9.4
P-value
P-value is one of the most crucial concepts in statistics.
P-value stands for the probability value. P-value is the probability that, if the null hypo…
When a test statistic is calculated from the sample statistic, such as sample proportion, it can be located in a probability distribution.
This value of the test statistic demarcates an area under the curve from the rest of the area.
This area at the tail of the distribution is the P-value, where P stands for probability.
Assuming that the null hypothesis is true, there is always a chance of observing the calculated test statistic, or a value higher than that, in the critical region of the given distribution.
A P-value provides the probability of getting that test statistic value in the critical region just by chance alone.
So, when the P-value is observed to be smaller than a predetermined value—such as 0.05—we reject the null hypothesis, as it indicates that the observed outcome is highly unlikely and the evidence against the null hypothesis is stronger.
The P-value can be calculated at the right tail, left tail, or both the tails depending on the hypothesis or the value of the test statistic.
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Q1: What does P-value represent in hypothesis testing?
The P-value, or probability value, represents the probability of observing a test statistic as extreme or more extreme than the calculated value, assuming the null hypothesis is true. It measures the likelihood of obtaining sample results by chance alone. A smaller P-value indicates stronger evidence against the null hypothesis.
Q2: How do you use P-value to make decisions about the null hypothesis?
Compare the P-value to a predetermined significance level, typically 0.05. If the P-value is less than 0.05, reject the null hypothesis, indicating the observed outcome is highly unlikely under the null hypothesis. If the P-value is greater than 0.05, fail to reject the null hypothesis.
Q3: Where is the P-value located in a probability distribution?
The P-value is the area at the tail of the probability distribution, demarcated by the test statistic value. It can be calculated at the right tail, left tail, or both tails depending on the hypothesis and test statistic value. This tail area represents the probability of observing extreme results by chance.
Q4: What does a large P-value indicate about your hypothesis?
A large P-value indicates insufficient evidence to reject the null hypothesis. However, a large P-value does not mean the null hypothesis is true. It simply suggests the observed data is reasonably likely under the null hypothesis, so you fail to reject it rather than accept it.
Q5: Is P-value the same as the probability of rejecting the null hypothesis?
No. P-value is not the probability of rejecting the null hypothesis, nor is it a statistical error rate or sampling error. P-value also does not indicate a 95% chance that the observed difference is real. It specifically measures the probability of observing the test statistic under the assumption that the null hypothesis is true.
Q6: Why is 0.05 commonly used as the significance level for P-values?
The 0.05 significance level is a predetermined threshold convention in statistics. When P-value is less than 0.05, results are considered statistically significant, meaning the observed outcome is highly unlikely by chance alone. This threshold balances the need to detect real effects while controlling false positives.
Q7: What information does P-value NOT provide about hypotheses?
P-value does not convey information about the truth of the null or alternative hypotheses. It does not indicate whether the null hypothesis is true, nor does it measure the magnitude or practical importance of an effect. P-value is solely a measure of evidence strength against the null hypothesis based on sample data.