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A respondent had to correctly recall the name of a character from the scenario. Both the first and the last names consisted of 5 letters each. For each letter, the respondent would get 0.2 points. If the respondent got correct the full first name of the character, the respondent would be awarded 1 full score. If the respondent got both the first and the last names right, the respondent would be awarded 2 full scores.

In this context, what is the level of measurement of the data derived from such question? In addition, what would be the appropriate test to use for determining and comparing averages of the respondents' performances on the question?

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It is somewhat hard to understand what you asking, as your question does not even have a superficial explanation of what you're after. But if you question is simply about the measurement scale of the outcome variable, it's not so difficult.

Your outcome is a count variable. (At least if I get you right that the respondent also gets 1 full score if he gets only the last name right). Though you seem to count not in steps of 1 but of 1/5... This is still a count variable. That means your scale is superior to an ordinal scale at least.

Wikipidia can help you figuring out what scale exactly this implies. If you want to rely on Steven's classification your scales would be a ratio scale (Nominal, Ordinal, Interval, Ratio). You have a natural zero, as you're just counting something. Put verbally your scale measures "How many of the letters are remembered by the participant", and you are able to make statements such as "Participant A remembered twice as many letters as participant B". With an interval-scale you'd only be able two make statements such as "Participant A remembered XYZ more than participant B"

Your problems with this (i.e. the natural max) indicate that there could be finer (or altogether different) classifications of scales.

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  • $\begingroup$ Thank you! The question is from a memory test which assessed the participants' recall of a narrative. Among questions the participants were asked to recall the names of the characters in the narrative. I also think the data is count. Since it does have an absolute 0, it is likely to be ratio. There are more arguments for that. However, I wonder if there are any flaws in my logic. For instance, my data has a maximum value. In addition, only 0.1, 0.2, 0.3, etc, points could be awarded. This would exclude such values as 0.25 or 1.75. Does count data allow for any of that? $\endgroup$ – Billy the Poet Aug 31 '15 at 23:56
  • $\begingroup$ It has the same absolute null as any count data: no letter is recalled correctly. $\endgroup$ – sheß Sep 1 '15 at 7:22
  • $\begingroup$ Also the fact that values in between are excluded is normal for count. When you count in natural numbers, you exclude 1.5. $\endgroup$ – sheß Sep 1 '15 at 7:23
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    $\begingroup$ There are different ways of characterizing scales. Depending on which you choose you'll end up with a different classification. Ratio implies a natural null, which you have... what's maybe different in your specific context is that you also have a max by design. Since you seem to be trying to avoid settling on a topology and checking what scale that implies for you, maybe it helps if you tell us why you're after that question $\endgroup$ – sheß Sep 1 '15 at 7:37
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    $\begingroup$ So, you mean typology, not topology? And, thank you for the update and all your help. It all makes sense. I am thinking of using Steven's criteria for describing my data. $\endgroup$ – Billy the Poet Sep 1 '15 at 10:00

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