Co-occurrence matrices

A co-occurrence matrix is a simple, powerful way of displaying and analysing results from card sorts. It shows how often participants group each card in a card sorts pack with each of the other cards.

In the example below, the numbers around the edges of the matrix are the numbers of the cards sorted by respondent 1. There were ten cards in the pack. This respondent used a different criterion for each sort (e.g. with a pack about drinking vessels, the criteria could be ‘whether it has a handle’, ‘what drink you’d have in it’, ‘what it’s made of’ etc).

The numbers in the inner rows and columns show the number of times respondent 1 grouped put two cards in the same group, i.e. the cards co-occurred. Card 1 and card 2 were grouped together in the same group twice, card 1 was grouped with card 3 four times, cards 1 and 4 co-occurred twice, and so on.

Co-occurrence matrix for respondent 1

One important advantage of using co-occurrence matrices to analyse card sorts is that the co-occurrence is based purely on how often two cards are put in the same group; this approach doesn’t involve the names of the groups, or the sorting criteria. So you could analyse card sorts done by someone speaking a language you didn’t understand, or by someone who couldn’t speak at all.

Co-occurrence matrices allow you to pool results across respondents. You can simply add up the co-occurrence matrices for different respondents to produce a pooled matrix, as in the example below.

Pooled co-occurrence matrix: values summed for respondents 1-5

The pooled co-occurrence matrix shows you the extent of agreement or disagreement between respondents about similarities and differences between cards. Some cards were often grouped together by respondents (e.g.  card 1 and card 5, with 18 co-occurrences), but other cards were grouped together far less frequently (e.g. cards 3 and 6, with 4 co-occurrences). This can be used as a measure of semantic distance, or in commercial settings can be used to identify nearest competitors.

You could also produce co-occurrence matrices to compare responses between sub-groups of respondents e.g. males and females, or between medical researchers and clinicians.

Another approach is to use card sorts projectively (e.g. asking one group of respondents to sort as if they were members of another specified group) and then to use co-occurrence matrices to find out how well the projective group were able to imagine how the other group would perform the sorts. For instance, you could ask designers to sort images of products as if they were the intended users for a new product, or you could ask male respondents to perform sorts as if they were female respondents.