Let’s go back to our first set of data and ask, how significant is our finding? Can we support the hypothesis that Fish-2-Whale works?
| n | average | standard deviation (SD) |
standard error in the mean (SEM) | difference of means | SEDM | |
|---|---|---|---|---|---|---|
| Fish-2-Whale | 8 | 267 g | 44g | 15.6g | 94g | 18.5 g |
| Control | 8 | 173 g | 28g | 9.9g |
We want to compare the SIZE OF THE EFFECT we have found (which is 94 g) to the SIZE OF THE ERROR (which is 18.5g).
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:
tcalc = 94g / 18.5g = 5.1
Notice that when we calculate a ratio like this, the units will cancel out.
This tells us that the difference in the sample means between the two tanks is about 5 times bigger than the expected variation in the difference between the sample means. In other words, the EFFECT is 5 times larger than the ERROR and it is likely that the Fish-2-Whale has a much bigger effect than any random factors.
We call this ratio “tcalc” because it is the calculated value of the t-statistic for this t-test — in other words, we calculate a value (also known as the test statistic) for the t-test.