Other Statistical Sites

Dr. Gary C. Ramseyer

Dr. Gary C. Ramseyer was an Emeritus Professor of Psychology with a specialty of statistics and measurement at Illinois State University.

Dr. Ramseyer began teaching at Illinois State in 1965 and retired in 1998. Prior to joining ISU, he taught at the University of Iowa in the College of Education and at University High School in Iowa City, Iowa.


Dr. Ramseyer passed away suddenly in the spring of 2012. In his honor, his websites are being managed by his daughter Vicki S. (Ramseyer) Morrow.

Gertrude M. Cox Hall

Welcome To The Gertrude M. Cox Commemorative Hall!

Gertrude Mary Cox (1900 - 1978) was the first female elected into the International Statistical Institute and was president of the American Statistical Association. She was also the founder of the department of Experimental Statistics at North Carolina State University. Her most important and influential work was in the area of experimental design. In 1950 she and William Gemmell Cochran published a joint work entitled Experimental Design which became a classic text. For additional information on Gertrude M. Cox, refer to http://www.agnesscott.edu/lriddle/women/cox.htm

Now displaying the humorous side of Statistics...


Then there was the story of the sociological statistician who retired early from his teaching position at the university. He had grown up on the farm as a youth and still feeling quite chipper, decided to buy a large dairy farm in southern Wisconsin. After a short time the milk and cheese from his herd of cows became famous for miles around. Since his research at the university had demanded the use of many Chi-Square Goodness of Fit Tests, he thought he should commemorate all these procedures. Every year he invited the public to what became the most publicized and extravagant wine and cheese festival in Wisconsin. It was fondly called the GOODNESS OF TIT FEST!!!!

Some of you experienced statisticians out there may well of heard this little reversal of letters before but not my story behind it. Maybe you heard it back in your graduate training days and all the snickers that accompanied it. I know I did. However, I always thought the original moniker was an awkward use of words and should have been renamed (Hear that Mr. Karl Pearson). The fact remains that this test is one of the most frequently appearing procedures in the literature, particularly in testing the independent of two nominal or ordinal variables.



The secretary of defense gave the president his daily briefing. He concluded by saying: "Yesterday, 3 Brazilian soldiers were killed."

"Oh No!" the president exclaimed, "That's Terrible!"

His staff was stunned at this display of emotion, nervously watching as the president sat, his head in his hands.

Finally, the president looked up and asked, "Just how many is a brazillion?"

Here is another example of the ubiquitous innumeracy that is gripping this country. Thanks to my good friend Merle (Pear Diver) Howard, an emeritus Professor of Speech Pathology at Illinois State University, for forwarding this little story to me. I wonder if the White House could us a good speech pathologist as a consultant these days?


A freshman college student had the misfortune of having several auto accidents while living at home with his parents. One day his statistics professor told his class that 83% of all auto accidents happen within 20 miles of your home. The very next day the student moved 22 miles from home and never had another accident during his entire college career!!!

This young man found a neat way to beat the odds. I just wonder what would have happened had his parents decided to move in with him? Thanks go out to Jon Holmen, a student at Illinois State University, for passing along this story.



Knock! Knock!

Who's there?


Em who?

MLE! The Maximum Likelihood Estimator!

This is the second Knock! Knock! joke that has met very stringent criteria to enter the Gallery. I promise to scrutinize with even higher standard future jokes of this genre. Many thanks to Gavin Desir for sending me this joke from the University College in London, England, via one of the last transcontinental telegrams.



A cannibal goes shopping for dinner. his wife wants to prepare brains that day. At the butcher's shop he is told that there are three prices: First, there is statistician's brain at 1 dollar per pound. Secondly, they have lawyer's brain at 2 dollars a pound. And finally, he can buy politician's brain at 4 dollars a pound.

The cannibal is bewildered at this price range and asks the butcher, "Why on earth should a pound of politician brain cost that much more than statistician brain? Do you really think that the quality is so much better?"

The butcher replies, "No, but if you count how many politicians it takes to get a pound..."

I wonder if the cannibal should agree to a plea bargain and buy the lawyer brain? This ghoulish joke was forwarded to me by a reader of the Gallery who wished to remain anonymous because this was not his creation. Many thanks to the sender anyway.



"The best thing about being a statistician," J.W. Tukey once told a colleague, " is that you get to play in everyone's backyard."

The colleague retorted, "But Professor Tukey, that is why a statistician is considered a Peeping-Top by many guardians of sensitive data in the world!!!!"

The first statement is an actual quote. The second is my own fictitious retort to further the humor. For a capsule version of the amazing life and astonishing contributions of one of the greatest American Statisticians that ever lived see Tukey.



Knock! Knock!

Whose there? (without opening the door)

"The census taker."

"Go away -- I don't want my senses taken."

"No, you don't understand, I just want to survey you."

"A statistical sample of one isn't valid -- go away."

"You aren't the only one."

"So you are bothering a whole bunch of people, go away."

"Look you are unique and I don't want to miss you in the survey."

"How do you know I'm unique when you haven't surveyed me yet?"

"O, I don't know you are unique, but you might be."

"You mean you think I'm an oddball."

"No, maybe more like an outlier."

"Now you are calling me an out and outlier, go away."

"No, I mean you are far from the average Joe."

"I hope so, I'm Sally."

"Look Sally, we are trying to get population data, how many people live here?"

"Gosh, how would I know, I think there are about 15 thousand in Smugville."

"No, I mean in this house!"

"Oh, that's a question of a different nature."

"So, how many?"

"Sometimes one, sometimes two, sometimes four, now -- go away."

"No, I need a precise number."

"Ok, how about 1.34"

"How did you come up with that?"

