Some researchers use the one sample t-test to determine the level of the examined variable(s) in their sample (i.e., high, moderate, low). They do so by comparing the midpoint of the scale (i.e, the theoretical mean) with the actual mean of the scores. On the other hand, other researchers prefer to develop their own criteria depending on the range of the responses (for example, saying that a medium score ranging from 1-1.32 is low, 2.33-3.65 is moderate, 3.66-5 is high). Which of these two way do you think is more accurate?
It is rather intiutive question. Sometimes there are outliers in data (so called leverage points) for example data A is 1,4,6,9,11,13,15, 100, in that case mean is not a good measure of central tendency instead median would be better.. while if theire are no outliers in data for example data B 1,4,6,9,11,13,15 than mean is okay.
So defining threshold depends on your data...
There is no good statistical for this sort of question. It depends on the nature of your sample, the question, and the response format.
Are you wanting to give a score to each respondent - High, Moderate, or Low? Why? Or are you wanting to give a summary score for a whole group of respondents: "Overall, this group rates the issue High while this other group rates the issue Moderate." If so, why not just compare the two means? (t-test)
Your example suggests that you have used a Likert-item, a 1-5 rating scale, for which you'd calculate the sample mean, and perhaps compare the means of sub-groups.
What if the question is something like, "In my career, I want to make my parents proud"? And you give a response form as a standard 5-point Likert-item: "Strongly-Disagree" to "Strongly-Agree"? Almost everyone in your sample will check "Strongly-Agree" or "Agree". No-one will check "Disagree" or "Strongly-Disagree". So you really have a two-point scale, not a five-point scale. To decide that a response of 4 or 5 means "high" just says everyone is "high". You don't learn anything.
If you really need to reduce the number of classifications to "high, moderate, low" (three-points instead of five-points), then look at the data first. Look at each question and look at the median and the distribution. If you want to transform the score for each respondent, then maybe divide the sample into strata based on distance from the median, so that the lower third is called "low", the middle third is called "moderate" and the higher third is called "high". This is always only approximate when you're working with rating scales. In the "make my parents proud" example, you'd end up with 1,2,3="low", 4="moderate", and 5="high" and there would be many more at "high" than at the others.
Dear Winzar
Thank you very much for your illustrations. Actually, my question was not about comparing between two groups nor about giving a score for each respondent. My question was to say to what extent the sample group (overall) manifest a trait? For example if I am applying a questionnaire about anxiety on a sample of university students and one of my questions is to know what is the level of anxiety among these students.
I think your last paragraph may give an answer.
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