INTRODUCTION TO SIGNIFICANCE TESTING

It is difficult to judge subjectively whether apparent differences or effects in data are real and you may need to check formally whether such patterns could have arisen by chance. Hypothesis testing is a statistical method to assess the extent to which the observed data are consistent with a specified hypothesis.

Read in the milk data which shows the daily milk yield and protein of 45 cows on each of 2 diets.
The main interest is whether the average milk and protein yields produced with the two diets differ from each other.

To get a quick impression about the dietary effects on milk yield, produce a Scatter Plot (Choose the second chart subtype and on step 2 of the chart wizard enter the yield of diet 1 as the Y-values of series 1 and similarly diet 2 as a second series) This plot suggests that the milk yield is higher, on average, for cows on diet 2, but there is a lot of variation.

Obtain a table of means etc. by copying and pasting yield into two columns for diet 1 and diet 2 and selecting Tools > Data Analysis.. > Descriptive Statistics. Use yield and the new columns as the input range, check Summary Statistics and remember the labels option if you put headings for the new columns. You get the output below which shows the difference is important.

If diet is affecting milk yield the model is:

yield = overall mean + diet effect + individual cow effect

In this case, from the table above, the model terms would be estimated as

	{	-1.64 for diet 1	}
yield = 20.04 +	{		}	+ individual cow effect.
	{	+1.64 for diet 2	}

You could describe a diet effect as a 3.28kg/day difference in average yields but this might be due to sampling variability and a simpler model could be generating the data e.g.

yield = overall mean + individual cow effect
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INTRODUCTION TO SIGNIFICANCE TESTING

Basic statistics in Excel 23.2.99 Page: 16 of 25