A Question of Timing

Quite often I’m alone on my morning walk and my mind has a tendency to wander. On this particular morning I wondered whether there was a clear relationship between the number of steps taken on the walk and the time taken. Of course, I had recently bought a stopwatch and was anxious to get good use out of it.

A moments pondering suggested that there would be an inverse relationship between number of steps and speed. I had measured the distance of our morning walk fairly carefully (see Measurement) so calculating speed was easy. By this time, I thought I’d enough data to evaluate whether there was indeed a correlation.

Excel is not regarded as a good statistical package, but it’ll do for my amateurish approach. I have 26 data points ranging from 5462 steps to 5846 at the high end.

Data points from my Morning Walk

When plotted on a scatter graph it gave a good impression of verifiable statistical relationship.

I have marked two data points that might be regarded as outliers. The problem with outliers is that I really have to justify their classification. Fortunately I maintain a contemporaneous commentary on the morning walks and both these data points had suitable remarks. These remarks provided the justification for their removal from the data set.

Looks may not be everything, but in this case the scatter graph provides a much more convincing case for a correlation between speed and the number of steps.

In fact in statistical terms the correlation coefficient improves from -0.85 to -0.90.