# How do I figure out low, high, and median scores?

I am not sure how to make this a problem and solve it. It's statistical data that I am trying to figure out for a paper I'm writing.

Basically, I am scoring candidates with 9 questions. Here's an example of a question:

1. Number of prior convictions
a. None (1)
b. 1-4 (2)
c. 5 or more (3)

Too low of an answer would make the person a bad candidate, too high would also make them a bad candidate. I'm trying to figure out what the low end, median, and high end ranges are. I know there must be a statistical formula in figuring this out, I just don't know what it is. Any help would be appreciated.

• What do you mean by "low end, median, and high end ranges"? It sounds like you are trying to categorize the candidates in three groups based on their score on your questionnaire. What is the intent of this classification? Apr 16, 2015 at 7:47
• Its not especially clear what you intend by 'low', 'median' and 'high' here. Apr 16, 2015 at 10:31
• There's a range that a person would be a good candidate. Between x and x they would be accepted. any numbers outside of the x and x would not be good candidates. It's a hypothesized test to determine if a person can be in a therapeutic program.
– Mel
Apr 16, 2015 at 10:49

This would need you to make some subjective choice on what is "low" and "high". There is no objective "low" and "high", e.g. is length of 100 cm "short" or "long"? (It depends.)

Notice that this is categorical data so the only thing you can do with it is to count answers - you cannot sum the answers because it would be meaningless.

What you can do is to do some kind of cluster analysis of your data to find clusters of people giving similar patterns of answers. One of the methods that may be appropriate in here is for example Latent Class Analysis (check the paper by Linzer & Lewis, 2011 on poLCA library that describes both the method and software you can use for it).

Other approach would be to use the answers to predict some outcome, e.g. a certain pattern of answers predicts not dropping out from a certain treatment. For this you can use a number of methods depending on what is your data and the outcome. Of course, this would need you to have data enabling you to do this kind of analysis.

Finally, the third thing you could do is to analyze the content of your scale. Are there any subscales? Are answers to some questions more informative then others? Here also a number of methods could be applied, for example Item Response Theory-based ones. DIF analysis could help figuring out if some questions are biased towards some groups (e.g. females are more inclined to answer "yes" for certain question, so "yes"-es are over-represented in this group).

You could also use expert judgment of the qualitative content of your scale. Do certain questions give information that suggests some possible interpretations? Maybe some questions are more important then others because they focus on themes that have a greater meaning in this area?

Of course this depends on your objectives and the data you have or plan to gather. There is no single answer to this, but it rather needs a decision to be done on what to focus on. So there are few questions you need to ask yourself, but I hope my answer gives you some possible directions and hints.

• Thank you for the explanation, but I'm still lost. Idk how I got a B in statistics last semester. I wrote a paper on recidivism. I added an appendix at the end of my paper in the form of a test. So, the test says if a person is between x and x scores they're good candidates. If they're < or > a certain score they're not good candidates. The very highest they can get is 27 (9 questions w/ 3 being the highest score on each question). The lowest is 9 (w/ 1 being the highest score on each question.) There are 5 static & 4 dynamic questions. Do I just throw #'s out there since it's a hypothesis?
– Mel
Apr 16, 2015 at 10:48
• @Mel In this case the sum would not have much mathematical meaning (you get 3 points for "5 or more" - what does it mean?). That is why I suggest few alternative approaches rather then summing and setting an arbitrary cut-off point.
– Tim
Apr 16, 2015 at 11:08