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Data analysis: hypothesis testing

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# 6.1 Defining the p-value

To conduct a hypothesis test using the p-value, you calculate the test statistic, such as a z-score or t-score, and then use it to determine the corresponding p-value from a probability distribution table or statistical software.

The decision rules for using p-values are:

• If p-value ≤ α, you reject the null hypothesis.
• If p-value > α, you fail to reject the null hypothesis (accept the null hypothesis).

You can use graphs to illustrate this decision rule. For example, in a one-tailed test, the orange region indicates the area outside the pre-determining α levels in the graph shown in Figure 22.

Figure 22 Alpha level and corresponding region to reject null hypothesis

If the p-value ≤ α (i.e. if the boundary of the shaded region falls inside the boundary of α), you will reject the null hypothesis.

Figure 23 P-value less than or equal to alpha level

If the p-value > α (i.e. if the vertical black line region is greater than the orange shaded region), you will not reject the null hypothesis.

Figure 24 P-value greater than alpha level

As you can see from these illustrations, the p-value reflects the tail area of the normal distribution (the vertical blue line region is smaller than the orange-shaded region). Therefore, you can determine the exact p-value by calculating the z-score representing the boundary of the tail area of the normal distribution, and using the pre-determined z-score table to determine the area right of the z-score.

Figure 25 Area right of z