What is p-value and its significance?

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P-value is a statistical measure used to determine the strength of evidence against a null hypothesis in hypothesis testing.

Definition:

The p-value is the probability of obtaining a result equal to or more extreme than what was actually observed, assuming the null hypothesis is true.

Interpretation:

• A low p-value (typically ≤ 0.05) indicates that the observed data is unlikely under the null hypothesis and suggests strong evidence against it.

• A high p-value (> 0.05) suggests that the data is likely under the null hypothesis and there is weak evidence against it.

Example:

Suppose you are testing whether a new drug is more effective than the current one.

• Null Hypothesis (H₀): No difference in effectiveness.

• You collect data and calculate a p-value = 0.03.

• Since 0.03 < 0.05, you reject the null hypothesis and conclude the new drug likely has a different (better) effect.

Significance Level (α):

The threshold for determining significance is called the significance level (commonly set at 0.05 or 5%).

• If p-value ≤ α, reject the null hypothesis.

• If p-value > α, fail to reject the null hypothesis.

Importance of p-value:

• Helps in making objective decisions in hypothesis testing.

• Widely used in fields like medicine, economics, marketing, and social sciences.

In summary, the p-value helps quantify evidence against the null hypothesis and plays a crucial role in determining whether an observed effect is statistically significant.

Read More:

What is the difference between population and sample?

What is the Central Limit Theorem?

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