How to Interpret a P-Value Greater Than 0.05 (With Examples)


A hypothesis test is used to test whether or not some hypothesis about a population parameter is true.

Whenever we perform a hypothesis test, we always define a null and alternative hypothesis:

  • Null Hypothesis (H0): The sample data occurs purely from chance.
  • Alternative Hypothesis (HA): The sample data is influenced by some non-random cause.

When performing a hypothesis test, we must specify the significance level to use.

Common choices for a significance level include:

  • α = .01
  • α = .05
  • α = .10

If the p-value of the hypothesis test is less than the specified significance level, then we can reject the null hypothesis and conclude that we have sufficient evidence to say that the alternative hypothesis is true.

If the p-value is not less than the specified significance level, then we fail to reject the null hypothesis and conclude that we do not have sufficient evidence to say that the alternative hypothesis is true.

The following examples explain how to interpret a p-value greater than .05 in practice.

Example 1: Interpret P-Value Greater Than 0.05 (Biology)

Suppose a biologist believes that a certain fertilizer will cause plants to grow more during a one-year period than they normally do, which is currently 20 inches.

To test this, she applies the fertilizer to each of the plants in her laboratory for three months.

She then performs a hypothesis test using the following hypotheses:

The null hypothesis (H0): μ = 20 inches (the fertilizer will have no effect on the mean plant growth)

The alternative hypothesis: (HA): μ > 20 inches (the fertilizer will cause mean plant growth to increase)

Upon conducting a hypothesis test for a mean using a significance level of α = .05, the biologist receives a p-value of 0.2338.

Since the p-value of 0.2338 is greater than the significance level of 0.05, the biologist fails to reject the null hypothesis.

Thus, she concludes that there is not sufficient evidence to say that the fertilizer leads to increased plant growth.

Example 2: Interpret P-Value Greater Than 0.05 (Manufacturing)

A mechanical engineer believes that a new production process will reduce the number of faulty widgets produced at a certain factory, which is currently 3 faulty widgets per batch.

To test this, he uses the new process to produce a new batch of widgets.

He then performs a hypothesis test using the following hypotheses:

The null hypothesis (H0): μ = 3 (the new process will have no effect on the mean number of faulty widgets per batch)

The alternative hypothesis: (HA): μ < 3 (the new process will cause a reduction in the mean number of faulty widgets per batch)

The engineer performs a hypothesis test for a mean using a significance level of α = .05 and receives a p-value of 0.134.

Since the p-value of 0.134 is greater than the significance level of 0.05, the engineer fails to reject the null hypothesis.

Thus, he concludes that there is not sufficient evidence to say that the new process leads to a reduction in the mean number of faulty widgets produced in each batch.

Additional Resources

The following tutorials provide additional information about p-values:

An Explanation of P-Values and Statistical Significance
Statistical vs. Practical Significance
P-Value vs. Alpha: What’s the Difference?

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