Hypothesis Testing

Two-tailed probability

Adding the probabilities in both tails separately.

Higher significance level

Increase your chance of a false positive but decrease chance of false negative.

Null Hypothesis

Statement that you want to test. In general, that things are the same as each other, or the same as a theoretical expectation. Usually boring.

"classical" statistics

Technique used by the vast majority of biologists. It involves testing a null hypothesis by comparing the data you observe in your experiment with the predictions of a null hypothesis.

Alternative hypothesis

That things are different from each other, or different from a theoretical expectation. Usually interesting.

Primary goal of a statistical test

To determine whether an observed data set is so different from what you would expect under the null hypothesis that you should reject the null hypothesis.

Main Goal of hypothesis testing

To estimate the P value if the null hypothesis were true. If the observed results are unlikely under the null hypothesis, you reject the null hypothesis.

If you reject the statistical null hypothesis

You then have to decide whether that's enough evidence that you can reject your biological null hypothesis.

Biological Hypothesis

Says something about biological processes.

Statistical hypothesis

Says something about the numbers, but nothing about what caused those numbers to be different.

False Positive

"Type 1 error". When your data fool you into rejecting the null hypothesis even though it's true.

False Negative

"Type II error". Failing to reject the null hypothesis, even though it's not true.

Need to ask

"what's the probability of getting a deviation from the null expectation that's large, just by chance, if the boring null hypothesis is really true?" Only when that probability is low can you reject the null hypothesis.

One-tailed probability

Adding the probabilities in only one tail of the distribution. More powerful in the sense of having a lower chance of false negatives.

Reporting your results

Conclude that the results are either significant or not; either reject the null hypothesis (if P < significance level) or don't reject the null hypothesis (if P > significance level). Also give raw data, or the test statistic and degrees of freedom in case anyone wants to calculate your exact P value.

Low significance level

Decrease your chance of a false positive but increase chance of false negative.

Significance Levels

Level of 0.05. This means that if the P value is less than 0.05, you reject the null hypothesis; if P is greater than or equal to 0.05, you don't reject the null hypothesis.

P value

Probability of obtaining the observed results

Biological null and alternative hypotheses

The first that you should think of; they are two possible answers to the biological question you are interested in.

Statistical null and alternative hypotheses

The statements about the data that should follow from the biological hypotheses.