# p-value Interpretation

The P-value is a probability, with a value ranging from zero to one. It is measure of how much evidence we have against the null hypothesis. P-value is a way to express the likelihood that $H_0$ is not true. The smaller the p-value, the more evidence we have against $H_0$.

p-value can be defined as

The largest significance level at which we would accept the null hypothesis. It enables us to test hypothesis without first specifying a value for $\alpha$. OR

The probability of observing a sample value as extreme as, or more extreme than, the value observed, given that the null hypothesis is true.

If the P-value is smaller then the chosen significance level then $H_0$ (null hypothesis) is rejected even when it is true. If it is larger than the significance level $H_0$ is not rejected.

If the P-value is less than

• 0.10, we have some evidence that $H_0$ is not true
• 0.05, strong evidence that $H_0$ is not true
• 0.01, Very strong evidence that $H_0$ is not true
• 0.001, extremely strong evidence that $H_0$ is not true

Misinterpretation of a P-value

Many people misunderstand P-values. For example, if the P-value is 0.03 then it means that there is a 3% chance of observing a difference as large as you observed even if the two population means are same (i.e. the null hypothesis is true). It is tempting to conclude, therefore, that there is a 97% chance that the difference you observed reflects a real difference between populations and a 3% chance that the difference is due to chance. However, this would be an incorrect conclusion. What you can say is that random sampling from identical populations would lead to a difference smaller than you observed in 97% of experiments and larger than you observed in 3% of experiments.

# Difference between a probability value and the significance level?

Basically in hypothesis testing the goal is to see if the probability value is less than or equal to the significance level (i.e., is p ≤ alpha). It is also called the size of the test or size of the critical region. It is generally specified before any samples are drawn so that the results obtained will not influence our choice.

• The probability value (also called the p-value) is the probability of the observed result found in your research study of occurring (or an even more extreme result occurring), under the assumption that the null hypothesis is true (i.e., if the null were true).
• In hypothesis testing, the researcher assumes that the null hypothesis is true and then sees how often the observed finding would occur if this assumption were true (i.e., the researcher determines the p-value).
• The significance level (also called the alpha level) is the cutoff value the researcher selects and then uses to decide when to reject the null hypothesis.
• Most researchers select the significance or alpha level of .05 to use in their research; hence, they reject the null hypothesis when the p-value is less than or equal to .05.
• The key idea of hypothesis testing it that you reject the null hypothesis when the p-value is less than or equal to the significance level of.05.