"I live here sometimes during the week, my sister visits me on weekends, and my mother visits me every second week, my two cats are sometimes here, and my ... and that's none of your business."

"Thanks Sally have a great day."
(censor taker wrote -- "NO PERSONS LIVING HERE -- UNOCCUPIED."

This is hilarious. It reminds me of the Abbott and Costello "Who's on first?" routine. Also it has to be the longest Knock! Knock! joke ever written. Many thanks to Collin Carbno for sending this clever exchange from Saskatchewan Canada.



A Statistics Professor had just completed an exhaustive review session for his students the day before the exam. At the end of the session, he stated emphatically , "One more thing! The exam is open-book and don't forget to bring a TABLE to the test." The students were relieved to hear this bit of good news that TABLES could be used.

Next day, the students filed into the room with textbooks and materials under their arms. The Professor greeted them with a sour and very puzzled look on his face. He then loudly pronounced, "Well ladies and gentlemen, I am very sorry, but you will have to take your tests STANDING UP!! They just refinished the floors in all the rooms of the building!!"

How sad that the students forgot the most important item on the test day! This joke is dedicated to the late Professor Paul J. Blommers of the University of Iowa. Professor Blommers chaired my dissertation committee and taught me the principles of concise statistical writing. He also championed the notion of open-book statistics exam (assuming of course, you have a TABLE to spread your materials out on). I later adopted this idea. I recall telling my students that the exams were always open-book, open-notes, open crib-sheets, and your choice of using any other statistics books. There was only exclusion -- You could not hire a statistical consultant to sit next to you in the test!! Oh, I would be remiss if I did not give credit to Alan Huang of the Australian Bureau of Statistics for giving me the idea for this joke. However, I fear it will be rated by my critics as the "Lamest of the Lame."



How is a normal probability distribution like a lion?

They both have a MEAN MEW.

Thanks are in order to Cynthia Gadol, an AP Statistics Teacher at Thomas Jefferson Classical Academy, for sending me this neat little pun. She claims she heard it years ago from Professor Rolf Bargmann at the University of Georgia. Cynthia, I have a reply for you: Q. How does a lion differ from a normal probability distribution? A. A lion can not go three standard deviations i pitch above or below its mean mew!! Oh well, this craziness makes the medicine go down a lot easier.



It is 1941 and the Germans are bombing Moscow. Most people in Moscow flee to the underground bomb shelters at night, except for a famous Russian statistician who tells a friend that he is going to sleep in his own bed, saying that "There is only one of me, among five million other people in Moscow. What are the chances I'll get hit?"

He survives the first night, but the next evening he shows up at the shelter. His friend asks why he has changed his mind. "Well," says the statistician, "there are five million people in this city, and one elephant in the Moscow Zoo. Last night, THEY GOT THE ELEPHANT!"

This should be a staple story for every probability course. It is almost as if the Probability Gods talk to one another after every occurrence of an event. The same individual sent me this that related the story about shopping for gourmet brains and insists on remaining anonymous. A big thanks, anyway!



What is the name of the only known motel chain that caters to professional draftsmen?

Hotelling's T2!

The wonderful statisticians who pioneered the field of multivariate analysis in the 1930's and 40's need much more recognition than what they have received and Harold Hotelling was among these (And think about his--they did it without computers!!!). This statistics, of course, is the bivariate counterpart of the univariate t-test. Story has it that William S. Gosset was granted a lifetime pass to any motel in Dr. Hotelling's chain.



Several weeks ago I received one of those infinitely forwarded e-mails that makes the rounds throughout the year. This one had some great graphical optical illusions along with a fascinating piece about how the human mind processes reading material. The following paragraph of prose was given in large print and the recipient was asked to read and attempt to understand the material even though the letters in each word were out of order and the words were thus atrociously garbled misspellings:

Cdnuolt blveiee taht I cluod aulaclty uesdnatnrd waht I was rdanieg. The phaonmneal pweor of the human mnid, aoccdrnig to a rscheearch at Cmabrigde Uinervtisy. It dn'seot mttaer in waht oreder the ltteers in a wrod are, the olny ipromatnt tihng is taht the frist and lsat ltteer be in the rghit pclae. The rset can be a taotl mses and you can sitll raed it wouthit a porbelm.

Most of my friends could read this with understanding and rather quickly I might add. Then I had them read a statistical bit of literature:

Miittluvraae asilyans sattes an idtenossiy ctuoonr epilsle is the itternoiecsno of a panle pleralal to the xl-yapne and the sruacfe of a btiiarave nmarol dbttiisruein.

In general, the outcome changed dramatically with my friends sputtering and spattering the words with great difficulty and most ending up throwing in the towel! Remember the same rules were followed but with a not so glorious ending! HOW COULD THIS HAPPEN? HAS STATISTICS RUINED A REASONABLE PREMISE?

Don't blame statistics. The words are just not as familiar and the concepts are more difficult to understand. The statistics statement reads: Multivariate analysis states an isodensity contour ellipse is the intersection of a plane parallel to the xy-plane and the surface of a bivariate normal distribution. Guuuulp! That's right and a tough one to visualize. If you do ever take a course in multivariate analysis, I assure you an exciting adventure awaits you. First you extend the familiar univariate analysis to bivariate analysis with some new concepts and ways of looking at things. Then the real thrills are experienced that bring goose bumps to your skin. The bivariate case is generalized to the multivariate case with only the use of MATHEMATICS itself and the godsend of matrix algebra to serve as your GPS unit. No more graphs and drawings to help your visualization when you progress into four dimensions or more. This may be the only time you have ever been without diagrams or pictorial aids in your life. But I can guarantee you that mastery of this material and the realization of its all-encompassing power will give you one of the most exhilarating mental highs ever and an on-top-of-the-world feeling that is hard to exceed. I rest my case!




