I'm on measurement scales (2 of 6) from chap 1 Intro of Hyperstat

I think it's interesting they mention a "controversy" over the appropriateness of computing a parameter like mean from ordinal level measurement scales, claiming that it will tell us nothing of value (for example, nothing about central tendency, unlike with a ratio or interval level of measurement scale.

I wrote this mostly to practice using Prof. Lane's language. I remembered everything except "interval" (I remembered it as "integer", which felt wrong).

Comments

[TGGP]

One way to understand their objection is to imagine that the numbers represent ranges or buckets (as is the case with income in the GSS). The actual average income could be in a different bucket from the average of numbers representing buckets.

[Hopefully Anonymous]

I'll finish the measurement scales 6 pages before commenting.

[Hopefully Anonymous]

I read through the Measurement Scales pages.
Unless I'm overthinking it, my grasp on the "controversy" is incoherent.

"The actual average income could be in a different bucket from the average of numbers representing buckets."

Explain this more?

[Hopefully Anonymous]

okay, at least with regards to "the behavioral sciences", it seems like ordinal scales are our best efforts at interval scales. So the problem of taking means seems like more of an asymptotic one with regards to "the behavioral sciences".

Is this what you mean by buckets?

Let's say I have 3 buckets, 1, 2, &3.

Bucket 1 holds incomes 0-1,000
Bucket 2 holds incomes 1,001-2,000
Bucket 3 holds incomes 2,001-3,000

Sorted into bucket 1:
(1) 999
into bucket 2:
(3) 1,999
(4) 1,999
(5) 1,999
(6) 1,999
(7) 1,999
bucket 3:
(6) 3,000
(7) 3,000

The "average of numbers representing incomes" would be in bucket 2, whereas the "actual average income" would be in bucket three.

So in the non-imaginary world, it's pretty much always a good idea to weight median more for central tendency than mean?

If so, this fits a preexisting suspicion I have that public intellectuals and public intellectuall discourse often uses "mean" or "average" to advance (and conform) to popular mythology, or to cover repugnant "truths" related to their field.

[Hopefully Anonymous]

Ok, at an intuitive level i think i understand everything except throwaway lines about how statistical tests can rule out chance as an explanation of findings.
I understand repeated replication of findings as a way to rule out chance as an explanation of findings, but that's more expensive than the actual experiment,
so I don't think it would be considered a statistical test.
I imagine it has to do with relatively efficient application of previously discovered probability rules and rigorus logical extrapolation
to determine that findings would be unlikely to be arrived at by chance.

[TGGP]

You did a good job of elaborating on my hypothetical. The hyperstat page also gave a good example. It should be noted that my Half Sigma vs Kevin MacDonald post egregiously violates such rules.

Levy & Peart have been promoting medians over means, but wound up with egg on their face when they took to task Surowiecki & Galton. It is generally preferred to use medians when it comes to income so Bill Gates or other outliers don't distort things, though I don't think money is clearly ordinal rather than interval/ratio (I guess if you measured it to the dollar you'd be overlooking cents and putting that range in a bucket, but whatever).

You're right that such tests can't completely rule out chance. I guess if you want to be really picky even repeated replications can't. It would just be very unlikely for it to be due to chance. You're also right that true interval scales are rare (at least the hyperstat page says so) with Fahrenheit temperature being a lone example.

[Hopefully Anonymous]

I'm way out of my league here, but wouldn't we have the same measurement problems of placing Fahrenheit temperatures on an interval (as opposed to ordinal) scale as we would anything else in nature?

At the end of the day isn't it all baskets (the basket being our error or uncertainty margins?)

I think it's helpful that you highlighted the difference of the problem of finding central tendencies with means due to outliers vs. due to to misleading ordinal scales (although it seems to me to be the same type of problem in principle, but perhaps not in human intuition and conception).

[Hopefully Anonymous]

Went back and clicked through some of the hyperlinks I skipped in the introduction through the end of measurement scales. Didn't go all the way down the rabbit holes with them, but ended up at stuff like standard deviation and histograms that I've learned before but that I don't have quick wit familiarity with. Looks like they appear later in the introduction chapter --I'll go deeper with them as I encounter them in the natural sequence.