2

Continuous variables can be split into three categories according to statements over here: http://www.unesco.org/webworld/idams/advguide/Chapt1_3.htm. One category is Interval - scale Variables. It also gives an example that Counts are interval scale measurements, such as counts of publications or citations, years of education. However, based on my understanding, 'counts' should be discrete variables.

Could anyone tell me why counts are continuous variables ? thanks !

Glen_b
  • 257,508
  • 32
  • 553
  • 939
tqjustc
  • 121
  • 1
  • 3
  • 3
    Counts *aren't* continuous. "Quantitative" and "continuous" are *not* synonyms. Don't believe everything you see on the internet ... especially when it comes to stats. (In fact, don't believe everything you see in quite a few intro. level stats textbooks either. There are some really poor ones to b e found.) There's a lot of misinformation to be found. – Glen_b Nov 08 '14 at 08:34
  • @Glen_b could you give me any materials about 'continuous variable', 'discrete variables', 'interval variables', 'ordinal variable', and so on ? Thanks – tqjustc Nov 08 '14 at 08:44

1 Answers1

4

Discrete vs continuous: The real difference here is that the values that a discrete random variable can take are countable, while a continuous random variable takes values in some set of intervals -- its possible values are not countable.

For example, atmospheric pressure would generally be regarded as continuous.

The number of eggs laid by a chicken per day is discrete (you can count the possible values that it can take). Not all discrete random variables are integer, nor even equispaced.

Those two classes are not exhaustive - there are random variables that are neither (for example, mixtures of discrete and continuous).

The rest of the things you mention are from Stevens' typology of levels of measurement.

Stevens' levels are:

Nominal: The values are category labels (e.g. political affiliation, car color). They have no intrinsic order.

Ordinal: ordered categories (e.g. socioeconomic status, level of educational attainment).

Interval: differences in two values are meaningful -- equal-sized differences mean the same thing (e.g. "5"-"3" is the same as "4"-"2". The classical example of this scale is temperatures (whether in Celcius or Farenheit).

Ratio: Interval, with a meaningful zero, in such a way that equal ratios carry the same meaning -- "2" is twice as much as "1", "6" is three times as much as "2" and so on. The volume of water in a dam is ratio-scale.

Stevens' typology isn't the only possible categorization (there are other typologies), and you must beware people being overly prescriptive about this particular way of classifying variables; the level of measurement isn't necessarily inherent, but a matter of what questions you ask of the variable.

Community
  • 1
Glen_b
  • 257,508
  • 32
  • 553
  • 939
  • Indeed, counts are both ratio and discrete. – Peter Flom Nov 08 '14 at 12:38
  • 1
    Some people like to restrict the name _discrete random variable_ to random variables that take on a (countable) set of _discrete_ values, that is, for each $x$ that is a value that $X$ takes with positive probability, there is a _neighborhood_ of $x$ such that $X$ does not take on any _other_ values in that neighborhood with positive probability. In other words, the _next larger_ or _next smaller_ value of $X$ cannot be arbitrarily close to $x$. Thus, $X \in \mathbb Q$ is not a discrete random variable, while $1/Y$ where $Y$ takes on all positive integer values is a discrete random variable. – Dilip Sarwate Nov 08 '14 at 16:23
  • @Dilip thanks for that (+1) - it's new to me; I've seen $X\in\mathbb Q$ explicitly mentioned as discrete-because-countable, but don't immediately recall (I may just be forgetting) having seen it excluded from being discrete (I think either could be a reasonable way to set up definitions, so it's not surprising to see that some people would define it that way). If you have one or two references you'd suggest on that, I'd be interested to see. [However, if you don't have any come to mind right now, don't waste any time finding one - I'll spend my own time on that rather than waste yours.] – Glen_b Nov 08 '14 at 22:44