NEW YORK, NY - A public school teacher was arrested today at John F. Kennedy International Airport as he attempted to board a flight while in possession of a ruler, a protractor, a box of plastic pocket protectors, and a graphing calculator.

In a morning press conference, the Attorney General said he believes the man is a member of a spin off group, St. Atistic, of the notorious Al-Gebra movement. He did not identify the man, who has been charged by the FBI with carrying weapons of math instruction. He also revealed that the situation was extremely tense and touch-and-go for a short time since the plastic protectors were discovered half-melted.

"Al-Gebra and particularly St. Atistic are problems for us," the Attorney said. "They recruit mean deviants who are then well trained in the use of multiple modes to search out an absolute value. They use secret code names like 'x' and 'y' and refer to themselves as 'unknowns', but we have determined they belong to a common denominator of the axis of medieval with coordinates in every country. As the Greek philanderer Isosceles used to say, 'There are three sides to every triangle.'"

When asked to comment on the arrest, the President said, "if God had wanted us to have better weapons of math instruction, He would have given us more fingers and toes." White House aides told reporters they could not recall a more intelligent or profound statement by the President.

Thanks to my good friends Sherry and Shailer Thomas for sending me this clever story by way of another looping e-mail. Shailer Thomas is an Emeritus Professor of Sociology at Illinois State University and understandably has a keen eye for deviant group behavior.



If a statistics course were a prerequisite for having sex, this country would not have a BIRTH CONTROL problem!!

is was an actual quote by a former graduate student of mine in a second statistics called Statistics II offered by our department. Interestingly enough this fellow was among the highest achieving students in the class. I had to e-mail him (Dennis Wright) to recover the exact wording of this joke. Thanks Dennis for your immediate reply. I think his statement was intended to illustrate the perceived difficulty of a statistics course in any curriculum.



Did you know Santa once took a statistics class? He had trouble remembering which hypothesis should have the equal sign so he would keep repeating: the null hypothesis, the null hypothesis, the null hypothesis.

In fact, to this day you can hear him say Ho, Ho, Ho!

Many thanks to Mark Eakin of the University of Texas at Arlington for allowing me to reprint his joke which is singularly appropriate this time of the year. By the way, Santa cell phoned me from the North Pol instructing me to announce to all statisticians that he is packing his bag of hand-carved walnut small case sigma signs to deliver in every "good" statistician on Christmas Eve.



A team of researchers from a large eastern university in the U.S. has recently published a monumental finding. The team discovered what the leading cause of divorce is.

It is marriage!!! You see, everyone who has been divorced has been married first.

Well, I wonder what journal was responsible for propagating in print this causal relationship. I was told the same journal had advocated a temporary moratorium on marriage as an attempt to cut the divorce rate. Thanks to Jonathan Schinhofen for suggesting this bit of sheer tomfoolery.



When a statistician is pounding a nail with a hammer but misses the nail and hits his thumb, what do we call it?

Sampling error.

When a statistician is pounding a nail with a hammer but misses the nail and hits his thumb 10 CONSECUTIVE times, what do we call it?

A Biased Statistic.

How do we correct for the bias?

Tell the statistician to place his thumb directly on the nail and then strike his thumb with the hammer!!!

We have all hear the expression, "I'm all thumbs." In this situation that is literally true. I hate to admit that during a weak moment this funyism hit me. Anyway, thanks to all the reviewers who gave me two thumbs up in my mailbox on this one!



Upon being mugged several weeks ago by the Cauchy Distribution, the Normal Distribution had these comments:

"I am still not back to normal yet but I do have my moments and the point of inflection in my voice has improved considerably. I just wish I had taken some ordinance along that night to fend off the attacker."

I did not know that distributions could engage in such outrageous behavior. The Statistics Crime Scene Investigative Unit (SCSIU) has mad major recommendations in distribution attacks of this nature. They have strongly urged any distribution to "Always be willing to give up a few moments to an attacker and the attacker like a panhandler will usually stroll away from the scene." This little tale was suggested by a reader whose e-mail got accidently mugged. Please notify me if you are out there.


I really can't see the attraction
Of trying to fit interaction.
The last time I tried
I woke up on my side
With an arm and a leg both in traction.
Of trying to fit interaction.

Thanks go out to Debby Apthorpe again from Australia for one of her famous statistical limericks. It appears that interaction is quite similar to some of the positions in the game Twister.


50% of marriages end in divorce. Thus if you don't file for divorce, your wife will.

This a cute little variation of all the 50-50 jokes. But wait a minute! This says the probability of any marriage ending in divorce is one. Sorry I don't have an attribution on this one.



It is believed by many humorists that statistical jokes are usually a flop in large nightclubs. Thus, if you examined graphically the frequency distribution of the number of statistics jokes told by every stand-up comedian in the USA, what would be the shape of the frequency polygon?

Shapeless---It would be a degenerate point distribution many units on the frequency scale above 0 on the score scale!

Oh! I am in big trouble now--lumping all these comedians as degenerate. The fact remains that my statement is probably very close to being true. All we need, though, is a counter example to prove me wrong. So please send me a stat joke told by a stand-up comedian!! It is obvious how these people feel toward statistics humor--they know they could not make a living on the topic. Or is it possible that statistical humor is such a new phenomenon that it hasn't been incorporated into their routines yet?



How many tents will a campground hold?

Ten tenths since that adds up to a whole!!!

