How do I know what statistical test to do, t-test (1-tailed or 2-tailed?) or ANOVA (which one?)

Question

I did an experiment and had one independent variable and 2 dependent variables. Basically I tested diff. concentrations of an inhibitor on an enzyme and determined the enzyme's activity by measuring change in temp. and pH. I know that the inhibitor will decrease the enzyme's activity, and decrease only.

I don’t understand t-test. I also heard there’s ANOVA which one should i be doing, and how? Using what values?

I have calculated the mean change in temp. and pH for every concentration also the standard deviation (I did 6 trials)

Answer 1

Okay, first off the obvious: pick your statistical tests before you collect your data. I'm not trying to beat you up here, just giving you some advice for the future. If you choose your tests after you've already seen the data, there's always the possibility that you might (intentionally or subconsciously!) pick the test(s) that give you an appealing p-value over those that might be more appropriate, a practice known as data snooping.

Now, the t-test basically looks at the area under that bell curve (the distribution you'd expect if there was no effect, just random variation) and says: does this observation lie SO FAR from the mean that there's only a 5% chance (the usual threshold) that you'd get a result at least that different by random chance alone? Graphically: is the area under the part of the bell curve that's further from the mean/expected value than this observation less than 5% of the total area under the curve?

But what does it mean to be further from the mean? Does it have to be further in the same direction (1 SD below the mean is further than 0.5 SD above it) or can it be further away in either direction (1 SD below the mean isn't further above the mean than 0.5 SD above). The former is the 1-tailed test, and the latter is the 2-tailed test.

If you have a reason to expect that the effect would be in one direction, then you should use the 1-tailed test. In your case, your alternative hypothesis predicts the inhibitor to decrease the activity of the enzyme, so it wouldn't be a significant result (to reject the null in favor of that alternative hypothesis) if it increased the activity instead! If you're not expecting a value specifically larger or specifically smaller but just different, you'd use the 2-tailed test.

So I'd say you should have used the 1-tailed test, but since you hadn't decided that before seeing the data, there's a good argument that now you have to use the 2-tailed test. If you look at the data and pick which direction to use for the 1-tailed test (i.e. picking the positive test if the value is positive and picking the negative test if the value is negative), you're really just doing a 2-tailed test and artificially doubling your power (halving the p-value) because there's no chance of the result being big enough but on the wrong tail.

Teal deer: do the 2-tailed test, but do the 1-tailed test next time. Remember, it's not data snooping if you collect new data but base the choice of test only on the old data!