Table of Contents

• Testing differences
• 1: How to convince your boss
• 2: Looking at the data
• 3: Is the average different?
• 4: How big is big?
• 5: How to combine SDs
• 6: Combining SDs for fun and profit
• t-calc and t-crit
• 7: Getting to t-calc
• 8: A formula for t-calc
• 9: Degrees of freedom
• 10: The bottom line (finally)
• Putting it all together
• 11: Give it a try
• 12: Once more for luck
• 13: The big picture

Getting to t_calc

	n	average	difference	standard deviation (SD)	combined SD a/k/a "pooled variance"
Fish-2-Whale	8	267 g	94 g	44	18.5 g
Control	8	173 g		28

So now we know how far apart the averages are (difference = 94g).

And we have a way to combine the information about variability in gains within each tank (combined SD = 18.5g).

All we need to do now is compare those two numbers. Whenever you need to compare the size of two numbers, that mathematician voice in your head should immediately be shouting "use a ratio!" So let's do that:

t_calc = 94g / 18.5g = 5.1

This tells us that the difference between the two tanks is about 5 times bigger than the differences inside either tank. In other words, the fish food makes a much bigger difference than any random factors happening within the tanks.

We call it "t_calc" because it is the calculated value of the t-statistic for this t-test -- in other words, we calculate a value for the t-test.