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

The bottom line (finally)

	n	average	diff	(SD)	comb. SD	tcalc	tcrit (df=7)
Fish-2-Whale	8	267 g	94 g	44	18.5 g	5.1
Generic Brand	8	173 g		28

 

degrees of freedom (df)	tcrit (for p-value = 0.05)
1	12.7
2	4.3
3	3.2
4	2.8
5	2.6
6	2.5
7	2.4
8	2.3
9	2.2
10	2.1
20+	2.0

Our t_calc showed that the difference between tanks was about 5 times more than the random differences within tanks. And our t_crit showed that anything over 2.4 times would be statistically significant. So... finally, we can say definitively that Fish-2-Whale had a statistically significant effect on fish growth. Time to party!

Once more with gusto: if your t_calc is bigger than your t_crit, your results are statistically significant.