Good Morning Ted and Jody:

As I thought, I did manage to escape yesterday morning with only bruises and a hurt pride—no bones were broken. When we got home from our trip into town yesterday, I finally took off my shoes and socks. The impact of my black and blue toes on Nancy occasioned a trip back to town to the emergency room. That nothing was broken was confirmed by a medical practitioner after said practitioner reviewed x-rays during our 4 hour visit to the emergency room yesterday afternoon, late. As we left the emergency room around 8 o’clock, Nancy confirmed that this was her way to avoid cooking dinner and get me to take her to dinner. I demurred, for even though nothing was broken I was in no shape to take her to dinner. Besides it was past my bedtime. So, she took me. We went to the Mast Head. You may recall it, for it is the place that had the “nice” big platter of onion rings.

Once again, my visit to medical authorities reminded me that I do need to write to the various Medial Collages, Health Insurance Institutes and the Medicare policy makers about their insistence on pain numbers. For well over 20 years I taught Empirical Research Methods in Political Science. A big part of that course was statistics. In statistics, one must know what kind of numbers one is dealing with. There are four different kinds of numbers: real, interval, ordinal, and nominal. There are different ways statistics handles each type of number because of the properties of the numbers.

**Real numbers** involve the assignment of numbers to categories of a variable such that the distance between any two adjacent numbers is the same as the distance between any other two. So the distance (difference) between one mile and two miles, a measure of length, is one and the difference (distance) between 55 miles and 56 miles is also one Real numbers have a fixed zero, which represents the absence of the variable–$0 means you don’t have any dollars (the variable is money measured in dollars). Real numbers allow one to use all normal mathematical operations in analyzing variables with real number assignments: addition, subtraction, multiplication, division, and so forth in. The use of all mathematical operations allows us to say things like $45 is twice as much as $22.50.

**Interval numbers** are the same as real numbers with distances and all representing the same interval between pairs of adjacent numbers, save interval numbers do not have a fixed zero. Rather 0 is an arbitrary point. For example, temperature measure heat If we measure heat in Fahrenheit or Celsius. 0 degrees is the point at which water freezes. There is heat present at 0 degrees F or C, but not the nice comforting amount of heat one wants when getting out of the shower. Since Interval numbers do not have a fixed zero, while we can use all mathematical operations on them, we need to be careful when we make comparisons. For example, while we may subjectively feel a lot warmer with an ambient temperature of 90 degrees F, it is not three times as warm as 30 degrees F. It is warmer; and, it is 60 degrees F warmer; but it is not three times as warm.

**Ordinal numbers** change all the rules about using mathematics and the numbers themselves. Ordinal numbers are the arbitrary assignment of numbers to categories of a variable such that any underlying order in the categories is preserved. We often use ordinal numbers to state the outcome of a race: 1^{st} place, 2^{nd} place, and etcetera. While we report winning by a nose or furlong or the like, the actual prizes awarded are fixed and do not represent any difference if 2^{nd} place come in a nose or a furlong or even a mile behind 1^{st}. Statistical manipulations of ordinal number are not directly done on the numbers them selves. Rather, statistical manipulations are done in charts and tables of such numbers, for adding a 1^{st} and a 2^{nd} makes no sense. Remember, these are arbitrary assignments. It would be just as easy to represent the winner, place, show in terms of the prizes won: $100 for first, $30 for second and $1 for third. This still represents the order and the distances are often very arbitrary between the prizes. Yes, during the Olympics we see metal counts and even attempts to weight the metals won by a given country. This stretches the use of ordinal numbers beyond the breaking point. Now to used pain levels we have to add a further complication the answer to the question “On a scale of 1 to 10 how much pain are you in right now?” That complication is reporter (patient) subjectivity. It is not clear that two patients reporting the same pain numbers are experiencing the same pain. So, when the nurse asked me to give her a number, I was, and remain, totally unable to do so. The scale is meaning less to me. It has been explained in several different ways. But, then it is relative to something called normal, customary, usual, or the worst pain I have ever experienced. I do not remember the pain of coming out of my mother; but, I should think that hurt.

To finish the types of numbers, **Nominal numbers** are the arbitrary assignment of numbers to categories of a variable. They are not subject to mathematical operations but can be put into tables and charts. Race is a nominal number 1=Black, 2=Brown and 3=Other. Your Social Security Number, Credit card numbers, zip and area codes as well as the number of the Congressional District in which you reside are all nominal numbers.

So, I need to cut and paste from this missive to a letter to all of those organizations mentioned above who are abusing ordinal numbers and thinking it makes some medical sense. When I went in to the emergency room, I hurt. That should be enough to get me treatment, not how much on a meaningless scale I hurt.

Warmest regards, Ed

I am with you 100% on this one, Theo. (Is 100% a Real Number? It is to me)

When I was an EMT, I refused to ask patients to give me a pain number. That had nothing to do with statistics, or Ordinal Numbers. It had to do with people lying. If they have called an emergency ambulance, they are highly unlikely to admit that their pain level is 1, or even 2. They would rather say 9 or 10, to make me (and often themselves) believe that they are in a bad way, and justify the ambulance being sent.

If someone is really in that much pain, they will usually answer that they don’t know, as they have more to worry about than pointless invented scales.

Best wishes, Pete.

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Yes, 100% is a REAL Number! However, one needs to know if the number is a Bayesian estimate or an observed relative frequency before one can know what it means and take action based upon it. None-the-less, any probability expressed in decimals or percentages is a real number. Unlike the folks you used to help, I am constitutionally unable to come up with a pain number. I do strongly suspect you are correct in your assessment of the veracity of the numbers people give in response to the question,

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I think my brain just exploded. (It didn’t hurt so no score from me.)

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I think you just explained how my students must have felt (and thanks for the chuckle).

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