The p-value is calculated using the test statistic calculated from the samples, the assumed distribution, and the type of test being done (lower-tailed test, upper-tailed test, or two-tailed test).

The p-value for:

- a lower-tailed test is specified by: p-value = P(TS < ts | H
_{0}is true) = cdf(ts) - an upper-tailed test is specified by: p-value = P(TS > ts | H
_{0}is true) = 1 - cdf(ts) - a two-sided test is specified by: p-value = 2 * P(TS > |ts| | H
_{0}is true) = 2 * (1 - cdf(|ts|))

Where:

- P
- Probability of a random variable having a range of values.
- TS
- Random variable associated with the assumed distribution.
- ts
- The test statistic calculated from your sample.
- cdf()
- Cumulative density function of the assumed distribution.

Minitab automatically displays p-values for most hypothesis tests. But you can also use Minitab to “manually” calculate p-values. To manually calculate a p-value in Minitab:

- Choose .
- Choose Cumulative probability.
- Provide the parameters if necessary.
- Choose Input constant and enter the test statistic.
- Click OK.

The result is the probability of observing a random variable less than the test statistic, cdf(ts).

- For a lower-tailed test, the p-value is equal to this probability; p-value = cdf(ts).
- For an upper-tailed test, the p-value is equal to one minus this probability; p-value = 1 - cdf(ts).
- For an upper-tailed test, the p-value is equal to two times the p-value for the lower-tailed test if the test statistic is negative, and for the upper-tailed test if the test statistic is positive; p-value = 2 * (1 - cdf(|ts|)).

Suppose you do a one-sample lower-tailed z test and the resulting test statistic is -1.785 (ts= -1.785). You want to calculate a p-value for the z-test.

- Choose .
- Choose Cumulative probability.
- If necessary, in Mean, enter
`0`and, in Standard deviation, enter`1`. - Choose Input constant and enter
`–1.785`. - Click OK.

This value is the probability of observing a random variable less than the test statistic, P(TS < -1.785) = 0.0371. Therefore, the p-value = 0.0371.

Now suppose you do a one-sample upper-tailed z test and the resulting test statistic is 1.785 (ts= 1.785). You want to calculate a p-value for the z test.

- Choose .
- Choose Cumulative probability.
- If necessary, in Mean, enter
`0`and, in Standard deviation, enter`1`. - Choose Input constant and enter
`1.785`. - In Optional storage, enter
`K1`. Click OK. K1 contains the probability of observing a random variable less than your test statistic, P(TS < 1.785) = 0.9629. For an upper-tailed test, you need to subtract this probability from 1. - Choose .
- In Store result in variable, enter
`K2`. - In Expression, enter
`1-K1`. Click OK. - Choose .
- Choose
`K2`. Click OK.

This value is the probability of observing a random variable greater than the test statistic, P(TS > 1.785) = 0.0371. Therefore, the p-value = 0.0371.

Because the normal distribution is a symmetric distribution, you could enter –1.785 as the input constant (in step 4) and then you do not have to subtract the value from 1.

Suppose you perform a one-sample two-tailed z test and the resulting test statistic is 1.785 (ts= 1.785). You want to calculate a p-value for the z test.

- Since the test statistic is positive, calculate an upper-tailed p-value. When the test statistic is negative, calculate a lower-tailed p-value and in step 5 enter
`K2`in Optional storage. Click OK. - This value is the p-value for a one-tailed test. For a two-tailed test, you need to multiply by this value by 2.
- Choose .
- In Store result in variable, enter
`K3`. - In Expression, enter
`2*K2`. Click OK. - Choose .
- Choose
`K3`. Click OK.

This value is 2 times the probability of observing a random variable greater than the absolute value of the test statistic, 2* P(TS > |1.785|) = 2 * 0.0371 = 0.0742. Therefore, the p-value = 0.0742.

Depending on the test or type of data, the calculations do change, but the p-value is usually interpreted the same way.