As a statistical expert with a background in data analysis and interpretation, I often encounter questions about statistical significance and the interpretation of P values. The P value is a critical concept in hypothesis testing, which is a fundamental part of statistical inference. It helps researchers determine whether the results of their study are likely due to chance or if there is a genuine effect or relationship between the variables being studied.

When we conduct a hypothesis test, we start with a null hypothesis (H0), which typically represents the status quo or a claim of no effect or no difference. The alternative hypothesis (H1 or Ha) represents the opposite of the null hypothesis, suggesting that there is an effect or a difference.

The P value is the probability of observing a test statistic as extreme as, or more extreme than, the one calculated from my sample data, assuming that the null hypothesis is true. It's important to note that a P value does not measure the probability that the null hypothesis is true or false; rather, it is the likelihood of the observed data under the assumption that the null hypothesis holds.

The significance level, often denoted by the Greek letter alpha (α), is a threshold that we set before conducting a statistical test to determine whether we should reject the null hypothesis. If the P value is less than or equal to the significance level, we reject the null hypothesis in favor of the alternative hypothesis. This is known as a statistically significant result.

Conventionally, the 5% (P < 0.05), 1% (P < 0.01), and 0.1% (P < 0.001) levels have been used as thresholds for significance. These levels represent the probability of making a Type I error, which is the error of rejecting a true null hypothesis.

A P value of 0.001 means that there is a 0.1% chance that the observed results occurred by random chance if the null hypothesis were true. In other words, if there truly is no effect or no difference, there would be a 1 in 1000 chance of observing a result as extreme as the one we have if we were to repeat the experiment an infinite number of times. This is a very low probability, suggesting that the evidence is strong against the null hypothesis.

When interpreting a P value of 0.001, it's crucial to consider the context of the study. A low P value does not necessarily mean that the effect is large or practically significant; it simply indicates that the results are unlikely to have occurred by chance. The size of the effect, the sample size, and the design of the study are also important factors to consider.

It's also important to avoid the misconception that a P value is the probability that the study's conclusions are correct, or that it measures the strength of the evidence. The P value is only one piece of the puzzle and should be interpreted in conjunction with other statistical measures and the study's design.

In summary, a P value of 0.001 is a very low probability that the observed results are due to chance, indicating strong evidence to reject the null hypothesis in favor of the alternative hypothesis. However, it is just one aspect of statistical analysis, and the interpretation of this value should be done with careful consideration of the study's design, the effect size, and the practical implications of the findings.

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The term significance level (alpha) is used to refer to a pre-chosen probability and the term "P value" is used to indicate a probability that you calculate after a given study. ... Conventionally the 5% (less than 1 in 20 chance of being wrong), 1% and 0.1% (P < 0.05, 0.01 and 0.001) levels have been used.read more >>