Sorry, I lost the attribution on this one. However, you may wonder what this has to do with statistics. A possible incorrect answer to this question would be "one tenth(tent)" since in a one-way analysis of covariance with one covariate, the pooled within groups regression coefficient is not obtained by adding the separate regression coefficients within each group but rather by dividing the pooled numerators of each of the within group coefficients by the pooled denominators of each of the within group coefficients. In our example, using regression-type pooling, 1/10 + 1/10 +1/10 + ...for ten terms = 10/100 or 1/10 but that is absurd! Now isn't that special! I am sure you followed me. Is it any wonder that students have trouble with statistics when they are presented with esoteric "word salad" like the above? Please don't take my ramblings seriously. I am only having FUN!!!




A professional runner views the glass as half empty since the water is from the tap and not from a natural spring.

An attorney views the glass as half empty since he believes his compensation is never enough.

A mathematician can just not decide since the glass can never be EXACTLY half full or half empty.

An accountant views the glass as half full but with tiny red asterisk chips floating on the surface.

A statistician views the glass as half full but with bubbly foam all the way up to the brim.

So just what is the point of stating these philosophical differences? It proves beyond a shadow of doubt that Statisticians are the most OPTIMISTIC professionals in the world because they view one-half a glass of water as essentially a FULL glass when one accounts for the ingenious inferences and extrapolations that produce this top layer of froth!! Go ahead and douse me with a BUCKET of water if you think this is lame.




Question: Is the Normal Curve every a Skewed Distribution?

Answer: Always!! The Lower Half of the Normal Curve is Negatively Skewed and the Upper Half is Positively Skewed!!

This is an unfair trick question. A Gestalt psychologist would urge you look at the normal curve as a single entity and not as two curves treated separately. Bit if you want to have some fun with your statistics professor ask him this question and see how he responds. Then after you give him the answer tell him he must begin thinking outside of the box. he may even give you extra credit!! I may be placed in a box and shipped away after this one.



(1) Does not like to be first or last to arrive at a party for fear of being an outlier.
It is the old principle of recency vs. primacy for a psychologist but the statistician doesn't subscribe to either option. Arrival somewhere in the middle of the pack makes the statistician anonymous.

(2) Is obsessed with how many miles per hour a human hair grows!
Many people still believe that hair just doesn't grow in miles per hour. But a mile is a length measure just as much as a millimeter is. It is simply that most people do not relate to very large or very small numbers. The actual calculation states that human hair grows at a rate of 10-8 or .00000001 miles per hour. What should the barbers do about this rate?

(3) Tends to follow other people when walking in a group because of a strong leaning toward a posteriori tests after rejecting the overall H0.
Rarely do you see a priori test in the literature particularly in the behavioral sciences. Could it be that statisticians do not want to perform ahead of time?

(4) Becomes despondent when lecturing on the normal curve because he knows down deep in his lifetime he will never encounter an EXACTLY normal set of real-life discrete scores.
The normal curve is a very specific mathematical function that involves a continuous variable. Some real-life distributions can only hope to APPROXIMATE this model. How sad!!

(5) As a behavioral-science statistician, harbors deeply rooted jealousy of a biometrician because the latter is blessed with ratio or interval scale data while the former muddles around with ordinal and normal data.
This is a fact of life but many in the behavioral sciences would cite all the robustness studies of parametric tests and say, "Damn the torpedoes, full speed ahead!!?



What's the difference between a dead possum and a dead statistician lying in the road?

Answer: There are skid marks in front of the possum.

Thanks Jim White for this tale of horror. Now, for the rest of the story. Santa Claus came along in his sleigh on this same road and immediately stopped at the scene. He thought the possum was playing possum so did nothing. For the statistician, he reached in his bag and pulled out a bivariate normal surface with a blinking star on the dome and draped it over the fallen statistician...a considerate gesture on Santa's part to commemorate a respected profession.



My scatterplot's not monotonic
I'm sad and a trifle ironic.
The dreaded kurtosis
Is causing psychosis;
Please bring me a strong gin and tonic.

Another limerick from the collection of Debby Apthorpe in Australia. Thanks Debby for starting the New Year off with a free round of drinks.



It is a well-established fact that Statin Drugs ($27.8 billion sales worldwide in 2006) lower the BAD cholesterol level by 20 - 50% in most individuals upon continuous treatment. In fact, in a recent TV ad for a certain Statin Drug endorsed by Dr. Robert Jarvik (the artificial heart man), it was stated that this drug "reduces the risk of heart attack by 36%... in patients with multiple risk factors for heart disease but no heart disease."

"Zowie, exclaimed a friend watching the TV ad, this is comparable to penicillin. Since they called these drugs Statins because they are "Statistics Insured," why not add this to our drinking water supply and let everybody from babies on up benefit??"

