As a statistical expert with a deep understanding of hypothesis testing and its implications, I can provide a comprehensive explanation of what it means when your p-value is significant.
When conducting a statistical analysis, the primary goal is often to test a hypothesis about a population parameter. This involves formulating a null hypothesis (H0), which represents the status quo or the assumption that there is no effect or relationship, and an alternative hypothesis (H1 or Ha), which represents the claim you want to test.

The p-value is a critical component in this process. It is calculated from the sample data and represents the probability of observing a test statistic as extreme as, or more extreme than, the one calculated from the sample data, given that the null hypothesis is true. It is a measure of the strength of the evidence against the null hypothesis.

Here are some key points about the p-value:


1. Range: The p-value ranges from 0 to 1. A value close to 0 indicates a strong evidence against the null hypothesis, while a value close to 1 suggests that the observed data is consistent with the null hypothesis.


2. Interpretation: A small p-value (typically ≤ 0.05) suggests that the results are statistically significant. This means that there is less than a 5% probability that the observed results occurred by chance if the null hypothesis were true. It is considered strong evidence to reject the null hypothesis in favor of the alternative hypothesis.


3. Significance Level (α): This is a threshold that you set before conducting the test to decide when to reject the null hypothesis. The most common significance level is 0.05, but it can be set to 0.01 for a more stringent test or 0.10 for a less stringent one.


4. One-Tailed vs. Two-Tailed Tests: The p-value can be calculated for both one-tailed and two-tailed tests. A one-tailed test examines the possibility of the effect in one direction, while a two-tailed test considers effects in both directions. The choice depends on the research question.


5. Not a Probability of Truth or Falsity: It is important to note that the p-value is not the probability that the null hypothesis is true or false. It is the probability of observing the data given the null hypothesis is true.


6. Multiple Comparisons: When performing multiple hypothesis tests, the chance of finding at least one significant result by chance increases. This is known as the multiple comparisons problem, and adjustments like the Bonferroni correction are used to control the family-wise error rate.

7.
Effect Size: A significant p-value does not necessarily mean a large or important effect. It is essential to consider the effect size and practical significance in addition to statistical significance.

8.
Confidence Intervals: Confidence intervals provide a range within which the population parameter is estimated to lie. They are often used in conjunction with p-values to give a more complete picture of the results.

9.
Assumptions and Robustness: The validity of the p-value depends on the assumptions of the statistical test being met. If these assumptions are violated, the p-value may not accurately reflect the evidence against the null hypothesis.

10.
Decision Making: In practice, a significant p-value is often used as a basis for making decisions, such as whether to proceed with a new drug in clinical trials or to implement a new policy. However, it should be interpreted in the context of the study design, the quality of the data, and the potential consequences of the decision.

In conclusion, a significant p-value is a statistical tool that provides evidence against the null hypothesis. It is crucial to interpret it correctly and consider it alongside other factors when making decisions based on the results of a statistical test.

read more >>

When you perform a hypothesis test in statistics, a p-value helps you determine the significance of your results. ... The p-value is a number between 0 and 1 and interpreted in the following way: A small p-value (typically -- 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.read more >>