Todd Landman Academic Magician
May 22, 2024Todd Landman

Cards and Statistics

I had a wonderful session today in a workshop on statistics. My chosen teaching tool was a deck of playing cards. My core text was the amazing book, Knapp. T.R. (1996) Learning Statistics Through Playing Cards (Sage Publications).

We began with a process of 'thick description', where each participant randomly selected a card and described it, including the colour, the number, the design, and other salient features. As we moved from one participant to the next, I asked the group to start to notice any patterns, regularities, and variables that recur across the different cards.

We began with the assumption that none of them had actually seen a deck of cards before (suspending disbelief), but that through aggregating what we learned through description, we could start to draw inferences about the full universe of cards contained in a standard deck of 52 cards.

Not only did they describe the cards they held in great detail, but they also took their descriptions to the next level by providing deep interpretations of what the cards meant to them: an image of heaven, the presence of a strong force, the presence of love, the presence of princes and princesses.

Of course, I divined one or two cards held by our participants without ever having seen their cards, just to add a certain frisson to the proceedings.

Our next exercise was to have the group work in pairs taking two random samples of 10 cards each and then recording the different variables on a spreadsheet.

They learned through this exercise that certain patterns emerge and that with repeated random samples, they would eventually learn both the totality of a deck's attributes and its total number.

Our next exercise was for our paired groups to select two random samples of 20 cards each and note simply whether a card had been selected or not, creating list A and list B. We then noted which of the cards had been selected across both A and B with a final column we called M.

This exercise involves the following matrix of possibilities:

Using a simplified equation for what is known as 'multiple systems estimation' (MSE) we calculated the total number of cards (N) from this known population (A, B, and M):

The final calculations varied tremendously, but the closest example came to a total calculation of 50 cards, which is not too bad given the constraints and the simplicity of the exercise.

We then completed the workshop with a debate as to the strengths and weakness of efforts to count things using samples and inferential statistics.

Overall, using playing cards in this way proved to be a useful and effective teaching tool that got our participants comfortable talking about quantitative analysis and its role in understanding the social world.

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