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

Is the average different?

So, what is the first step for the amazing (but not super-powered) t-test? Well, if you're going to compare averages, you need to know what those averages are first, right? I'll assume that if you've gotten this far, you know how to calculate an average (if you don't, now is a great time to find out). So, take a look at the data below, and then just click on the buttons below to have the module do the busy work for you:

OK, so the Fish-2-Whale fish grew about 267 grams vs. 173 for the generic fishfood -- almost 100 grams more. That certainly SEEMS like a big difference.

But is it really? If you grew your fish on a fish farm, and every fish in the control treatment was within 2 grams 173g, and every Fish-2-Whale specimen was within 2 grams of 267g -- then 100 grams would certainly be a big difference. On the other hand, the same species in the wild might exhibit huge differences. If there was a 500 gram difference between the largest and smallest fish, then 100 grams would not look so important.

So, how can you get a handle on how big a difference has to be, in order to matter?