# Statistics / Sadistics Juggling Basic Statistical Notions Important For Teachers While Maintaining Sanity 1.

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Statistics / Sadistics Juggling Basic Statistical Notions Important For Teachers While Maintaining Sanity 1

Remember... There are three kinds of people in the world. Those who are good at math, and Those who aren’t. 2

Raw Scores: without organization or context, scores by themselves are meaningless George Carlin’s famous line: “Here’s a partial football score just in, Green Bay 6.” Ohio State 35; Michigan 32 Annika Sorenstam 35; Lorena Ochoa 32 John and Charley are taking a trip together. Charley has lived for 7 years; John has lived for 27. Who is the older of the two? Charley John Charley is a dog. In human years he is 46; e.g., (7-1) x 5 +16 = 46. John is a man. In human years he is 27. 3

Edward L. Thorndike (1874-1949)... his pioneer investigations in the fields of human and animal learning are among the most influential in the history of Psychology. 4 “Whatever exists, exists in some quantity. If it exists in quantity, it can be measured.” – E. L. Thorndike (quote paraphrased)

The McNamara Fallacy... attributed to economist Charles Handy The first step is to measure whatever can be easily measured. This is okay as far as it goes. The second step is to disregard that which can’t be easily measured, or to give it an arbitrary value. This is artificial and misleading. The third step is to presume that what can’t be measured easily isn’t important. This is blindness. The fourth step is to say that what can’t be easily measured doesn’t exist. This is suicide. Bottom Line of the Robert McNamara fallacy: “What does not get counted does not count.” 5

English Lesson – When Speaking of Data As a teacher, you will see lots of data. The dictionary defines “data” as facts or figures. Notice the word “data” is plural and when speaking of data you need to use plural verb forms. It is an unfortunate giveaway that you might NOT know what you are talking about if you use the phrase “this data is” instead of “these data are” in professional conversation. “Datum” is the singular form for data. No one ever uses this term. 6

Scales of Measurement – Organizing and Comparing Data; the use of Zero The first is Nominal. It is data that is categorized and can't be arranged in an order from low to high; e.g. answer a question yes or no, colors of cars in a parking lot, race and gender. The second is Ordinal. It is data that is categorized and can be arranged in an order from low to high, but differences between the scores can not be determined, or are meaningless; e.g. grades A, B, C, D, E or grade levels 9th, 10th, 11th, 12th, or survey type questions such as do not like, somewhat like, like, love; or another is movie ratings. The third is Interval. It is the ordinal scale, but with the additional property that the difference between the data (i.e. the interval size) is equal, but the scale does not have a natural zero starting point; e.g. the years (2009, 2000, 1610, etc), the temperature scale (50, 68, 90, etc degrees F). The fourth is Ratio. It is the interval scale, but with the additional property that it does have a natural zero starting point. Money and weight are examples; 0 money means you have none, and \$4.00 is 2 X \$2. Likewise with weight; no weight means there is none and 4 pounds is 2 x 2 pounds. Note: Despite evidence that grading as punishment (such as the use of zero for missing work) does not work (Guskey, 2000) and the mathematical flaw in the use of the zero on a 100-point scale (Reeves, 2004), some teachers persist. Will you? Guskey, T. R. (2000). Grading policies that work against standards … and how to fix them. NASSP Bulletin, 84(620), 20–29. Reeves, D. B. (2004). The case against zero. Phi Delta Kappan, 86(4), 324–325. 7