The Amazing Shrinking Sermon

A Church article with View Comments posted 3 July 2010.
Tags: statistics

In early October 2002, I was both a smart alec undergraduate doing a minor in Mathematical Statistics and the guy at church who was recording sermons to put them on the internet.¹ I noticed over a span of six weeks that Pastor’s sermons were getting progressively shorter each week. Taking to heart the saying Mark Twain popularized, that “there are three kinds of lies: lies, damned lies, and statistics,” I thought I’d apply some intentionally faulty reasoning and write it up for fun.

I stumbled upon it recently while cleaning up some old computer files, and it shows something very important about trusting models. More on that below.

We² seek to prove that the length (in seconds) of Pastor’s sermons is getting exponentially shorter. We are concerned that eventually, Pastor may stand at the pulpit and, for his sermon, say nothing at all. Hence the following hypotheses:

• Null Hypothesis: There is no distributional relationship in the length of Pastor’s sermons.
• Alternate Hypothesis: There is an exponential relationship (with parameters derived from the data) expressed in the length of Pastor’s sermons.

I then plugged in six weeks of data, ran a Kolmogorov-Smirnov test, and reported the results:

Output from SPSS

The p-value of this test is .024, so there is only a 2.4% chance that this data does not fit an exponential distribution. The chances of this happening randomly in this manner are fewer than one in forty. The regression equation is y(x) = 1335.42*(.9811^x).

Next, observe that Pastor’s short prayer at the end of the sermon lasts approximately 15 seconds, so solve the equation y(x)=15 for x. X = 236 weeks.

Thus, in 4 years and 28 weeks from October 6, 2002, (namely, Sunday, March 4, 2007), Pastor will stand at the pulpit, smile, and say only, “May the peace of God, which passes all understanding, keep your hearts and your minds through faith in Christ Jesus until life everlasting. Amen.”

And then sit back down again.

I suppose it’s good that he retired so we never had to find out if my dire prediction came true!

Of course, this is all nonsense.

I think I actually surprised myself to get a p-value so low — meaning so good a match with the model I picked. I remember wondering how I would talk my way past data that wouldn’t fit what I wanted it to do. It would have been fun! To have it fit so well at the same time was just icing on the cake.

Today I’m wondering what models you and I have chosen that fit some of our data about the world, but don’t make cohesive sense. I invite you to share your thoughts below!