The p-value is calculated using the sampling distribution of the test statistic under the null hypothesis, the sample data, and the type of test being done (lower-tailed test, upper-tailed test, or two-sided 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) - assuming that the distribution of the test statistic under H
_{0}is symmetric about 0, 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 an event
- TS
- Test statistic
- ts
- observed value of the test statistic calculated from your sample
- cdf()
- Cumulative distribution function of the distribution of the test statistic (TS) under the null hypothesis

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 (cdf(ts)) is the probability that the test statistic is equal to or less than that value actually observed based on your sample under H_{0}.

- 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 a two-sided test, the p-value is equal to two times the p-value for the lower-tailed p-value if the value of the test statistic from your sample is negative. However, the p-value is equal to two times the p-value for the upper-tailed p-value if the value of the test statistic from your sample is positive.

Suppose you do a one-sample lower-tailed z test and the resulting value of the statistic calculated from the data 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 that the test statistic assumes a value equal to or less than that value actually observed based on your sample (under H_{0}). 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 value of the statistic calculated from the data 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 that the test statistic assumes a value equal to or greater than that value actually observed based on your sample (under Ho). 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 that the test statistic assumes a value equal to or greater than that value actually observed based on your sample (under H_{0}). 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 calculated value of the test statistic from the sample is positive, calculate an upper-tailed p-value. When the calculated value of the test statistic from the sample 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 that the test statistic assumes a value equal to or greater than the absolute value of that value actually observed based on your sample (under H_{0}). 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.