GARY C. RAMSEYER'S FIRST INTERNET GALLERY OF STATISTICS JOKES BY TOPIC

TOPIC : HYPOTHESIS TESTING


59.
Did you know that if you torture the data long enough, that eventually it will confess?

*Does this include using the Chinese water torture? Thanks Cliff Lee from Caterpillar for passing this one my way.


73.
Two statisticians and their accountant buddy were having lunch together one day at a top-secret government research installation in the desert. The two statisticians were discussing how that afternoon they would finish analyzing data from four groups of aliens captured from spacecrafts. The first statistician stated firmly that the experimentwise error rate should be controlled by using Tukey. The second statistician disagreed vigorously and replied that the experimentwise error rate should be controlled by using Bonferonni. Suddenly the accountant's face became white as a sheet. He yelled, "I always knew that experiment with aliens would get us into big trouble someday. Since the aliens are going to attack us this afternoon you are both dead wrong. The only way to control the AIR RAID is to use the installation's bomb shelter!!!! I'm out of here........"

*The above was inspired by a graduate student in an intermediate level class one day. After what I thought was a scintillating lecture on error rate, the puzzled student asked me at the end of the hour what an AIR RAID had to do with statistics.


79.
Did you hear about the statistician who was about to analyze data gathered from a nudist colony? He didn't know whether to use a one or a two-tailed test!!!!

*This joke was told to me by my good friend and colleague Jazzbo Johnson a counseling psychologist in the Psychology Department at Illinois State University. He assured me that it meets all the standards for a PG rated joke!


87.
Two students were walking out of statistics class one day. One was grinning ear to ear and the other was frowning woefully. The one that was grinning said, " Boy the instructor sure gave an inspired lecture on hypothesis testing today. He said that out of the four outcomes that can occur when you test the null hypothesis, two are correct decisions and two are errors. He praised this procedure as the Holy Grail of statistical analysis."

The other student looked at his classmate in dismay. He stated, "Well I certainly was not impressed with his lecture and totally disagree with him. ANY STATISTICAL PROCEDURE FOR MAKING A CORRECT DECISION THAT IS NO BETTER THAN FLIPPING A COIN IS PRETTY BAD!!!"

*This discussion would make Neyman turn over in his grave. Please Sir Ronald don't force me to reject or not reject my joke!!!


138.
Three of the Most Embarassing Outcomes for a Statistician and Their Workarounds:

(1) Result: The intercorrelations between a fairly large set of variables has exactly 5% of the coefficients that are significant at the .05 level. Solution: Try to remain upbeat. Lighten up and use the .10 level of significance and stress to the readers that these results represent an early exploratory study!

(2) Result: In a 3x3x4x4x5 Factorial ANOVA the Five-Way Interaction turns up significant at the .01 level. Solution: Curse under your breath that you used a five-factor design. Then instruct your graduate assistant to conduct FIVE Four-Way ANOVAs, one for each of the five levels of the 5th independent variable, to take two aspirin, and call back in the morning!

(3) Result: The F-test for a One-Way ANOVA with five treatment groups is significant at the .05 level but NONE of the pairwise comparisons between the five means is significant. Solution: Cry hard and then work your tail off to find some obscure, meaningless complex comparison that is significant such as the average of the first three treatment means is significantly different from the average of the last two treatment means!

*The above are my own dreaded results. I am sure the readers have their own convoluted and shocking statistical anomalies. Please email me your most feared and or realized statistical outcome and I will put it in the Gallery.


139.
Variance is what any two statisticians are at. How sad because this automatically violates the assumption of homogeneity of variance. However, if the statisticians are robust then everything will work out between them.

*Thanks to Sweta Sorab of GE Energy Servicees Marketing Forcasting for forwarding me the first line of this quip. I added several lines to continue the fun-poking at the statisticians.


141.
I don't know why people are so negative about statistics and statisticians. I'm only a first-year student, and statistics has already taught me everything I need to know about life--always Proceed with Caution and Reject H0!

*Thanks to Priscilla Mok at the Hong Kong International School for sending me this little testimonial about the field of statistics. Don't forget, Priscilla, to mention that the statistical literature is laced with all those positive Chi-Squares and F-ratios that also perk up your day.


151.
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 independence of two nominal or ordinal variables.


161.
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 this--they did it without computers!!!). This statistic, 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.


165.
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 Pole instructing me to announce to all statisticians that he is packing his bag of hand- carved walnut small case sigma signs to deliver to every "good" statistician on Christmas Eve.


187.
  • 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 news 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 know we know. We also know 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 χ2 = Σ[(O - E)2/E] to get the test statistic Frequency Chi-Square 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..., WHOPEE!! 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 misclassification 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 mimmick his style of taking something simple and making it convolutedly complex. Did I succeed? It was sure loads of 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.


    189.
    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 hypotheisis 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.


    192.
    We know that a Type I error is rejecting a true null hypothesis H0 and a Type II errror 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 3 (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 where n 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.


    199.
    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.


    203.
    A beautiful young woman invited a brilliant statistician friend to her Company dinner-dance.
    The invitation stated that she could either bring her spouse or her significant other as a guest. Having just met this chap and being unmarried, she felt certain that he would more than fill the bill since all statisticians are by definition statistically significant. When they arrived at the door, the maitre d' inquired as to the status of her escort. She smiled and promptly introduced him as an up-and-coming statistician that was her significant other for the evening. The maitre d' was stunned and his face grew red. He finally stammered in an embarrased tone of voice, "I am so sorry madam, we cannot admit your friend. STATISTICAL SIGNIFICANCE DOES NOT IMPLY PRACTICAL SIGNIFICANCE!"

    *You have to empathize with this young lady on the shocking news from the maitre d'. Her whole evening was no doubt ruined. But you know something, the maitre d' was absolutely correct. Statistical significance does not imply practical significance but the converse is true, practical significance does indeed imply statistical significance. This fact is probably not emphasized enough in an introductory statistics class. Let me give you a simple example that illutrates this principle. A researcher was testing a two-tailed hypothesis that all the 6 th graders in the city's school system was from a population that had a mean IQ of 100 (i.e., H0: = 100 vs. H1: < 100 and H2: > 100). The sample data were as follows: N = 1600, = 101, s = 20. Now computing the est. standard error of the mean we obtain s/sq.rt.(N-1) = 20/sq.rt(1600-1) = 20/40 = .5. Finally computing the z-statistic we have z = (101 - 100)/.5 = 2.00. Holy Toledo! This observed z is significant at the .05 level and we can reject H0 and accept H2: > 100. Before the researcher gets all excited though and gives high-fives to all the principals of the schools, he should reflect on the whole situation. He had a HUGE sample which led to a dinky standard error and this in turn produced a significant z for a difference of ONE between the hypothesized and the observed IQ means. You must be kidding----No we are not! Most sane people would consider a difference of one in means as trivial and therefore practically unimportant in any meaningful endeavor that would be performed on this population. Thus the moral of the story is that when a researcher is blessed with a very large sample(s), and a hypothesis test results in a statistically significant result, ALWAYS reflect on the dependent variable(s) to make sure that the mean difference or whatever produces a judged practical value in real life. I realize this is somewhat subjective but it is a vital step in the process of interpreting a hypothesis test. Now all the young woman has to do the next time she invites this talented statistician out is to tell the maitre d' she did NOT use a very large sample!!!


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