Gosset was a bright man, with two degrees from Oxford, and was hired by Guinness to help them brew the best beer using statistical methods instead of the “tribal knowledge” approach most brewing companies employed at the time.
Gosset’s main issue
Gosset’s main issue was sample sizes. At the time the Z-test was the most prevalent test available for someone who wanted to compare a sample mean to some known target, or hypothesized mean.
The problem with the Z-test was it used the population standard deviation (s) which required large sample sizes. This was impossible for Gosset as his resources were limited for economical reasons. I mean there is only so much beer allowed for experimentation… wink, wink.
For example, in one experiment Gosset was attempting to determine the optimal type of barley to use. Initially, these experiments started with 4 farms each growing one plot of each variety. So assuming he knew the “population” standard deviation from this small sample was dangerous and wrong. Lucky for all of us, Gosset challenged the status quo and went against the teachings of many well known statisticians of his time.
Introducing the one sample t-test
Gosset’s big, and somewhat controversial move, was to tweak the Z-test ever so slightly, creating what we now call the one sample t-test. The tweak dealt with using the “sample” standard deviation (s) instead of the “population” standard deviation (s). There are some mathematical reasons for this related to the fatness of the tails and other fun stuff but I will spare you from this discussion. I’ll point to some additional reading at the end if you wish to read more.
With the one sample t-test Gosset was now able compare a sample mean to some hypothesized mean (target). And most importantly he did not have to worry about his small sample sizes.
Does it really matter?
A fair question, when comparing the Z-test with the one sample t-test, is does it really matter? The best answer I can offer is – it depends.
If you are dealing with large sample sizes the results from a Z-test and one sample t-test are likely to be close to one another in which case it doesn’t really matter as much as some purists may say.
However, if you are dealing with smaller sample sizes the one sample t-test is likely the best choice due to the whole standard deviation conundrum.
Tomorrow night I will discuss the rubrics of the one sample t-test. There are some assumptions we need to satisfy as well as some tricks we can play making this hypothesis test extremely powerful for both lean and six sigma practitioners alike.
- “Student” by R.A. Fisher
- Guinness, Gosset, Fisher, and Small Samples by Joan Fisher Box
- Everything you wanted to know about the one-sample t-test (but were afraid to ask) by Keith Bower
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