SIGNIFICANCE TESTING

To resolve the question of whether a diet effect should be included in the model, let us try to find the probability of obtaining a difference as big as this if there really was no diet effect.
This probabilty is known as a significance level or p-value. If it is small (5% is a conventional cut-off value), then sampling variability is not an acceptable explanation of the diet differences.

One crude but easy way to calculate the probability is to find out how many observations are above and below the overall median.
For diet 1, highlight the three columns with data and select Data > Filter > Autofilter. Select the custom option from both pull-down menus and choose Equals 1 for diet and Is less than 20.1 for yield. Counting the number of cows left reveals there are 30.

If there were no difference between the diets, you would expect as many to be below the overall median as above.
The probability of observing 30 by chance is the same as the probability of getting 30 heads if you tossed an unbiased coin 45 times - about 1 in 100. (a table of the probabilities is on the right).
However, all individual outcomes have small probabilities and you actually want to know how likely is something as extreme as 30 heads to occur (ie the probability of 30 or more). This is the significance level and the answer here is 0.036 (got by adding the appropriate probabilities).
The result says that the diet effect is statistically significant.

A difficulty with this approach is that it makes no use of how far above or below the overall median are the observations.

SIGNIFICANCE TESTING

Basic statistics in Excel 23.2.99 Page: 17 of 25