Today in class i learned what is p value how it is used to interpreted
Imagine you’re flipping a coin to see if it’s fair (meaning it has an equal chance of landing on heads or tails). If you flip it a few times and it comes up heads most of the time, you might start to wonder if the coin is biased. The p-value is like a tool that helps you decide if the coin is likely biased or if the results could have happened due to random chance.
If the p-value is very low (usually below a certain threshold, like 0.05), it suggests that the results are unlikely to be due to chance, and you might conclude that the coin is probably biased. On the other hand, if the p-value is high (greater than 0.05), it suggests that the results could easily happen by chance alone, so you wouldn’t have strong evidence that the coin is biased.
Lower p-values indicate stronger evidence against randomness, while higher p-values suggest that the observed results might be due to chance.
Scenario: You have a coin, and you want to determine if it’s a fair coin (meaning it has an equal chance of landing on heads or tails). You decide to conduct an experiment by flipping the coin 100 times and recording the results.
Null Hypothesis (H0): The coin is fair; the probability of getting heads or tails is 50% (0.5).
Alternative Hypothesis (Ha): The coin is biased; the probability of getting heads or tails is not 50%.
After conducting your experiment, you observe that the coin landed on heads 60 times and on tails 40 times.
Calculating the p-value: Using a statistical test (like a chi-squared test), you calculate the p-value. In this case, let’s say the p-value is 0.03.
Interpretation: If your chosen significance level (alpha) is 0.05, which is a common threshold, the p-value of 0.03 is less than alpha. This means there’s only a 3% chance of observing such an extreme result (60 heads) if the coin were truly fair (null hypothesis). Because the p-value is less than alpha, you reject the null hypothesis and conclude that the coin may be biased.
In simple terms, the p-value helps you decide if your coin is likely fair (p-value > 0.05) or if there’s evidence that it’s biased (p-value ≤ 0.05) based on your experiment’s results.
In your regression model, we are examining the relationship between the predictor variable “%Inactivity” and the response variable “%Diabetic.” Specifically, you’re interested in checking for homoscedasticity, which means that the variability of the errors (residuals) in our model should be consistent across different levels of “%Inactivity.” In simpler terms, it suggests that the spread of your data points around the regression line should be roughly the same for all values of “%Inactivity.”
Here’s what the results of the Breusch-Pagan test are indicating:
LM Statistic: The LM statistic is a measure used in the Breusch-Pagan test to assess whether there is heteroscedasticity (varying levels of error variance) in your model. A very low p-value (close to 0) for the LM statistic suggests strong evidence against the null hypothesis of homoscedasticity. In our case, the p-value is extremely close to zero (3.607×10^-13), indicating that there is significant evidence that the errors in your model do not have consistent variances across different levels of “%Inactivity.”
F-test: The F-test associated with the Breusch-Pagan test is used to support the LM statistic. In our case, it yields a p-value of 1, which is unusual. Normally, a p-value of 1 would suggest homoscedasticity (consistent error variances). However, you shouldn’t solely rely on the F-test in this situation because the LM test has provided strong evidence against homoscedasticity.
In conclusion, even though the F-test may not suggest heteroscedasticity, the LM test’s extremely low p-value indicates strong evidence that your model does indeed have varying error variances across different levels of “%Inactivity.” As a result, it’s recommended to consider the presence of heteroscedastic errors in your regression model when interpreting the results and making any necessary adjustments or transformations to address this issue.