Simple explanation of a t-test and its meaning using Excel 2013

For those of us you say that stats are ‘dry’ – you are clearly being shown the wrong numbers! Statistics are everywhere and it’s well worth understanding what you’re talking about, when you talk about data, numbers or languages such as R or Python for data and number crunching. Statistics knowledge is extremely useful, and it is accessible when you put your brain to it!

So, for example, what does a pint of Guinness teaches us about statistics? In a visit to Ireland, Barack Obama declared that the Guinness tasted better in Ireland, and the Irish keep the ‘good stuff’ to themselves.
Can we use science to identify whether there is a difference between the enjoyment of a pint of Guinness consumed in Ireland, and pints consumed outside of Ireland?
A Journal of Food Science investigation detailed research where four investigators travelled around different countries in order to taste-test the Guinness poured inside and outside of Ireland. To do this, researchers compared the average score of pints poured inside of Ireland versus pints poured outside of Ireland.

How did they do the comparison? they used a t-test, which was devised by William Searly Gosset, who worked at the Guinness factory as a scientist, with the objective of using science to produce the perfect pint.
The t-test helps us to work out whether two sets of data are actually different.
It takes two sets of data, and calculates:

the count – the number of data points
the mean, also known as the average i.e. the sum total of the data, divided by the number of data points
The standard deviation – tells you roughly how far, on average, each number in your list of data varies from the average value of the list itself.

The t-test is more sophisticated test to tell us if those two means
of those two groups of data are different.

In the video, I go ahead and try it, using Excel formulas:

COUNT – count up the number of data points. The formula is simply COUNT, and we calculate this
AVERAGE – This is calculated using the Average Excel calculated formula.
STDEV – again, another Excel calculation, to tell us the standard deviation.
TTEST – the Excel calculation, which wants to know:

Array 1 – your first group of data
Array 2 – your second group of data
Tail – do you know if the mean of the second group will definitely by higher OR lower than the second group, and it’s only likely to go in that direction? If so, use 1. If you are not sure if it’s higher or lower, then use 2.
Type –
if your data points are related to one another in each group, use 1
if the data points in each group are unrelated to each other, and there is equal variances, use 2
if the data points in each group are unrelated to each other, and if you are unsure if there are equal variances, use 3

And that’s your result. But how do you know what it means? It produces a number, called p, which is simply the probability.

The t-test: simple way of establishing whether there are significant differences between two groups of data. It uses the null hypothesis: this is the devil’s advocate position, which says that there is no difference between the two groups It uses the sample size, the mean, and the standard deviation to produce a p value.
The lower the p value, the more likely that there is a difference in the two groups i.e. that something happened to make a difference in the two groups.

In social science, p is usually set to 5% i.e. only 1 time in 20, is the difference due to chance.
In the video, the first comparison does not have a difference ‘proven, but the second comparison does.
So next time you have a good pint of Guinness, raise your glass to statistics!

 


 

Love,
Jen

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