The risk of making a Type I Error.
The level of significance in a hypothesis test. If the p-value is less than the alpha value the alternative hypothesis will be accepted and the null hypothesis rejected. The alpha value is selected based on the importance of the test, a value of 0.05 would be common, with 0.01 for tests that are critical, and even 0.001 in life or death situations. In a hypothesis test the alpha risk is equal to the level of significance, alpha.
The proposition that is to be proven in a hypothesis test, see Hypothesis Testing.
The risk of making a Type II Error, see Type II error.
See Single Sided Tests for an explanation.
The null hypothesis, see Hypothesis Testing
The alternative hypothesis, see Hypothesis Testing
A hypothesis test consists of two complementary propositions. For example, suppose that the test is to see if a process mean differs from zero:
H0 the mean equals zero (this is the 'null hypothesis')
H1 the mean does not equal zero (this is the 'alternative hypothesis')
The test will determine the probability of getting the observed results if H0 were true. This probability is known as the p-value.
Note that the p-value is not the probability that the null hypothesis is true.
The complementary proposition to the alternative hypothesis. The alternative hypothesis is only accepted if the results show that the null hypothesis is not feasible, see Hypothesis Testing.
See Single Sided Tests
The probability of rejecting the null hypothesis when it is false. The Power varies with the amount that the process varies from the target and so is specified for a particular value of the error.
The power of a test at a specified mean is calculated from (1-b), where b is the probability of a Type II error.
The probability of getting the observed results in a hypothesis test if the null hypothesis were true.
Also known as the Alpha Value, see Type I Error
A hypothesis test for the mean may be expressed as a double sided test, or a single sided test:
If a two sided test then the p-values and alpha values are shared between the two tails. Thus the calculated p-value must be compared to half the alpha value.
|Statistical v Practical Significance
The practical problem with hypothesis tests is that if the sample is sufficiently large the alternative hypothesis will be accepted, no matter how small the deviation from the null hypothesis condition. In the example above, we are only interested in identifying departures from the mean of zero that are meaningful in terms of the process; that is departures that are of practical significance.
See Single Sided Test for an explanation
The probability of rejecting the null hypothesis when it is true. In the case of control charts, this is equivalent to the probability of a point plotting outside the control limits despite the process being in control.
The probability of failing to reject the null hypothesis when it is false. In the case of control charts, this is equivalent to the probability of a point plotting inside the control limits despite the presence of a 'special cause'.