Help With Statistics

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LP, you are on the right track. The first thing to determine with a variable is if it is continuous or categorical (discrete). Once you do that, then you have one of two choices. If it is discrete/categorical, then you know it must be either nominal or ordinal (I won't get into the actual psychometrics/econometrics of what is really categorical versus continuous). For instance, if you have a bunch of different categories for like types of basketballs but they aren't ranked in any way, it's nominal. Student classification is a little more vague since military rank would be considered ordinal. Just remember, for ordinal, there must be a ranking system but no real way to determine the differences between the categories, just that they are ranked (e.g., big, kind of big, kind of small, small).

For interval and ratio, which are continuous variables, the real difference lies in the zero point, and whether it is arbitrary or not. For interval, you can use negative numbers and the zero point exists arbitrarily while for ratio, it is not arbitrary (i.e., Kelvin). I would say ratios are the hardest to come by and many statisticians treat ordinal as interval.

 

Crudder has an excellent recap. I'm taking a biostats course this semester and we finished discussing this topic a while ago. From my notes, a good starting point is to describe how variables can be classified. My instructor stated they can be thought about in two ways. First, with respect to "gappiness", that is, are there gaps between successive measures? For example, asking several people how many kids they have. The answers will be whole numbers and there will be gaps between them, i.e. 2, 4, or 0 kids if asking 3 women. No one could have 2.4 kids so because there are gaps between these value, these data are discrete.

For data without gaps in between successive values, they are continuous. This is to say between any two values, there could potentially be another observable value. Height, weight, income, etc. Basically, I remember this as data that can only be expressed using integars are discrete and those described as rates or with floating points are continuous.

The second way to describe this is by levels of measurement. Here's were they are broken into nominal, ordinal, interval and ratio. Nominal is only for named observations (Sex, Race, Ethnicity, Marital Status, etc). Ordinal allows grouping or provides some sort of order and the intervals are not equally spaced (Age groups). Interval and Ratio have equally spaced units with the difference being in interval data, zero does not mean a null value while in Ratio data, zero stands for a null value. For example, on the temperature scale, 0 does not mean a null value, it actually means something (freezing point of water on the Celsius scale) so it would be interval. While if you're measuring weight, 0 means a null value for weight so it would be ratio data.

*all the notes are courtesy of Dr. Yamal at UT SPH (don't want to come off as plagiarizing )

 

My degree was in statistics so I should know this stuff. However, we never did this, but I'll try to help anyway.

For this question, I can guarantee that B and C are not interval or ratio. If it is continuous then there has to be infinite values. So 4.5839 would be a value between bad and very bad. I don't think that's possible.

Saying that, I think those are ordinal and the teacher had a typo. I found an example that had that same thing and it said it was ordinal.

 

The answer for C was based on what I mentioned in an earlier post. Although it technically is ordinal, most statisticians treat it as an interval scale because it is likert ranked i.e. 1-5 where 1=very good and 5=very good. They treat the variable as continuous although it is technically categorical by nature. By this standard, B can also be treated as an interval scale.

 

Statistics is hard (plus I suck at anything that has numbers). Got a C-