Overview
Statistical Testing
Both the mathematical and the stochastic models are based on a set of assumptions. This set is called a statistical hypothesis. Different assumptions result in different hypotheses. Statistical testing is used to verify the hypotheses. A special set of assumptions is referred to as the null-hypothesis H0.
This hypothesis implies that:
This hypothesis implies that:
- Your observation does not have any gross errors (blunders).
- Your mathematical model delivers a correct description of the relations between your observations and unknown parameters.
- The chosen stochastic model for your observations appropriately describes the stochastic properties of the observations.
It is clear that there are two possible results for the testing of a hypothesis: Acceptance or rejection. A specific cut-off point or critical value decides on acceptance or rejection. The critical values establish a window of acceptance. The further beyond this window a result is, the less certain the set of assumptions is satisfied. Critical values are determined with you choosing a level of significance α. The probability that the critical value is exceeded, although the set of assumptions is valid, is equal to α. In other words, α is the probability of an incorrect rejection. Alternatively, the complementary level of confidence 1-α, is a measure of the confidence you can have in the decision.
While testing the null-hypothesis H0 there are two unfavourable situations that might occur:
While testing the null-hypothesis H0 there are two unfavourable situations that might occur:
- Rejection of H0 while in fact it is true. The probability of this situation occurring is equal to the significance level α. This situation is called a Type I error (see the following table).
- Acceptance of H0 while in fact it is false. The probability of this situation occurring is 1-β, with b being the power of the test. This situation is called a Type II error (see the following table).
| Situation | Decision: accept H0 | Decision: reject H0 |
|---|---|---|
| H0 true | correct decision:probability = 1-α | Type I error:probability = α |
| H0 false | Type II error:probability = 1-β | correct decision:probability = β |
H0 true
H0 false
See the following topics for further information on testing the null-hypothesis and alternative hypotheses:
See the following topics for further information on testing the null-hypothesis and alternative hypotheses:
F-Test
W-Test
T-Test