Term | Description |
---|---|
D | Difference |
Test mean | |
Reference mean |
The mean of the reference sample, , is given by:
The standard deviation of the test sample, S1, is given by:
The standard deviation of the reference sample, S2, is given by:
Term | Description |
---|---|
X i | Observations from the test sample, with i = 1, ..., n1 |
Y i | Observations from the reference sample, with i = 1, ..., n2 |
n1 | Number of observations in the test sample |
n2 | Number of observations in the reference sample |
If you select the option to assume equal variances, then Minitab calculates the pooled standard deviation, Sp, and the standard error of the difference, SE, using the following formulas:
Term | Description |
---|---|
S1 | Standard deviation of the test sample |
n1 | Number of observations in the test sample |
S2 | Standard deviation of the reference sample |
n2 | Number of observations in the reference sample |
Sp | Pooled standard deviation |
Let k1 be the value that you specify for the lower limit and k2 be the value that you specify for the upper limit. By default, the lower equivalence limit, δ1, is given by:
and the upper equivalence limit, δ2, is given by:
By default, the degrees of freedom for the test, v, are given by the following formula:
Minitab displays v rounded down to the nearest integer.
If you select the option to assume equal variances, then Minitab calculates the degrees of freedom as follows:
Term | Description |
---|---|
S1 | Standard deviation of the test sample |
n1 | Number of observations in the test sample |
S2 | Standard deviation of the reference sample |
n2 | Number of observations in the reference sample |
By default, Minitab uses the following formula to calculate the 100(1 – α)% confidence interval (CI) for equivalence:
CI = [min(C, Dl), max(C, Du)]
where:
If you select the option to use the 100(1 – 2α)% CI, then the CI is given by the following formula:
CI = [Dl, Du]
For a hypotheses of Test mean > reference mean or Test mean - reference mean > lower limit, the 100(1 – α)% lower bound is equal to DL.
For a hypothesis of Test mean < reference mean or Test mean - reference mean < upper limit, the 100(1 – α)% upper bound is equal to DU.Term | Description |
---|---|
D | Difference between the test mean and the reference mean |
SE | Standard error |
δ1 | Lower equivalence limit |
δ2 | Upper equivalence limit |
v | Degrees of freedom |
α | The significance level for the test (alpha) |
t1-α, v | Upper 1 – α critical value for a t-distribution with v degrees of freedom |
For a hypothesis of Test mean > reference mean, δ1 = 0.
For a hypothesis of Test mean < reference mean, δ 2 = 0.
Term | Description |
---|---|
D | Difference between the sample test mean and the sample reference mean |
SE | Standard error of the difference |
δ1 | Lower equivalence limit |
δ2 | Upper equivalence limit |
H0 | P-Value |
---|---|
Term | Description |
---|---|
Unknown difference between the mean of the test population and the mean of the reference population | |
δ1 | Lower equivalence limit |
δ2 | Upper equivalence limit |
v | Degrees of freedom |
T | t-distribution with v degrees of freedom |
t1 | t-value for the hypothesis |
t2 | t-value for the hypothesis |
For information on how the t-values are calculated, see the section on t-values.