Statistical Errors and Data Interpretation

I was asked the following question recently, “From a statistical standpoint, how do you see three ‘No’s’ votes out of a possible 23 board members. Can you find out specifically what the error would be?”

This brings up a common misconception when thinking about statistics and interpreting your data.

THE SITUATION ABOVE HAS NOTHING TO DO WITH STATISTICS.

Statistics is the science which deals with random variation. There is no statistical issue involved because there is no sampling or variation in the data.

In the question asked, they aren’t trying to estimate what percentage of board members would really say “No”. The 23 board members is the total population and we know without error that 3 of the 23 said “No”. So before thinking about “statistical error” or “statistical significance,” first determine what the sources of variation are.

That said, there still is the question of how we interpret and act on this information.

For the case in point, the board voted 20-3 on whether to approve a new member. Proper interpretation and action is all about the context.

The board is used to making approvals based on a unanimous vote, so what significance should be placed on the 3 dissenting votes?

To help us think about this question, consider that 3 out of 23 is a huge number if it’s the number of babies that are dropped in the delivery room. However, 3 out of 23 isn’t so many if it’s the number of adults that think they may have lied at least once when they were kids.

So, it all depends on the context and that is best understood by those involved in the decision-making. In this case they need to decide the gravity of a single “No” vote and act accordingly.

I’ll address a related topic, statistical significance versus practical significance in my next blog entry.

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