Now before you petition your city council or go out and buy stock in this drug company, let's take a very careful look at this 36% figure which the Company itself tagged with an asterisk in the original report. Here is another prime example of innumeracy and number enhancement at its best. In smaller print the company explained that this means in a large clinical study that lasted 3 and 1/3 years, for every 100 subjects treated with the drug, 2 people had hear attacks, as compared with 3 heart attacks in a group of 100 subjects that received a placebo. In other words, for every 100 subjects who took the drug, 1 less subject was spared a heart attack (i.e. 1/3 = 33% ~ 36%). But this is a spurious percentage so we need to put hits in terms of a relatively unknown but useful statistic called the NNT. I want all my readers to etch this in their mind. The NNT is the number needed to treat for one person over the expect number to benefit! In our case, the NNT is 100...that should have a very sobering effect on the exuberant 36% reported earlier! Now to show you some other examples of this NNT: (a) NNT = 2 to cure a stomach ulcer with an antibiotic cocktail in one year of treatment (this is a great NNT); (b) NNT = 16 - 23 to prevent one hear attack with a Statin in people that have had a heart attack or other signs of heart disease (most likely group to benefit from a Statin); (c) NNT = 500+ to prevent death or serious medical condition with a Statin among patients without heart disease that have a single risk factor like high blood pressure (Probably should not be on Statin at all); (d) NNT = 1000+ for Avandia, a drug for controlling blood sugar to prevent heart disease or heart attack. (Even companies admit that this NNT is way too high for any benefits.) Of course, along with the NNT, one must also consider the side effects of the drug in making any decision about long-term usage. In the case of the State we mentioned before, it is very interesting that the Company essentially uses the NNT to downplay these side effects like muscle aches and memory problems. It states that only 1 in a 100 will experience side effects of some sort. WONDER WHY THE COMPANY CAN'T EMPHASIZE THE NNT FOR BOTH ISSUES? Much of this discussion is based on an article in the January 28, 2008 issue of BusinessWeek magazine. I urge all students of statistics and actually everyone to read this article online. This is one of the most illuminating articles on drug research that I have read and covers other key issues of drug effectiveness. By the way, the name "Statins" did not come from "Statistics Insured"...this was just part of the humor.



What happens if you find the inverse of a variance-covariance matrix?

You get an upside down statistician balancing on his head and looking up and admiring his black patent leather wing-tipped shoes. Since he was now nonsingular his friends were anxious to mingle with him and free him from his reputation as an introvert.

At least we got a statistician to look up at his shoes instead of down. Now to his friends the shoes were at eye level and gave off a brilliant glossy sheen. What an impressive scene that was the epitome of class! The friends finally understood why shoes are best measure of a person's character.



A wise woman once said if all the statisticians in the world would claim all the DEGREES OF FREEDOM then the CEO's of all the corporations would have none. The Chiefs would be forced to go on a merit system tied to valid earnings and upon severance for poor performance would receive a black life preserver instead of a golden parachute.

Moreover, if the statisticians do not take an infinity of degrees of freedom, many tables in textbooks would be one-row and lots of pages would be saved. It sounds like a win-win situation!



What are stadium statistics?

They are ball park estimates that are foul and land in the stands or on the roof!

Thank Ken Finstuen for the idea for this little quip. Would you say these estimates have run afoul of the ball park and do not even fall within the 99% confidence limits for the parameter?



Student A: What is the name of the theorem in statistics that states the sum of squares total is equal to the sum of squares between groups plus the sum of squares within groups (i.e., h2 = a2 + b2)?

Student B: Oh that is easy. That is called the Pythagorean Theorem.

Student A: I am sorry but that is wrong. You must have the right triangle for the Pythagorean theorem to hold and we did not assume that here.

Student B: OK so I had the wrong triangle. If you assume the right triangle then this statement becomes the Pythagorean Theorem.

Student A: You are now correct and it demonstrates how closely intertwined the relationship is between geometry and statistics!

Holy Cow! What kind of statistics course are these students taking? Poor Pythagorus. He knew all about triangles and squares but statistics and variances never entered his life. The above statement is called the Basic Theorem of Analysis of Variance but the Pythagorean Theorem has no connection with it. In words, it simply states that if you take any set of scores, divide them up into a number of groups (not necessarily equal n's) and compute the three sums of squares, then SST = SSB + SSW. This assumes nothing about triangles or where the scores came from. Elegant huh?



An F-Curve was complaining to a Standard Normal z-Curve one day at the shopping mall.

The F-Curve said, "I am really envious of you. Here I am with a big bulge on one end and a drain pipe on the other end and you have a perfect symmetrical figure."

The z-Curve replied, "Yes MR. F but you are a far more prestigious curve in that you are the star in major applications like ANOVA and ANCOVA."

"Well Mr. z, another thing that gripes my soul is that you never need any degrees of freedom and I always have to lug around two distinct df-values on my back!"

"Mr. F," the z-Curve responded, "that is very misleading. You know very well that a z-Curve is nothing more than a mature t-Curve with an infinite number of degrees of freedom. now that is a real load to carry. Take some away from me and I still have an infinity left!"

The F-Curve paused shortly with his mouth wide open, then smiled broadly, and said in a conciliatory voice, "Mr. z, Let's go down to the ice cream shop and I will treat you to an Orange FFreeZZ! I guess statisticians really could not get by without either one of our curves."

What a nice ending to a story that had such a contentious beginning. Yes, statistics as a discipline could not exist without both the F- and the z-Curves.




A boy asked his statistician father, "Why is my body not well-proportioned just like my brother's?"

His father's response, "Because, when you mother had your pregnancy, its distribution was skewed!!"

Does Medical Science know about this? Does this mean if your pregnancy is normally distributed you will have a perfectly proportioned baby? Thanks to Okunola Olajide Ezekiel for sending this. It has been sitting in my files for 9 months.



A statistician was reliving a weird and vivid dream for an accountant friend one day.

He explained, "In this strange dream, 20 or 30 accountants were sitting stark naked together in a large room at separate computers. But the eerie and contradictive part of this scene was that the accountants were all on the same auction website on their screens, each attempting to sell a spanking new package of a single pair of 'Jockey Shorts' that each was waving in his hand."

The statistician in a puzzled tone continued, "I just could not understand why the accountants just didn't slip on their pair of shorts instead of selling them on the Internet. This is the most vexing part of the dream!"

The accountant, with a sly little grin, immediately piped up, "Oh that has a simple interpretation. This is a perfect example of NAKED SHORT SELLING!"

