Interaction between series and co-contributors

One analysis that every law firm can carry out on its survey data relies on a contingency table.  A contingency table contains counts by levels of a factor (also known as a “categorical variable”), which is a nominal variable that has levels, such as the variable “Position” might have levels of “GC,” “Direct Report,” “Other Lawyer” and “Staff.”

As an example of a contingency table, a survey might ask respondents about their company’s headquarters country and whether their company is publicly traded or privately held. Country would be a factor with two or more levels (let’s say the U.S. is one level and has 55 respondents while Canada is a second level, with 35 respondents); public or private would also be a factor but it has only two levels, perhaps 20 and 70, respectively.

So, a contingency table of counts (frequencies) for these two factors and their levels has a total of four categories (Public/US, Private/US, Public/Canada and Private/Canada) and would look something like this one:

Traded Stock   US   Canada
Public               12     8
Private             43    27

Easy to create, yet law firms miss many opportunities to deepen their analyses by exploring such contingency tables.

Here is an illustration that can also teach us about surveys identified so far. When law firms survey, they often decide to team with another organization, referred to here as a co-contributor. Separately from that decision, law firms also frequently conduct surveys on a topic more than once, referred to as a series. A question is whether co-contributors are more commonly associated with series. In other words, given a contingency table of the four counts, is there a statistical association between series and co-contributors?

Conributor           NotSeries  Series
Alone                     94               23
Co-Contributor   60               23

The contingency table above derives from 200 different surveys, where each series is treated as a single survey, for which I have located a published report. Reports are necessary to determine whether there was a co-contributor. Of that set, 23 are series in which a co-contributor took part (the bottom right count in the table); the same number are series where the law firm proceeded alone (top right). Of the “NotSeries” surveys, 94 were done by the law firm alone while 60 of them had a co-contributor. We must stress that this data is preliminary because we identified co-contributors at various times and may not have spotted all co-coordinators and fully matched them to series and non-series.

We can learn much from the data in the contingency table whether there is a statistical association between series and co-contributors. One methodology available to us is called a chi-square test.

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