Let’s add two more columns to our table that contain the calculated and critical values of t and also the degrees of freedom.
| n | mean |
standard deviation (SD) |
(standard error in the mean (SEM) | difference of means | SEDM | tcalc | tcrit (df=7) | |
|---|---|---|---|---|---|---|---|---|
| Fish-2-Whale | 8 | 267g | 44g | 15.6g | 94g | 18.5g | 5.1 | |
| Generic Brand | 8 | 173g | 28g | 9.9g |
Our tcalc showed that the difference between tanks was about 5 times more than the random differences within tanks. And our tcrit 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 tcalc is bigger than your tcrit, your results are statistically significant.