1: p-value – The p-value is a statistical measure that is commonly used in hypothesis testing to assess the strength of evidence against a null hypothesis.
- Small p-value (typically ≤ α): Strong evidence against the null hypothesis. Researchers may conclude that there is a significant effect or difference, supporting the alternative hypothesis.
- Large p-value (typically > α): Weak evidence against the null hypothesis. Researchers do not have enough evidence to reject the null hypothesis.2: Breusch-Pagan test – Significance of p-value in this test is as follows:
- If p-value ≤ α: This indicates that there is strong evidence to reject the null hypothesis. In other words, you conclude that there is heteroscedasticity in the regression model, suggesting that the variance of the error term is not constant across the levels of the independent variables.
- If p-value > α: This suggests that there is not enough evidence to reject the null hypothesis. In this case, you would conclude that there is no significant heteroscedasticity in the regression model, and it is reasonable to assume that the variance of the error term is constant across the levels of the independent variables.
- In summary, the p-value in the Breusch-Pagan test helps you assess whether there is heteroscedasticity in your regression model. If the p-value is low (typically less than 0.05), you conclude that there is evidence of heteroscedasticity, which can have implications for the validity of your regression analysis. If the p-value is high, you do not have strong evidence to suggest heteroscedasticity, and you can proceed with more confidence in the assumptions of homoscedasticity.3: Chi-Square Distribution – As the degrees of freedom increase, the chi-square distribution becomes more bell-shaped and approaches a normal distribution (the central limit theorem applies). Chi-square distributions are an essential tool in statistical analysis, particularly for drawing inferences about population variances, testing hypotheses, and assessing relationships between categorical variables.