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.