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I recently learned about Level of measurements and I am really confused in this MCQ where I think the right answer is a and d both. Lets say the three participants finished in a race in 45 seconds,35 seconds and 30 seconds, this is a interval data since there is fixed order and 0 has no meaning and if we convert it to ordinal 30s becomes first 35s second and 45 second third,according to this option a perfectly fits. What am i missing here?enter image description here

Bilal Alam
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    It is not quite clear to me what your question is but if the one which is ticked, the happiness one, is supposed to be the correct answer then I would find a new course. In fact any course which teaches about Steven's typology is probably best avoided as the classification confuses things which are usefully separated. – mdewey Jul 17 '18 at 16:44
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    Happiness 1 to 10 is ordinal. So that's fine ordinal to coarse ordinal. But the question is a confused mess with examples of different flavours. Perhaps that's deliberate, but I'd grade the grader similarly to @mdewey. – Nick Cox Jul 17 '18 at 17:28
  • @mdewey This question was part of a short exam in one of the most famous course for data science on edx "data science essentials", and yes I checked A as the right answer only to know that my answer is wrong and the right answer is D – Bilal Alam Jul 18 '18 at 07:47
  • I do not understand which part of "my" question is confusing, yes the MCQ is confusing but my question is clear. @mdewey – Bilal Alam Jul 18 '18 at 07:49
  • Your question was "What am I missing here?" and I was not sure which part of the typology you wanted to ask about or possibly which of the four options you were unsure about. – mdewey Jul 18 '18 at 08:30
  • Alright my bad I should have added more context in the question, I wanted to say that I am pretty much sure that option A is the right answer and I explained the my reason for it too, but I found out that D is the right answer which I could not digest, I thought I must have missed some key concept while understanding the typology. @mdewey – Bilal Alam Jul 18 '18 at 09:00
  • I have paused my learning because I think I am not sure I understand the typologies well enough, but as you said "In fact any course which teaches about Steven's typology is probably best avoided" , should I resume the learning ignoring typologies? – Bilal Alam Jul 18 '18 at 09:03
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    Picky point: person in question was S.S. Stevens. Stevens' scale and Stevens's scale would both be defensible punctuation, or even the Stevens scale, but Steven's is a typo. – Nick Cox Jul 18 '18 at 09:45

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Going through the options in order.

Marathon finish time has a true zero: if you take five hours you took twice as long as someone who took two hours thirty minutes. So this would be reducing a ratio scale to an ordinal.

Age has a true zero: a seventy year old is twice as old as a thirty five year old. Whether that is a meaningful doubling is another question.

Temperature in Fahrenheit has no true zero so if you are prepared to say the difference between twenty and thirty is the same as between thirty and forty that is interval. If you believe that the intervals on the categorised variable are also equal then this is interval to interval, otherwise interval to ordinal.

The happiness scale has neither true zero nor equal intervals so is only ordinal unless you are prepared to believe that from 1 to 2 is the same as 2 to 3.

As I mentioned in a comment I do not believe this typology is a helpful one in understanding the richness of the measurements we impose on the world around us, but it is widely taught.

For another take on the issue see Mosteller and Tukey as quoted in the Wikipedia entry on Level of measurement

Mosteller and Tukey noted that the four levels are not exhaustive and proposed:

Names
Grades (ordered labels like beginner, intermediate, advanced)
Ranks (orders with 1 being the smallest or largest, 2 the next smallest or largest, and so on)
Counted fractions (bound by 0 and 1)
Counts (non-negative integers)
Amounts (non-negative real numbers)
Balances (any real number)

For a light hearted analysis see also Lord's article On the statistical treatment of football numbers

mdewey
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