All About Statistics
Statistics and Basketball, of course!
People wonder how accurate our test results are? This section helps explain basic statistics in test design, which also covers how medical tests differentiate normal from pathological. You’ve heard of the normal bell curve and it is not too hard to understand how we use that to differentiate normal (health) from “mild” and “major” pathology. Consider: If you lined up one-hundred 6th graders from shortest to tallest in order to buy basket ball uniforms and measured the 50th kid in line and bought uniforms in that size, you could expect them to fit the “average” student. Under the bell curve, we say the height of the 16th through the 67th kid in line represents the average range.
Yes, it is arbitrary, but the statistics turn out such that this range (16th–67th) works well to describe the “average” range for everything from IQ to shoe size. This range for about 68 kids, between the 16th and 67th in height, is considered ± 1 standard deviation (SD) around the mean; i.e., above or below the 50th “perfectly” average tall kid. So the Average range is two SDs, with one SD encompassing 34 of the shorter kids ranging up another SD which includes 34 of the taller than the average kids. In this example a total 64 kids fall either ±1 SD around the mean, of average kid’s height.
Wait a minute. What about the remaining 36 kids? Well, half of them (16) are taller by at least another SD and the remaining half (16) are shorter by another SD or more. In basketball we worry more about the short kids, than we do about tall ones. Our statistics say that the 2nd kid in line up through the 15th are more than 1 SD below the mean range, that’s 14 out of the 16 short kids. We worry a bit about these 14 “mildly” short kids and we might warn them they could spend a lot of time sitting on the bench if selected for the team. But, what about the two (2) shortest kids in line? Heck they are the two shortest out of 100 kids trying out. They fall two or more SDs below the mean; i.e., at or even below the 2nd %ile. This range (≤ 2 SDs) is “severely” short – the coach might advise them to try out for the swimming team rather than basketball. So anyone falling 1–2 standard deviations below the mean is mildly short, while people ≥2 SDs below the mean are severely short. It’s all about SD determining what range you fall in.
Germs and Cut-off Points
We use the range of 2 or more SDs below (or sometimes above) the mean as the indicator of pathology in most medical and psychological testing. If your culture’s germ count ranges from 16% through 67% of the average number of germs people culture, you are in the normal (better stated as “average”) range. If you have 68% to 97% the number of germs (ranging 1–2 SDs more than average) you “may” have a mild infection, so no drugs for you but we wait and watch just in case. However, if your culture show 98% or more germs than average (i.e., ≥2 SDs above the mean) this falls in the pathological range which means you meet criteria to get penicillin. If you have 99.9% more germs you are > 3 SDs having more germs than 998/1000 people so you are on your way to the hospital. You see how handy this standard is, especially as all medical professionals use the same standard of care.
You can see how this system yields standardized “cut off” points to differentiate Mild from Major to even Profound pathology. If someone uses exactly the same culture technique, or NP tests, and gives it in the same way (a standardized practice) then any tester anywhere in the US will get the same result. This means it is a reliable test, which is a necessary condition before a test can be considered valid. After all if different users routinely got different results while testing the same patient, that would be unreliable testing and thus clearly not valid; i.e., a valid measure of the criterion. Another type of validity is to give several different tests (like for memory) and see if they all yield similar results. We give three tests of short-term memory to increase the reliability of our findings, and thus the more the three tests agree the more valid our findings.
When we see a patient scoring 2 or more SDs below the mean on multiple tests, we have a reliable indicator of probable Major NCD; i.e., s/he is scoring 2 or more SDs below the mean or at the ≤2nd %ile which is far below average (50th %ile). That person is among the one or two worst performing out of 100 randomly chosen people in their age range. Moreover, if you move to Baltimore you can get the same test done at the Johns Hopkins Memory Center a year later to see if you are better, worse or the same. Major NCD, by definition, is a progressive disorder.
An Example without Germs
An example follows of exactly opposite the one above where someone with 99.9% of the average number of germs places them them at the extreme top of 1000 clearly indicating sickness: A 6th grader at the 1st %ile is the shortest out of 100, or roughly the shortest student out of three 6th grade classrooms. Our basketball coach might come across a youngster trying out for basket ball, every couple years, at the 0.1st %ile which means s/he is the shortest out of 1000 students. This kid would be the shortest kid out of about 30 6th grade classrooms with 35 students in each, or the entire 6th grade in a school district. Once in an entire career, the coach might see a student at the 0.01st %ile, who would be the shortest out of 10,000 6th grade students–maybe the entire state of Massachusetts! That kid might be referred to Boston Children’s Hospital for endocrinology studies of possible dwarfism.
To Sum Up
Many of our Major NCD patients display scores well below the 1st %ile, often at the 0.1st %ile and even at the 0.01st %ile making their degree of pathology very clear, almost indisputable if they put forth their best effort. Mentally subaverage people (we used to call this Mental Retardation) have IQ scores of 69 or below, which falls at or below the 2nd %ile. Profoundly MR people would fall at or below 3SDs below the mean. So when we see a retired bank teller who graduated from high school and managed their own life until age 79 starts to show define in ADLs and they score on NP testing 2 SDs below the average expected, similar to a mentally subaverage person, we know there is a probable Major NCD.
