9.6: Decision Making: P-value Method

The process of hypothesis testing based on the P-value method includes calculating the P- value using the sample data and interpreting it.

First, a specific claim about the population parameter is proposed. The claim is based on the research question and is stated in a simple form. Further, an opposing statement to the claim is also stated. These statements can act as null and alternative hypotheses: a null hypothesis would be a neutral statement while the alternative hypothesis can have a direction. The alternative hypothesis can also be the original claim if it involves a specific direction about the population parameter.

Once the hypotheses are stated, they are expressed symbolically. As a convention, the null hypothesis would contain the equality symbol, while the alternative hypothesis may contain >, <, or ≠ symbols.

Before going further in the hypothesis testing, an appropriate significance level must be decided. There is a general consensus to set significance levels at 95% (i.e., 0.95) or 99% (i.e., 0.99) level. Here the α would be 0.05 or 0.01, respectively.

Next, identify an appropriate test statistic. The proportion and the mean (when population standard deviation is known) is the z statistic. For the mean, when the population standard deviation is unknown, it is a t statistic, and for the variance (or SD), it is a chi-square statistic.

After calculating the test statistic, find the P-value electronically or from the respective P-value table, and compare it with the pre-decided significance level. If the P-value is less than the pre-decided significance level, reject the null hypothesis.

The interpretation of the original claim from the hypothesis or the property of the population must be based on the P-value.

The P-value method uses a calculated P-value instead of the critical value to arrive at a decision about the hypothesis.

As a first step, a hypothesis is stated and expressed symbolically.

For testing the proportion, mean, or standard deviation of a population, the null and alternative hypotheses are expressed as follows.

As a next step, a significance level α is decided, which commonly is either 0.05 or 0.01.

Further, an appropriate test statistic is chosen and calculated using the sample data.

This test statistic is then used to compute the P-value directly.

The P-value is the probability of getting a test statistic value at least as extreme as the one obtained from sample data. We can plot a distribution that shows the given test statistic and P-value.

If the computed P-value is equal to or smaller than the decided significance level, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.