Types of Data: Categorical vs Continuous

Full transcript

Word for word what is said in the video — the same text as the subtitles. Times are minutes:seconds into the video.

0:00Two averages from one results list ▶

One school fun run, five kilometres, eight runners, and one list of results with six columns. Four of those columns hold numbers, so a spreadsheet will happily average any one of them. The average bib number, the number pinned to each runner's shirt, is one hundred and forty-eight point five. The average finishing time is twenty-seven minutes and thirty seconds. Both answers look equally solid, but only one of them tells you anything about the runners. By the end of this video: how to tell which is which.

0:33Isn't every number an amount? ▶

Every dataset starts with one question, before any chart or any average: what kind of data is this? It is easy to skip, because a column of numbers looks like an amount, and amounts can be averaged. But a number is not always an amount: a phone number is just a name written in digits. Nobody adds two phone numbers together, and telling these two kinds apart is the first step of this course.

0:57The average test ▶

Here is a simple test for any column: if you take its average, what would that average mean? For the finishing times, the answer is a sentence: on average, a runner took about twenty-seven and a half minutes. For the team column, gold, red and purple, there is nothing to average at all. Those are categories: names for groups, and a column of them is called categorical. A column that passes the test holds amounts, and one that fails holds categories, whatever it looks like. And one column on this sheet is not quite what it looks like.

1:28Which columns can you average? ▶

Back to the full results sheet, with all six columns side by side. Which of these columns can you average and still say something about the runners? Pick yours before the numbers start to move.

1:42Swap the bibs, swap the times ▶

Here is the bib column again, and its average is one hundred and forty-eight point five. Now let the winner and the runner who came last swap their bib numbers. Same runners, same times, same finishing order: nothing about the race has changed. Swap their finishing times instead, and the race itself changes: the runner who came last suddenly wins. The organisers could just as well have printed five hundred and one up to five hundred and eight, shuffled in any order. Then the average bib would be five hundred and four point five, for exactly the same race. So that average describes the printed numbers, not the runners who ran. A spreadsheet cannot tell you which columns are names: you have to know what each number stands for. So what about a column that does have an order, like first, second and third?

2:28An ordered category: ordinal ▶

The place column is a category with an order: first comes before second, and second before third. But look at the times right next to it. First and second are two seconds apart, a close finish, while second and third are two minutes and twenty-eight seconds apart. The places go up in equal steps of one, but the gaps behind them are anything but equal. That is a category with an order, called ordinal: it gives you an order, but not a distance. People still average star ratings and survey scales all the time, and statisticians argue about whether they should.

3:00Two options: dichotomous ▶

Then there is a column with only two possible answers: did this runner set a personal best, yes or no? A category with exactly two options has its own name: dichotomous. Two options make it simple, because one number says it all: how many runners got a yes. Here that is three of the eight runners.

3:20Measured or counted: continuous and discrete ▶

The finishing time is an amount you measure, and that makes it continuous. Here is a quick check: take two values and ask whether the point halfway between them makes sense. Halfway between the third and the fourth time is twenty-seven minutes and two and a half seconds, a perfectly real time. The races column counts how many races each runner ran this year, so it is discrete. Halfway between one race and two races is one and a half races, and nobody runs half a race. An average of counts still works, though: these runners ran three races each, on average.

3:53One tree: category or amount ▶

Put together, every column hangs on one small tree. On one side are categories: without an order, like the teams, with an order, like the places, or with just two options. On the other side are amounts: measured, like the times, or counted, like the races. And the bib numbers sit next to the teams, because they are names that happen to be written in digits. So the columns whose average tells you about the runners are the times and the races, and the places only give an order.

4:21One look back ▶

Back to the video on misleading graphs, with bus seven and bus four. Which branch of the tree do the bus numbers belong on? The bus numbers are names, like the bibs, while the minutes late are a measured amount.

4:34In one picture ▶

So, in one picture: before you average a column, ask what each number stands for. Categories name groups, ordinal ones give a rank without equal steps, and dichotomous means just two options. Amounts are measured or counted, and an amount is the kind of column whose average really tells you something,

4:52Next time ▶

so if averaging a category tells you nothing, what can you do with it? Next time: counting, proportions and the most common answer. And if a number has ever fooled you into averaging it, tell me in the comments which one. And if you want to keep learning, subscribe, the next video will find you. Until then: happy learning.