Language
Country/Area
No result found
P-value and null hypothesis: What is their relationship?
In various fields such as economics, social sciences, and perhaps even medicine, the use of p-values seems to have become a tacit understanding. However, the interpretation of this number is often controversial. Many data scientists and researchers say that the true meaning of the p-value is often misunderstood, which makes it vague in the academic community. This therefore raises a number of important questions about the relationship of the p-value to the null hypothesis.
The p-value is a probability measure based on the null hypothesis that reflects how extreme the observed test statistic would be if the null hypothesis were true.
According to the statistical definition, the null hypothesis is the hypothesis being tested, usually assuming that a certain effect or difference does not exist. For example, if a study is designed to test the effectiveness of a drug for a certain condition, the null hypothesis might be "the drug has no effect." The p-value is a tool used to quantify this hypothesis. Specifically, it represents the probability of obtaining a result or a more extreme result if the hypothesis is true. If the p-value is very small, it indicates that the observed results are extremely unlikely to occur given the null hypothesis, which may prompt the researcher to reject the null hypothesis.
In 2016, the American Statistical Association (ASA) issued a statement stating that "the p-value does not measure the probability that the research hypothesis is true, nor does it indicate the probability that the data occurred by chance."
In response to this, many scholars and statisticians have called for a re-evaluation of the use of p-values. They argue that the p-value does not represent the size of the evidence or the significance of the results, and should not be used simply as the sole criterion for rejecting or accepting a hypothesis. Misleading conclusions are likely to occur, especially when multiple trials are conducted or the sample size is small.
In practice, researchers often set a "significance level", usually 0.05, which means that when the p-value is less than 0.05, the researcher will reject the null hypothesis. Although this standard is widely used in the statistical community, there are many problems hidden behind it. Studies using this standard sometimes ignore other relevant factors such as test design and measurement quality, leading to incorrect interpretation of data results.
"In fields such as mental health and clinical medicine, researchers must consider every aspect of the design to ensure reasonable conclusions."
On the one hand, the size of the p-value reflects the confidence of the result to some extent; on the other hand, relying on a single number as the basis for decision-making also has risks and may lead to phenomena such as the "p-value hook". In this case, researchers may seek to adjust or filter data in data analysis to make it significant rather than objectively reflect the true situation.
It is worth noting that the p-value is not just a number derived from sample data, but also involves the interpretation of the entire sample. Therefore, in addition to reporting p-values, research should also focus on other statistical indicators, such as confidence intervals, effect sizes, etc. These statistical tools can help provide more comprehensive analysis results.
Many statisticians have suggested that more attention should be paid to other inferential statistical methods, such as confidence intervals and likelihood ratios, rather than relying solely on p-values to draw conclusions.
Such debates have prompted a rethinking of statistical methods in economics and other scientific fields. In 2019, ASA formed a special group to review the use of statistical methods in scientific research. They note that different uncertainty measures can complement each other and emphasize that "when p-values and significance tests are correctly applied and interpreted, they can improve the rigor of conclusions drawn from the data." Therefore, it is particularly important to find appropriate statistical tools and correctly interpret the data.
On the whole, the relationship between the p-value and the null hypothesis is not simple and clear, but contains more intersections of scientific methods and theories. Perhaps the real challenge is not just how to calculate or interpret p-values, but how to ensure that they are used correctly and reasonably in research. Have you ever thought about how to properly use the p-value in your research, rather than just relying on its size to make decisions?
