Getting to t_{calc}
n  average  difference  standard deviation (SD) 
combined SD a/k/a "pooled variance" 


Fish2Whale  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 tstatistic for this ttest  in other words, we calculate a value for the ttest.
Copyright University of Maryland, 2007
You may link to this site for educational purposes.
Please do not copy without permission
requests/questions/feedback email: mathbench@umd.edu