Timeline for Why do some tests have a (nonzero) minimum score?
Current License: CC BY-SA 3.0
16 events
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| Jan 8, 2016 at 12:04 | comment | added | ff524 | @ToddWilcox "they do not tell you anything about how many questions you got right." - It's possible for an exam score on any kind of scale, including ratio scale, to not tell you how many questions you got right. (e.g., if questions are not weighted uniformly.) But for a detailed explanation of different kinds of scales of measurement, try Cross Validated - it's probably out of scope of this answer. | |
| Jan 8, 2016 at 12:00 | comment | added | Todd Wilcox | You wrote "not really". Which one(s) of my statements is/are not correct? | |
| Jan 8, 2016 at 9:38 | comment | added | ff524 | @Falco The reason we often start interval scales at a number that isn't zero is to signal that there's no true reference, and that people shouldn't apply operations that "feel natural" to this scale. Most people intuitively associate a zero with an absolute reference, as you know, which would be a wrong thing to do in this case. (The specific choice of non-zero number is not meaningful, but the fact that it's non-zero is a convention that serves as a deliberate signal.) | |
| Jan 8, 2016 at 9:34 | comment | added | Falco | @ff524 exactly that makes the 200 completely arbitrary! Blank page could also be 5million points. But most people would probably assign intuitively 0 Points for zero effort, just because it feels natural. So why the arbitrary 200 ? Even 100 feels more natural than 200. | |
| Jan 8, 2016 at 9:31 | comment | added | ff524 | @Falco When you say "get 200 points" you assume that the reference is 0 (i.e. that you get 200 points more than 0.) That's not valid on an interval scale, where there's no absolute reference. You might also say that the 200 minimum score means you get 400 points for zero effort (400 more than -200) or 1 point for zero effort (1 more than 199.) All of those statements are meaningless on an interval scale. | |
| Jan 8, 2016 at 9:25 | comment | added | Falco | This doesn't answer the question at all. The question was not "what are the properties of an interval scale" but why does someone get 200 Points for handing in a blank paper (zero effort) ? | |
| Jan 8, 2016 at 8:45 | comment | added | ff524 | @Todd Not really. The key idea is that the interval scale has no real reference point ("absolute zero "), and relationships involving division or multiplication (e.g. "twice as much") have no meaning without a real reference point. For example: is an 800 score twice as high as a 400 score? If I shift all the scores down by 200 (which I can do, because there's no true reference point), so those same scores become 600 and 200 - is 600 twice as good as 200? No to both. That's the idea. | |
| Jan 8, 2016 at 6:28 | comment | added | Matt | @cagirici, sure, I don't disagree that the scores are meant to be interval (i.e., "Celsius") measurements, but I think that adding an offset to the scores (and hoping people notice) is an odd and subtle way of indicating that. Wouldn't it be easier to write "INTERVAL MEASUREMENT" or something somewhere in the guide to interpreting the scores? | |
| Jan 8, 2016 at 3:36 | comment | added | Todd Wilcox | Ok I followed the comment link and I suggest this answer would be improved a lot by explaining some of what is in there. If I understand correctly, test scores that have no zero point can only tell you if you did better or worse than the others taking the test, and they can tell you how much better or worse you did, and they can tell you if you did better or worse than last time, but they do not tell you anything about how many questions you got right. Do I understand that correctly? | |
| Jan 8, 2016 at 3:24 | comment | added | Todd Wilcox | I did notice that but I don't understand the significance. Two questions come to mind: 1) Why use an interval scale instead of any other kind of scale (this seems to be the thrust of the original question)? And 2) Can an interval scale score be converted to a ratio scale score? If not, what does an interval scale score tell us in the first place? | |
| Jan 8, 2016 at 3:14 | comment | added | ff524 | @ToddWilcox You're right: the first paragraph is also true of ratio scales (which do have a "true zero.") The second paragraph is true of interval scales but not true of ratio scales - that is, multiplication and division are valid operations for ratio scales but not valid for interval scales. Also see this wikibook. | |
| Jan 8, 2016 at 3:09 | comment | added | Todd Wilcox | The block quote seems authoritative and valuable and for me it is not clear enough to understand completely. Pointing out that the difference between 150 and 160 is the same as the difference between 80 and 90 does not illuminate anything to me because that's what is normally the case for scores that do start at 0. In short: I still don't get it. | |
| Jan 8, 2016 at 2:04 | comment | added | padawan | @Matt I think what ff524 says is the relation between Celsius and Kelvin. Why is 0C != 0K but 0C = 273.15K? The answer is xC - yC = xK - yK for all x and y. And no other ratio would satisfy this equation. | |
| Jan 8, 2016 at 1:12 | comment | added | Matt | I'm not sure this answers the question very well: it's certainly true that the scores are interval measurements, but it seems strange that the scores would be offset ONLY to to indicate that--it just seems oddly subtle. | |
| Jan 6, 2016 at 21:36 | history | edited | ff524 | CC BY-SA 3.0 |
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| Jan 6, 2016 at 20:33 | history | answered | ff524 | CC BY-SA 3.0 |