I have explored about the p-value which the professor has explained and when I delved into this topic, I got to know about null hypothesis also.
NULL HYPOTHESIS:
The null hypothesis, often abbreviated as H0, is a fundamental concept used in hypothesis testing. It represents a statement or assumption that there is no significant difference, effect, or relationship between variables or groups in a population. The null hypothesis is typically formulated as the default or initial hypothesis to be tested against.
The null hypothesis serves as a baseline or point of reference for statistical inference. It is essential for drawing conclusions from data and making decisions based on evidence. However, it’s important to recognize that failing to reject the null hypothesis does not prove that it is true; it simply means that the data you collected did not provide sufficient evidence to suggest otherwise. Statistical hypothesis testing is a way to quantify and formalize this decision-making process in statistics.
p-Value:
In statistics, the p-value can be called as probability value and is a measure that helps assess the evidence against a null hypothesis. It quantifies the likelihood of observing a test statistic as extreme as, or more extreme than, the one calculated from the sample data if the null hypothesis were true. In simpler terms, it tells you whether the results you’ve obtained from your sample data are statistically significant or simply due to random chance.
Here’s how I am thinking the concept of p-value works:
1. Formulating a null hypothesis (H0): This is a statement that there is no effect, no difference, or no association in the population we are studying. It’s often the hypothesis you want to test against.
2. Collecting and analyzing data: You collect data from your sample and perform the necessary statistical analysis to calculate a test statistic. The choice of test statistic depends on the type of analysis you’re conducting.
3. Calculating the p-value: The p-value is calculated based on the test statistic and the probability distribution associated with the test. The p-value represents the probability of observing a test statistic as extreme as, or more extreme than, the one you calculated, assuming the null hypothesis is true.
4. Comparing the p-value to a significance level (A): If we assume the significance level as A, then it is predetermined before conducting the test and represents the threshold for statistical significance. Common choices for A include 0.05 (5%) and 0.01 (1%).
– If p-value ≤ A: You reject the null hypothesis. This suggests that the observed results are statistically significant, and there’s evidence to support your alternative hypothesis.
– If p-value > A: You fail to reject the null hypothesis. This means that the observed results are not statistically significant, and you do not have sufficient evidence to support your alternative hypothesis.
It’s important to note that a small p-value (typically ≤ 0.05) does not prove that the null hypothesis is false; it only suggests that your data provide evidence against it. The p-value does not provide information about the effect size or the practical significance of the results.
Interpreting p-values requires caution, and they should be considered in the context of the specific research question, study design, and the potential for other sources of bias or error in the data collection process. Additionally, p-values are just one component of statistical hypothesis testing, and it’s essential to consider effect sizes, confidence intervals, and other relevant statistical measures in the interpretation of your results.