To understand my little joke you must at least dabble in the stock market. I have nothing but disgust and distrust toward the entire market and financial system in the United States after the total collapse of investments during the Spring and Summer of 2008. The permitting of "Short Selling" has contributed greatly to the debacle we are still witnessing at this writing. I ASK YOU, WHERE ELSE ARE YOU ALLOWED TO SELL THINGS YOU DON'T OWN? Enough said!



Each of two squaws had 2 sons sleeping inside tepees about 20 yards apart. A third squaw had 3 sons playing outside between the two tepees. A statistics student remarked that this happy scenario demonstrates very nicely The Basic Theorem of ANOVA: The TOTAL sons of squaws is equal to the sons of squaws WTIHIN plus the sons of squaws BETWEEN. That is, 7 = 4 + 3!!!!

Although this play upon words is internally accurate, it is NOT an example of The Basic Theorem of ANOVA. The correct Theorem is one of the most pervasive themes in all of statistics and is the cornerstone of Experiment Design. ANOVA SUMMARY TABLES that you see in many published studies display the application of this Theorem and accompanying tests of significance for groups of data sets.



One legacy of the Iraq War will be the unstated but implied "so-called" Rumsfeld Test. This was suggested serendipitously from a Department of Defense new briefing on Feb. 12, 2002. The Secretary stated, "Reports that say that something hasn't happened are always interesting to me because as we know, there are known knowns; these are things we known we know. We also known there are known unknowns; that is to say we know there are some things we don't know. But there are also unknown unknowns - the ones we don't know we don't know." (This sounds like gibberish but Rummey is on to something here.)

Now Mr. Secretary, to validate your intelligence work, we suggest that you look at a fourth category of perceiving something unknown that is really known (Yes, we said that), and this gives us the basis for a neat 2x2 chi-square test. This would be the famed nonparametric test of independence whose table of observed (O) and expected (E) counts of Intelligence Items appears for each cell in the above diagram.

Now theoretically, if our intelligence system is operating with high efficiency, for any large set of intelligence items, the perceived observed proportion of known knowns should significantly exceed the perceived observed proportion of unknown knowns and correspondingly the perceived observed proportion of unknown unknowns should significantly exceed the perceived observed proportion of known unknowns. This is the desired direction of the dependence (Look at main diagonal of table). Remember under the assumption of independence of perceived and true items, the expected E for any cell is the row sum of O's that cell is in times the column sum of O's that cell is in divided by the overall sum of all the O's. This is repeated to get the expected E for each cell. We then substitute into the formula x2 = Σ [O - E)2/E] to get the test statistic Frequency Chi-Sqaure with df = 1. Finally, this value from the data table is referred to either the 95th or 99th percentile from the Table of the Chi-Square Distribution. For Rummey's sake we hope and pray that this obtained value is larger than the critical percentile. If it is... WHOOPEE!! RUMSFELD's INTELLIGENCE TEAM HAS BEEN VALIDATED!! But wait just one moment. We have ONE thing to check yet. Bad Dependence can also occur! If the perceived observed proportion of unknown knowns should significantly exceed the perceived observed proportion of known knowns and correspondingly the perceived observed proportion of known unknowns should significantly exceed the perceived observed proportions of unknown unknowns (Look at secondary diagonal of table), significant masculinizing of the true nature of the items has occurred. THIS WOULD MEAN UTTER FAILURE OF THE INTELLIGENCE TEAM!! SO THE RUMSFELD TEST IS FRAUGHT WITH DANGER FOR INEXPERIENCED STATISTICIANS. WE MUST ONLY APPLAUD RUMSFELD'S SUCCESS WHEN KNOWN KNOWNS AND UNKNOWN UNKNOWNS PILE UP SIGNIFICANTLY IN THE TABLE. THIS IS INTUITIVELY OBVIOUS BUT MUST ALWAYS BE VERIFIED AFTER A SIGNIFICANT TEST.

Thanks to John A. Hansen of Indiana University for suggesting the new Rumsfeld Test. Quite frankly, I originally decided it was too esoteric to mess with as are many of Rummeys long and dry explanations. Finally, with some trepidation, I decided to finish what Rumsfeld had started at the news conference and write it in a fashion that would mimic his style of taking something simple and making it convolutedly complex. Did I succeed? It was sure load so fun and I even, quite honestly, had trouble keeping my mind focused enough to proof read the material. But in all seriousness...NO, and I repeat NO statistical concepts should ever be explained in the gobble-de-gook word obfuscation that this writing produced. We certainly can't blame students for rebelling against instructors who intentionally or unintentionally spew out garbage such as this in the classroom? Knowing and understanding the material thoroughly and being able to clearly and concisely explain it to someone else are two entirely separate but critical components of the teaching enterprise.



Husband returns home from a doctor's visit with a sad face.

Wife: "What did the doctor say?"

Husband: "I have Dyscalculia. It's a math disorder."

Wife: "How bad is it?"

Husband: "The Doctor said not to worry. 100 out of every 15 people have it.">

This has to be one of the worst examples of innumeracy I have heard. Regarding comedians shying away from statistics jokes, this joke was attributed to David Letterman. If this occurred, this has to be a rarity where a stand-up comedian told a statistical joke. Thanks much to Larry DiFiore, Ph.Dl, Malloy College of Rockville Centre, NY for sending this counter-example.



Don't kid yourself. The deep recession of 2008-09 is really a depression. Then to witness business guests clapping at the close of the NY Stock Exchange at the podium every single day is like statisticians clapping for nonsignificant results on hypothesis tests!

Maybe this is the core problem. Financial people have lost their way and have been unable to distinguish good performance from bad performance. From loan approvals to CEO compensation, they have lost all sense of what laudable behavior means.



In a Standard Normal Curve, the total area under the curve is ONE. Why then has it never been proven that no matter how far you go out away from the middle of the score scale at 0 in either direction there will always be some portion of the area under the curve beyond either point?


