Please, help bring in some lucidity and fill in any possible gaps in my reasoning.
The research assessed the participants' recall of a narrative story. One day after the presentation of the narrative, the participants were given the memory test. Their answers to some of the questions are then processed as correct, or 1, or incorrect answers, or 0. Those participants in the questionnaire who answered correctly deserve to be given scores whereas those who answered correctly get nothing Sort of like back in school when they gave out quizzes. These are clearly dichotomous data.
Now, I need to apply Stevens's typology and see which one of the four levels of measurement these data belong to. Usually, binary data are seen as nominal level. Examples of such are female/male, smoker/non-smoker, yes/no, etc. In these cases all the data would be equal and would differ only in the nominal characteristics. However, if the data are binary, but not equal and one value is greater than the other, it indicates the distance between the two values. Among scales measuring distance are ordinal, interval and ration. The last two are out as the data are, again, binary, have absolute 0, are discrete, and no information is given about how much one value is greater than the other.
This all points out to ordinal data that happens to be organized as dichotomous. In such case, the data can be compared and ranked. There is a clear difference between the values and it is also meaningful to the context of the analysis (correct answers vs incorrect). However, nothing can be said about how the difference itself. All what is certain is that 1 is superior to 0.
My question is, do you think there are any flaws in my reasoning? And, if no, do you know of any sources, such as books or papers, which mention the case of ordinal being dichotomous? This is important because I would like to see what others have written about it. One problem here is that there is not much what can be done with such data. If the data are ordinal, it means the only descriptive at disposal is a median, but that would result merely in either 1 or 0 of values, since the values are limited in range. I also have doubts about inferential tests. Maybe, there is another way around it.
The research assessed the participants' recall of a narrative story. One day after the presentation of the narrative, the participants were given the memory test. Their answers to some of the questions are then processed as correct, or 1, or incorrect answers, or 0. Those participants in the questionnaire who answered correctly deserve to be given scores whereas those who answered correctly get nothing Sort of like back in school when they gave out quizzes. These are clearly dichotomous data.
Now, I need to apply Stevens's typology and see which one of the four levels of measurement these data belong to. Usually, binary data are seen as nominal level. Examples of such are female/male, smoker/non-smoker, yes/no, etc. In these cases all the data would be equal and would differ only in the nominal characteristics. However, if the data are binary, but not equal and one value is greater than the other, it indicates the distance between the two values. Among scales measuring distance are ordinal, interval and ration. The last two are out as the data are, again, binary, have absolute 0, are discrete, and no information is given about how much one value is greater than the other.
This all points out to ordinal data that happens to be organized as dichotomous. In such case, the data can be compared and ranked. There is a clear difference between the values and it is also meaningful to the context of the analysis (correct answers vs incorrect). However, nothing can be said about how the difference itself. All what is certain is that 1 is superior to 0.
My question is, do you think there are any flaws in my reasoning? And, if no, do you know of any sources, such as books or papers, which mention the case of ordinal being dichotomous? This is important because I would like to see what others have written about it. One problem here is that there is not much what can be done with such data. If the data are ordinal, it means the only descriptive at disposal is a median, but that would result merely in either 1 or 0 of values, since the values are limited in range. I also have doubts about inferential tests. Maybe, there is another way around it.