What does the P value not tell you?
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Owen Turner
Works at the International Organization for Standardization, Lives in Geneva, Switzerland.
As a domain expert in statistical analysis, I'd like to clarify some common misconceptions about p-values. P-values are a cornerstone of hypothesis testing in statistics and are used to determine whether the results of an experiment or study are statistically significant. However, they are often misunderstood and misinterpreted. Here's what a p-value does not tell you:
1. Causality: A p-value does not provide any information about whether there is a causal relationship between variables. It only indicates whether an observed effect is likely due to chance.
2. Effect Size: As the statement suggests, "A p-value can tell you that a difference is statistically significant, but it tells you nothing about the size or magnitude of the difference." A small effect can be statistically significant if the sample size is large enough, but this does not mean it is practically significant.
3. The Truth of the Alternative Hypothesis: Saying "The p-value is low, so the alternative hypothesis is true" is a misinterpretation. A low p-value indicates that the evidence is against the null hypothesis, but it does not confirm the alternative hypothesis as true.
4. **Probability of the Null Hypothesis Being True**: A p-value is not the probability that the null hypothesis is true. It is the probability of observing the data (or more extreme) assuming the null hypothesis is true.
5. Error Rate of the Study: If you use an alpha level of 0.05, there's a 5% chance you will incorrectly reject the null hypothesis (Type I error). However, this does not mean there's a 95% chance that the null hypothesis is true; it's the probability of incorrectly rejecting a true null hypothesis.
6. Strength of Evidence: A p-value does not measure the strength of the evidence for or against the null hypothesis. It is a threshold-based decision tool, not a measure of the quality or weight of evidence.
7.
Repeatability of Results: A low p-value does not guarantee that the results will be replicated in future studies. It is possible to have a statistically significant result that is not reproducible due to various factors such as sampling variability, bias, or chance.
8.
Quality of the Study: A statistically significant result does not imply that the study was well-designed or free from bias. Poorly designed studies can produce statistically significant results that are not reliable.
9.
Individual Probability: A p-value is not the probability that an individual subject experienced an effect. It is a population-level statistic.
10.
Decision-Making: P-values should not be used as the sole basis for making decisions. They are one piece of the puzzle and should be interpreted in the context of the study design, the quality of the data, and the external evidence.
In summary, while p-values are a crucial tool in statistical analysis, they are just one part of the story. They provide a way to assess whether the data provide evidence against the null hypothesis, but they do not provide a complete picture of the research question at hand. It's important to consider p-values in conjunction with other statistical measures, such as confidence intervals and effect sizes, as well as the broader context of the research.
1. Causality: A p-value does not provide any information about whether there is a causal relationship between variables. It only indicates whether an observed effect is likely due to chance.
2. Effect Size: As the statement suggests, "A p-value can tell you that a difference is statistically significant, but it tells you nothing about the size or magnitude of the difference." A small effect can be statistically significant if the sample size is large enough, but this does not mean it is practically significant.
3. The Truth of the Alternative Hypothesis: Saying "The p-value is low, so the alternative hypothesis is true" is a misinterpretation. A low p-value indicates that the evidence is against the null hypothesis, but it does not confirm the alternative hypothesis as true.
4. **Probability of the Null Hypothesis Being True**: A p-value is not the probability that the null hypothesis is true. It is the probability of observing the data (or more extreme) assuming the null hypothesis is true.
5. Error Rate of the Study: If you use an alpha level of 0.05, there's a 5% chance you will incorrectly reject the null hypothesis (Type I error). However, this does not mean there's a 95% chance that the null hypothesis is true; it's the probability of incorrectly rejecting a true null hypothesis.
6. Strength of Evidence: A p-value does not measure the strength of the evidence for or against the null hypothesis. It is a threshold-based decision tool, not a measure of the quality or weight of evidence.
7.
Repeatability of Results: A low p-value does not guarantee that the results will be replicated in future studies. It is possible to have a statistically significant result that is not reproducible due to various factors such as sampling variability, bias, or chance.
8.
Quality of the Study: A statistically significant result does not imply that the study was well-designed or free from bias. Poorly designed studies can produce statistically significant results that are not reliable.
9.
Individual Probability: A p-value is not the probability that an individual subject experienced an effect. It is a population-level statistic.
10.
Decision-Making: P-values should not be used as the sole basis for making decisions. They are one piece of the puzzle and should be interpreted in the context of the study design, the quality of the data, and the external evidence.
In summary, while p-values are a crucial tool in statistical analysis, they are just one part of the story. They provide a way to assess whether the data provide evidence against the null hypothesis, but they do not provide a complete picture of the research question at hand. It's important to consider p-values in conjunction with other statistical measures, such as confidence intervals and effect sizes, as well as the broader context of the research.
2024-05-12 11:00:26
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Works at the International Atomic Energy Agency, Lives in Vienna, Austria.
A p-value can tell you that a difference is statistically significant, but it tells you nothing about the size or magnitude of the difference. "The p-value is low, so the alternative hypothesis is true." ... If you use an alpha level of 0.05, there's a 5% chance you will incorrectly reject the null hypothesis.Jun 20, 2011
2023-06-25 07:04:27
Amelia Davis
QuesHub.com delivers expert answers and knowledge to you.
A p-value can tell you that a difference is statistically significant, but it tells you nothing about the size or magnitude of the difference. "The p-value is low, so the alternative hypothesis is true." ... If you use an alpha level of 0.05, there's a 5% chance you will incorrectly reject the null hypothesis.Jun 20, 2011