Of course this was a bold face lie and it has been proven. In all seriousness though, it does seem like a contradiction that you can keep accumulating area under the curve as you keep moving out away from the middle and yet never exceed ONE. In simple language, just think of the concept of limits in mathematics. As you move in either direction toward minus infinity and plus infinity, the area under the curve does increase but only approaches ONE as a limit. Certainly not as exciting as proof of Fermat's Last Theorem a few years back but it does seem counter intuitive and excites your block just a wee bit.



Statisticians, as a group, tend to be reserved and keep their feelings under wraps. But because they are trustworthy, they have always been viewed by other mathematicians as guardians of the subset of real numbers between 0 and 1 inclusively. One issue that does elicit extreme fervor one way or the other among statisticians is some of the probabilities that are represented by these numbers they protect. They passionately love ALMOST uncertainties (.05, .01, .001) or ALMOST certainties (.95, .99, .999). They have utter disdain for values like .10 or .90 because of the false hope that these values spawn in a researcher's mind. Finally, there is unmitigated hatred for the value .50. It absolutely give statisticians no direction whatsoever to lean and it forces them to admit defeat and say decision-making is nothing more than a flip of a coin.

Bet you didn't know that statisticians were that hung up emotionally on some of these values. Showing attitudinal differences toward certain values in this set of numbers is introducing bias of the worst type. Shame on you statisticians! The next thing that will happen is that the number theorists will be annointed caretakers of the pristine real numbers from 0 to 1. Woe is me!



We know that a Type 1 error is rejecting a true null hypothesis H0 and a Type II error is retaining a false H0.

What then is a Type III error?

Just so statisticians have an odd number of errors for closure, it is a researcher paying absolutely no attention whatsoever to Type I and Type II errors in hypothesis testing!!!!

Not only that folks but the number 2 (III in Roman Numeral) is a celebrated Mersenne Prime Number, a number that number theory considers the Jewel of the field. A Mersenne Prime is a prime number of the form 2n - 1 is a prime number. In our case n=2 and 22 -1 =3. Also 3 is the very smallest Mersenne Prime in the set of prime numbers... the largest Mersenne prime is... well, we don't really know. But surprisingly just recently only the 47th known Mersenne since the ancient Greeks was discovered and it is nearly 13 million digits long. Simply unbelievable. This was discovered through banks and banks of high power computers working days and nights 24/7. There is also a society called GIMPS founded in 1996 (Great Internet Mersenne Prime Search) that focuses all their energy on this topic. Now, you ask, what is the practical application of Mersennes? Well, you have one right here in this joke. Statisticians and other scientists have always paid homage to the number 3 as sort of a magical number of steps for a procedure or list to contain. Please don't ask me why? Maybe they must have unconsciously wanted to use the smallest Mersenne. For an illuminating and relatively easy read, see NPR: Mersenne Primes



Why does the Normal Curve not need any degrees of freedom?

It is very content and smug about its status... It is ALREADY a t-Curve with infinite degrees of freedom so a few more would not help!

Many students think of these two curves as separate entities because the Normal Curve is usually taught first. However, remember that the Normal Curve is the limiting case of a t-Curve with infinite degrees of freedom. Thus, the t-Curve, in reality, is the more general concept. in successive graphs of t-Curves, as the degrees of freedom increases starting with 3, the area in the tails shrink and the are in the middle of the curve increases approaching the Normal curve as a limit. Even at a degrees of freedom of 30 for the t-Curve in a moderately scaled drawing, graphs of the two curves are practically indistinguishable to the naked eye and the difference would only be detected by a high definition camera.



An energetic young statistician was hired at a large corporation. On his first day of work he was greeted by the senior statistician who decided immediately to put him through his paces. He asked him to double check the files in several dust-gathering boxes on the second floor that were boldly labeled, "NONSIGNIFICANT STUDIES." He told the young man that the files in these boxes were destined for the incinerator unless he could find mistakes or evidence in the summary reports that would salvage them back to the land of Recommended for Replication.

The young statistician began his arduous task. After inspecting five of the studies, the results were quite surprising. He yelled at his senior that he found several studies with probabilities below 1 in a 100 or, most alarming to him in one study, as low as 1 in a 1000 recorded as nonsignificant and the null hypotheses retained in all of these. This was outrageous since these low probabilities exceed almost anyone's definition of improbable. What was going on?

The senior statistician looked squint-eyed at the rambunctious and perturbed young statistician and exclaimed, "Young man I respect your extensive training in the statistical field, but the first thing you should have realized where you joined our organization is that we are on the BINARY SYSTEM here and consequently 1 IN 4 AND 1 IN 8 ARE NOT IN ANYONE'S BOOK IMPROBABLY!!!

You have to feel sorry for this inauspicious start to the young statistician's career. How many corporation in our society would have been on the BINARY instead of the DECIMAL system? As a reminder 100 (Binary) = 4 (Decimal) and 1000 (Binary) = 8 (Decimal). This story is all mine but I must give some credit to Patti Peters of Kent State University who made a Binary comment in my Guestbook.




Imagine The Shock:

Cardiology researchers at the U.S. Armed Forces Institute of Pathology (AFIP) ordered 24 whole hearts for a medical experiment. Many months passed, and then one day, 5 semi-tractor trailer rigs arrived at the receiving dock and started unloading 24 large wooden crates. The chief scientist and his statistician went to the dock to sign for the wooden crates. The chief scientist and his statistician went to the dock to sign for the shipment. Amazed at the number of huge packing cases, they checked the consignment bill of lading. Sure enough, it was a shipment of one each, quantity 24, WHALE hearts.

