to
Term | Description |
---|---|
mean of the first sample | |
mean of the second sample | |
t_{α}_{/2} | inverse cumulative probability of a t distribution at 1 – α/2 |
α | 1 - confidence level / 100 |
s | sample standard deviation as calculated for the test statistic |
When you assume unequal variances, the sample standard deviation of is:
The degrees of freedom are:
If necessary, Minitab truncates the degrees of freedom to an integer, which is a more conservative approach than rounding.
The test statistic degrees of freedom are:
DF = n_{1} + n_{2} – 2
Term | Description |
---|---|
mean of the first sample | |
mean of the second sample | |
s | sample standard deviation of |
δ_{0} | hypothesized difference between the two population means |
s_{1} | sample standard deviation of the first sample |
s_{2} | sample standard deviation of the second sample |
n_{1} | sample size of the first sample |
n_{2} | sample size of the second sample |
VAR_{1} | |
VAR_{2} |
Suppose C1 contains the response, and C3 contains the mean for each factor level. For example:
C1 | C2 | C3 |
---|---|---|
Response | Factor | Mean |
18.95 | 1 | 14.5033 |
12.62 | 1 | 14.5033 |
11.94 | 1 | 14.5033 |
14.42 | 2 | 10.5567 |
10.06 | 2 | 10.5567 |
7.19 | 2 | 10.5567 |
In Expression, enter SQRT((SUM((C1 - C3)**2)) / (total number of observations - number of groups))
For the previous example, the Expression for the pooled standard deviation would be:
SQRT((SUM(('Response' - 'Mean')**2)) / (6 - 2))
The value that Minitab stores is 3.75489.
The calculation for the p-value depends on the alternative hypothesis.
Alternative Hypothesis | P-value |
---|---|
When you assume unequal variances, the degrees of freedom are:
If necessary, Minitab truncates the degrees of freedom to an integer, which is a more conservative approach than rounding.
When you assume equal variances, the test statistic degrees of freedom are:
DF = n_{1} + n_{2} – 2
Term | Description |
---|---|
μ_{1} | population mean of the first sample |
μ_{1} | population mean of the second sample |
n_{1} | sample size of the first sample |
n_{2} | sample size of the second sample |
δ_{0} | hypothesized difference between the two population means |
t | t-statistic from the sample data |
t | a random variable from the t-distribution with DF degrees of freedom. |
VAR_{1} | |
VAR_{2} |