.34
- Wins per $ million of payroll (slope of linear fit): +0.13/0.16
In this case, a high leverage point does not exert the potential influence, that is, the end result does not change due to its location. If you’d like to simulate how leverage impacts fit, download this educational simulation posted by Hans Lohninger, Associate Professor of Chemometrics at Vienna University of Technology.
What value for p is right for testing t (or tasting tea)?
Posted by mark in Basic stats & math, history on July 25, 2010
Seeking sponsors for his educational website, statistician Keith Bower sent me a sample of his work – this 5 minute podcast on p-values. I enjoyed the story Keith tells of how Sir Ronald Fisher, who more-or-less invented design of experiments, settled on the p value of 5% as being a benchmark for statistical significance.
This sent me scurrying over to my office bookshelf for <em>The Lady Tasting Tea – a delightful collection of stories* compiled by David Salsburg.** Page 100 of this book reports Fisher saying that below p of 0.01 one can declare an effect (that is – significance), above 0.2 not (that is – insignificant), and in-between it might be smart to do another experiment.
So it seems that Fisher did some flip-flopping on the issue of what value of p is needed to declare statistical significance.
PS. One thing that bothers me in any discussion of p-values is that it is mainly in the context of estimating the risk in a test of the null hypothesis and almost invariably overlooks the vital issue of power. For example, see this YouTube video on Understanding the p-value. It’s quite entertaining and helpful so far as it goes, but the decision to accept the null at p > 0.2 is based on a very small sample size. Perhaps the potential problem (underweight candy bars), which one could scope out by calculating the appropriate statistical interval (confidence, prediction or tolerance), merits further experimentation to increase the power. What do you think?
*In the title story, originally told by Sir Ronald Fisher, a Lady claims to have the ability to tell which went into her cup first—the tea or the milk. Fisher devised a test whereupon the Lady is presented eight cups in random order, four of which are made one way (tea first) and four the other (milk first). He calculates the odds of correct identification as 1 right way out of 70 possible selections, which falls below the standard 5% probability value generally accepted for statistical significance. Salsburg reveals on good authority (H. Fairfield Smith–a colleague of Fisher) that the Lady identified all eight cups correctly!
**Salsburg, who worked for some years as a statistician at a major pharmaceutical company offers this amusing anecdote from personal experience:
“When I first began to work in the drug industry…one…referred to…uncertainty [as] ‘error.’ One of the senior executives refused to send such a report to the U.S. Food and Drug Administration [FDA]. ‘How can we admit to having error in our data?’ he asked [and]…insisted I find some other way to describe it…I contacted H.F. Smith [who] suggested that I call the line ‘residual’…I mentioned this to other statisticians…and they began to use it…It seems that no one [in the FDA, at least]…will admit to having error.”
A breadth of fresh error
Posted by mark in politics, Uncategorized on June 20, 2010
This weekend’s Wall Street Journal features a review by Stats.org editor Trevor Butterworth of a new book titled Wrong: Why Experts Keep Failing US – And How to know When Not to Trust Them. The book undermines scientists, as well as financial wizards, doctors and all others who feel they are almost always right and thus never in doubt. In fact, it turns out that these experts may be nearly as often wrong as they are right in their assertions. Butterworth prescribes as a remedy the tools of uncertainty that applied statisticians employ to good effect.
Unfortunately the people funding consultants and researchers do not want to hear any equivocation in stated results. However, it’s vital that experts convey the possible variability in their findings if we are to gain a true picture of what may, indeed, transpire.
“Error is to be expected and not something to be scorned or obscured.”
– Trevor Butterworth
