As a statistical expert with a deep understanding of hypothesis testing and statistical significance, I can provide a comprehensive answer to your question regarding the significance of a P-value of 0.02.
Statistical significance is a concept that is used to determine whether the results of a study are due to chance or if there is a true effect. The P-value is a statistical measure that is used to make this determination. It represents the probability of obtaining the observed results (or more extreme) if the null hypothesis were true. The null hypothesis is a statement that there is no effect or no difference between groups.

When conducting a statistical test, researchers typically set a significance level, denoted as alpha (α), which is the threshold for determining statistical significance. The most commonly used significance level is 0.05. This means that if the P-value is less than 0.05, the results are considered statistically significant, and the null hypothesis is rejected.

In the case of a P-value of 0.02, it is indeed significant according to the conventional definition of statistical significance. Here's why:


1. Lower Than the Significance Level: The P-value of 0.02 is less than the commonly accepted significance level of 0.05. This means that there is less than a 2% probability of observing the data if the null hypothesis were true.


2. Rejection of the Null Hypothesis: Because the P-value is below the significance threshold, it provides evidence against the null hypothesis. Researchers would typically reject the null hypothesis in favor of the alternative hypothesis, which posits that there is an effect or a difference.


3. Evidence of an Effect: A significant P-value suggests that there is a statistically detectable effect. However, it is important to note that statistical significance does not necessarily imply practical significance. The size and relevance of the effect should also be considered.


4. Confidence Intervals: When a P-value is significant, it is often accompanied by a confidence interval that provides a range within which the true effect is likely to lie. This can give a better understanding of the magnitude and direction of the effect.


5. Multiple Comparisons: If multiple statistical tests are conducted, the chance of finding at least one significant result by chance increases. This is known as the multiple comparisons problem and may require adjustments to the significance level or the use of more stringent tests.


6. Effect Size and Practical Significance: A significant P-value is not the only factor to consider. The effect size, which measures the magnitude of the difference or effect, is also crucial. A small effect size with a significant P-value may not be practically meaningful.

7.
Contextual Considerations: The significance of a P-value also depends on the context of the research question and the field of study. What is considered significant in one field may not be in another.

8.
Replicability: The ability to replicate findings is a key aspect of scientific research. A significant P-value from a single study should be interpreted with caution until it can be replicated by other researchers.

9.
Statistical vs. Clinical Significance: In fields like medicine, a statistically significant result may not always translate to a clinically significant outcome. It is important to consider the impact on patients or the population when interpreting results.

10.
Publication Bias: There is a tendency for studies with significant results to be published more often than those without. This can skew the perception of the evidence base.

In conclusion, a P-value of 0.02 is statistically significant as it falls below the conventional threshold of 0.05. However, it is essential to consider the broader context, including the effect size, the possibility of multiple comparisons, the practical significance of the findings, and the potential for replication. Statistical significance is just one piece of the puzzle in understanding the results of a study.

read more >>

Let us consider that the appropriate statistical test is applied and the P-value obtained is 0.02. Conventionally, the P-value for statistical significance is defined as P < 0.05. In the above example, the threshold is breached and the null hypothesis is rejected.Dec 1, 2007read more >>