Topics: Hypothesis Testing, Statistics

The 1949 film A Connecticut Yankee in King Arthur's Court includes the song “Busy Doing Nothing,” and this could be written about the Null Hypothesis as it is used in statistical analyses.

The words to the song go:

We're busy doin' nothin'
Workin' the whole day through
Tryin' to find lots of things not to do

And that summarises the role of the Null Hypothesis perfectly. Let me explain why.

## What's the Question?

Before doing any statistical analysis—in fact even before we collect any data—we need to define what problem and/or question we need to answer. Once we have this, we can then work on defining our Null and Alternative Hypotheses.

The null hypothesis is always the option that maintains the status quo and results in the least amount of disruption, hence it is “Busy Doin’ Nothin'”.

When the probability of the Null Hypothesis is very low and we reject the Null Hypothesis, then we will have to take some action and we will no longer be “Doin Nothin'”.

Let’s have a look at how this works in practice with some common examples.

 Question Null Hypothesis Do the chocolate bars I am selling weigh 100g? Chocolate Weight = 100g   If I am giving my customers the right size chocolate bars I don’t need to make changes to my chocolate packing process. Are the diameters of my bolts normally distributed? Bolt diameters are normally distributed. If my bolt diameters are normally distributed I can use any statistical techniques that use the standard normal approach. Does the weather affect how my strawberries grow? Number of hours sunshine has no effect on strawberry yield Amount of rain has no effect on strawberry yield Temperature has no effect on strawberry yield

Note that the last instance in the table, investigating if weather affects the growth of my strawberries, is a bit more complicated. That's because I needed to define some metrics to measure the weather. Once I decided that the weather was a combination of sunshine, rain and temperature, I established my null hypotheses. These all assume that none of these factors impact the strawberry yield. I only need to control the sunshine, temperature and rain if the probability that they have no effect is very small.

## Is Your Null Hypothesis Suitably Inactive?

So in conclusion, in order to be “Busy Doin’ Nothin’”, your Null Hypothesis has to be as follows: