types of data

I am trying to figure out if the data from this question would be considered discrete, continuous or nominal data.

How many antibodies (in ng/dl)?
a) 1 to 10
b) 10 to 20
c) 20 to 30


****I originally think that it's continuous since the data isn't stepwise but at the same time it's broken down into intervals does this mean that would be discrete? It's really difficult for me to distinguish between them

Is it possible to change continuous data to discrete data?


help?

I had the same dilemma while reading the problem statemenf for the first time. It really depends on what sort of measurement you are making and how you are looking at it. Most fundamentally, you are counting antibodies. This makes is discrete. 1,002,405 is not the same as 1,002,406.

Now let's mess with it a little. If you were calculating the proportion of the solution that is antibodies, is that continuous? It is more continuous-looking, but really it is also discrete. I explain. If dropping one more antibody into the solution gives a different result, it must be discrete. If it doesn't change the result (because your error is more than one, or you are using only one decimal place, or whatever), then your data may be continuous.

The Dropping One Theory (I just invented it.)

10/99 = 0.101010
11/99 = 0.111111
12/99 = 0.121212

#1 - We are counting, so I'm thinking discrete.
#2 - We really cannot get 0.112233, since we cannot possilbly count 11.11111111 things. Missing values are a good clue that things are not continuous.

Let's try that again.

10/9999999 = 0.00000100000010...
11/9999999 = 0.00000110000011...
12/9999999 = 0.00000120000012...

Clearly discrete, since we cannot get 0.0000011111...
HOWEVER, if we record only six (6) decimal places:

10/9999999 = 0.000001
11/9999999 = 0.000001
12/9999999 = 0.000001

It's just not as obvious that this is not continuous.

Obviously, the Dropping One Theory needs some standardization and fundamental rigor, but are we seeing any more clearly? Another example comes to mind as I type. Height of humans really is continuous date, but we don't normally measure things that way. Many folks in the U.S. are 5' 4" or 5' 5" - maybe 5' 5½" - but it is unlikely anyone will report his or her height as 5' 5.4618561548465654548654564" The way we record the data make discretize the data. This is actually quite a common thing in Digital Signal Processing. A continuous signal is produced, but it is made discrete before being transmitted.

Well, I have enjoyed this little discussion about discrete and continuous. I hope I have helped rather than further confused.

THANKS tkhunny!

Looking back at the question, I got thinking if we were collecting the data based on whether the individual chose to answer a), b) or c) would it really be ordinal qualitative data since the magnitude of the number withing those ranges are not important (we lost the detail in the data by changing a discrete data set to a ordinal data set) but the issue with that is the variable we're looking at was quantitative when ordinal should be strictly qualitative.

I guess I am partially still stuck on whether we are looking at the variable or "the options of the questions" and if ordinal qualitative data can be derived from something that was truly quantitative. I think normally we won't consider the magnitude of the numbers in an ordinal data set to be important? which makes this even more tricky

thanks again

It is hard to call an ordered choice other than ordinal, even though it might be the intent. This is important on an election ballot. Even though names clearly are neither ordinal nor quantitative, that top name is almost sure to get more votes just because it is listed first. If position matters, it's hard to say it's not ordinal.