P-value

Definition

A p-value is a statistical measure that helps determine the strength of evidence against a null hypothesis in hypothesis testing. It indicates the probability of obtaining test results at least as extreme as the observed results, assuming that the null hypothesis is true. The smaller the p-value, the stronger the evidence that you should reject the null hypothesis.

5 Must Know Facts For Your Next Test

1. A p-value less than or equal to the significance level leads to rejection of the null hypothesis, suggesting that there is sufficient evidence to support the alternative hypothesis.
2. P-values do not provide a definitive answer, but rather indicate how compatible the observed data is with the null hypothesis; they do not measure the probability that either hypothesis is true.
3. In regression analysis, p-values help determine which coefficients are statistically significant, influencing decisions on which variables to include in the model.
4. When conducting multiple hypothesis tests, p-values can be adjusted using techniques like Bonferroni correction to control for Type I error rates.
5. Interpreting p-values should be done cautiously; a small p-value does not imply a large effect size or practical significance.

Review Questions

• How does a p-value assist in making decisions about the null hypothesis during hypothesis testing?
  • A p-value provides a quantifiable measure of evidence against the null hypothesis. When the p-value is less than or equal to the predetermined significance level, it suggests that the observed data is unlikely under the assumption of the null hypothesis, leading researchers to reject it. This helps in determining whether there is sufficient statistical evidence to support an alternative hypothesis based on observed data.
• Discuss how p-values relate to OLS estimation in regression analysis and their implications for model selection.
  • In Ordinary Least Squares (OLS) estimation, p-values are used to evaluate the significance of each predictor's coefficient. A low p-value indicates that there is strong evidence against the null hypothesis that a particular coefficient equals zero, suggesting that variable significantly contributes to explaining the dependent variable. This aids in deciding which variables are important to include in a regression model and assists researchers in building a more accurate predictive model.
• Critically assess the limitations of relying solely on p-values when conducting hypothesis tests and making conclusions about economic relationships.
  • Relying solely on p-values can lead to misconceptions about statistical significance versus practical significance. For instance, small sample sizes can produce misleadingly small p-values while large samples might yield trivial results with low p-values. Moreover, p-values do not convey information about effect size or real-world importance, making it crucial to consider confidence intervals and context in interpreting results. Therefore, informed decision-making should incorporate comprehensive statistical analysis beyond just p-values.

Related terms

Null Hypothesis: A statement that there is no effect or no difference, and it serves as the default assumption in hypothesis testing.

Significance Level: A threshold set by the researcher (commonly 0.05) below which the null hypothesis is rejected, indicating a statistically significant result.

Type I Error: The error made when a true null hypothesis is incorrectly rejected, also known as a false positive.