As a statistician, just wondering if generalizing from whale hearts to human hearts is more valid than the proverbial generalizing from mice to humans? After all folks, whales are mammals and that should throw some credibility in favor of whales in comparative studies. Thanks go out to Ken Finstuen of San Antonio, Texas, for this one. This is a real hoot because it is so unimaginable.



There was a bright student named Bobby
Who collected stat jokes as a hobby
But when his friends deemed them lame
He was stricken with shame
And mailed them in bulk to Abu Dhabi.

Yes, this one is all mine. I know this is not the greatest stat limerick to ever hit print but at least it is a starter. I have been yearning to write one of these for a long time. Our expert, Debby Apthorpe in Australia, will have to pass judgement on it. Debby, are you out there?



See Santa at the North Pole by his sleigh
He regrets using statistics each and every day
If naughty is the null adoption
And nice is its only option
He must greatly inflate alpha or stay.

Maybe this prompts us to cut some slack to the researchers who elevate their alphas to .10 a posteriori to calculating the statistic. Just kidding of course. This is only my second limerick so bear with me. The Christmas song "Santa Clause Is Coming To Town" inspired me to express Santa's concern here.



What famous person was credited with telling the very first statistics joke and what was it?

Sigmund Freud the Father of Psychoanalysis. A hot-headed patient of his when lying on the couch got cold feet and failed to reveal the origin of his pent up rage. Freud admonished him and ordered that before they continue he should place his head in a bucket of ice and his feet in a stove and that would on the average make him feel fine!

That is strange. I could swear that I have always heard this the opposite way with the head going in the oven and the feet in the bucket of ice. But that would only exacerbate the poor client's problem. I would never want to be accused of making a Freudian Slip here.



Testing a statistical hypothesis is like flushing a water-saving toilet...

It must be run past you a number of times before it becomes clear.

I hope my crazy comparison does not stray too far from a vital statistical technique. The American Standard Company now has an innovative line of toilets that are essentially guaranteed to be plunger free. They are so high performing that they can flush a bucketful of golf balls in 1.6 flushes. Statistical methods should be so efficient, huh? See a funny movie on these toilets.



I want to remind all our readers that this joke represents the bicentennial joke recorded in the Gallery. Who in their wildest dreams would of thunk it? I have heard bloggers exclaim many times that recognizing any humor in statistics is the biggest joke of all (Maybe this should be considered the 201st?). But we did it and will continue to create, with your help, many many more funnyisms and transform the statistical enterprise into a light-headed discipline.

Two graduate students were spending their spring break in a large city in southern Florida. One night they decided to visit a casino for a little relaxation and fun. However, being college educated, they knew the games always favored the "House" so they set limits on their play and analyzed which games were inclined to have more favorable odds toward the player. As they walked into the casino amidst darting lights and piercing sounds, the students spotted a strange game near the entrance that they had never seen before. A metal drum rotated on a spindle attached to a table with 100 identical balls inside the drum with dollar amounts stamped on each ball. The frequency and probability distribution were as follows:

X f p  
$1000 1 .01 Mean = $13.18
10 5 .05  
5 43 .43 Median = $2.00
2 2 .02  
1 49 .49 Modes = $1.00, $5.00
  100 1.00  

Instructions stated that for a charge of $12, the player was entitled to rotate the drum a number of times to mix the balls thoroughly and then reach through a latched door on the side of the drum to pick a single ball, sight unseen. The attendant running the game would then pay the player the dollar amount stamped on the ball. Finally, the drawn ball was returned to the drum and the entire process was repeated per interest in the game.

The students decided that if the game were deemed close to being fair, each would play the game 15 times for a total of 30 trials and any winnings would be split evenly. The first student looked worriedly at this buddy and remarked, "I never have subscribed to the notion of an expected value in gambling games. The concept is entirely too subjective and unreliable. In our case the value that is expected is a $160 total loss over all 30 trials. My reasoning is that we will draw primarily $1's and $5's (the modes) and a couple $10's and this would get us up to about $100 of winnings overall. But this is $260 short of the $360 expenditure we would put out over 30 trials! On the other hand, the "House" has a value that is expected that is even higher than this first estimate. The "House" reasons that since $2 is the median value of the balls, 40% of the draws are below this. Thus, $12 - $2 = $10 and 30 x $10 = $300 is the expected total winnings for the "House." "Either way, the expected values do not favor us."

The second student nods his head and retorts, "Good friend, I agree with you that the expected value is just not well-defined. However, I would tend to pick the mean of $13.18 to help evaluate our chances of winning. Since this value is barely larger than the cost to play of $12 and the odds are 99:` against our winning on any trial, the game tips decisively toward the "House."


Holy Cow! The statistical misinformation and falsehoods are running rampant in this story. It is certainly apparent that these students were not introduced to basic statistics at the undergraduate level. The expected value is indeed the mean of a relative frequency distribution. However, the expression is commonly used in math stat to impart a touch of mystery (only kidding) and in applied statistics when a gambling experiment is associated with the frequency or probability distribution and repeated an infinity of times. In our example, a student pays $12 per draw, receives the value on the ball, the "House" replaced the ball, and the experiment is repeated many many times. The most fascinating interpretation of expected value here is that it represents the fair price to pay per trial ($13.18) or the price that in the long haul, both the player and the "House" break even. The first student was just flat out off base in his logic. However, the second student correctly identified the mean as critical but totally bungled the conclusion. Surprisingly, the game favored the students since the charge of $12 was less than the expected value of $13.18. With an infinity of trials (30 may be too few), the "Big smacker" of $1000 should be drawn just enough times to give the students modest winnings (About $35.40!) All right hotshot statistics students out there--Where did this value come from?"