People wonder how accurate our test results are? This section helps explain basic statistics in test design, which also covers how medical tests differentiate normal from pathological. You’ve heard of the normal bell curve and it is not too hard to understand how we use that to differentiate normal (health) from “mild” and “major” pathology. Consider: If you lined up one-hundred 6th graders from shortest to tallest in order to buy basket ball uniforms and measured the 50th kid in line and bought uniforms in that size, you could expect them to fit the “average” student. Under the bell curve, we say the height of the 16th through the 67th kid in line represents the average range.
Yes, it is arbitrary, but the statistics turn out such that this range (16th–67th) works well to describe the “average” range for everything from IQ to shoe size. This range for about 68 kids, between the 16th and 67th in height, is considered ± 1 standard deviation (SD) around the mean; i.e., above or below the 50th “perfectly” average tall kid. So the Average range is two SDs, with one SD encompassing 34 of the shorter kids ranging up another SD which includes 34 of the taller than the average kids. In this example a total 64 kids fall either ±1 SD around the mean, of average kid’s height.
Wait a minute. What about the remaining 36 kids? Well, half of them (16) are taller by at least another SD and the remaining half (16) are shorter by another SD or more. In basketball we worry more about the short kids, than we do about tall ones. Our statistics say that the 2nd kid in line up through the 15th are more than 1 SD below the mean range, that’s 14 out of the 16 short kids. We worry a bit about these 14 “mildly” short kids and we might warn them they could spend a lot of time sitting on the bench if selected for the team. But, what about the two (2) shortest kids in line? Heck they are the two shortest out of 100 kids trying out. They fall two or more SDs below the mean; i.e., at or even below the 2nd %ile. This range (≤ 2 SDs) is “severely” short – the coach might advise them to try out for the swimming team rather than basketball. So anyone falling 1–2 standard deviations below the mean is mildly short, while people ≥2 SDs below the mean are severely short. It’s all about SD determining what range you fall in.
Germs and Cut-off Points
We use the range of 2 or more SDs below (or sometimes above) the mean as the indicator of pathology in most medical and psychological testing. If your culture’s germ count ranges from 16% through 67% of the average number of germs people culture, you are in the normal (better stated as “average”) range. If you have 68% to 97% the number of germs (ranging 1–2 SDs more than average) you “may” have a mild infection, so no drugs for you but we wait and watch just in case. However, if your culture show 98% or more germs than average (i.e., ≥2 SDs above the mean) this falls in the pathological range which means you meet criteria to get penicillin. If you have 99.9% more germs you are > 3 SDs having more germs than 998/1000 people so you are on your way to the hospital. You see how handy this standard is, especially as all medical professionals use the same standard of care.
You can see how this system yields standardized “cut off” points to differentiate Mild from Major to even Profound pathology. If someone uses exactly the same culture technique, or NP tests, and gives it in the same way (a standardized practice) then any tester anywhere in the US will get the same result. This means it is a reliable test, which is a necessary condition before a test can be considered valid. After all if different users routinely got different results while testing the same patient, that would be unreliable testing and thus clearly not valid; i.e., a valid measure of the criterion. Another type of validity is to give several different tests (like for memory) and see if they all yield similar results. We give three tests of short-term memory to increase the reliability of our findings, and thus the more the three tests agree the more valid our findings.
When we see a patient scoring 2 or more SDs below the mean on multiple tests, we have a reliable indicator of probable Major NCD; i.e., s/he is scoring 2 or more SDs below the mean or at the ≤2nd %ile which is far below average (50th %ile). That person is among the one or two worst performing out of 100 randomly chosen people in their age range. Moreover, if you move to Baltimore you can get the same test done at the Johns Hopkins Memory Center a year later to see if you are better, worse or the same. Major NCD, by definition, is a progressive disorder.
An Example without Germs
An example follows of exactly opposite the one above where someone with 99.9% of the average number of germs places them them at the extreme top of 1000 clearly indicating sickness: A 6th grader at the 1st %ile is the shortest out of 100, or roughly the shortest student out of three 6th grade classrooms. Our basketball coach might come across a youngster trying out for basket ball, every couple years, at the 0.1st %ile which means s/he is the shortest out of 1000 students. This kid would be the shortest kid out of about 30 6th grade classrooms with 35 students in each, or the entire 6th grade in a school district. Once in an entire career, the coach might see a student at the 0.01st %ile, who would be the shortest out of 10,000 6th grade students–maybe the entire state of Massachusetts! That kid might be referred to Boston Children’s Hospital for endocrinology studies of possible dwarfism.
To Sum Up
Many of our Major NCD patients display scores well below the 1st %ile, often at the 0.1st %ile and even at the 0.01st %ile making their degree of pathology very clear, almost indisputable if they put forth their best effort. Mentally subaverage people (we used to call this Mental Retardation) have IQ scores of 69 or below, which falls at or below the 2nd %ile. Profoundly MR people would fall at or below 3SDs below the mean. So when we see a retired bank teller who graduated from high school and managed their own life until age 79 starts to show define in ADLs and they score on NP testing 2 SDs below the average expected, similar to a mentally subaverage person, we know there is a probable Major NCD.