What is the best way to interpret p-values in a Machine Learning experiment?

Understanding the nuanced relationship between p-values and statistical power is essential for conducting and interpreting statistical analyses accurately. It serves as a reminder that statistical significance does not equate to practical significance and that both the likelihood of observing data under the null hypothesis (p-value) and the likelihood of correctly identifying true effects (power) are vital considerations in hypothesis testing.

The best way to interpret p-values is as a measure of the evidence against a null hypothesis, with lower values (typically <0.05) indicating stronger evidence of a significant effect or difference present. It's crucial to remember that p-values do not measure the magnitude of an effect or the probability that the null hypothesis is true, but rather the probability of observing the data, or something more extreme, if the null hypothesis were true.

This is mostly asked questions in ML interviews and I have seen that candidates just gives answers bases on p values is less than 0.5 then null hypnosis.. but most of times hard to explain the concept. The ML is totally based on statistics and mathematics. We are defining a null hypothesis and try to make it wrong or another words we are collecting evidence to reject it.

in machine learning, where multiple hypotheses are often tested simultaneously (e.g., through feature selection or hyperparameter tuning), relying solely on p-values without correction for multiple comparisons can lead to an increased risk of false positives. Therefore, it's essential to consider p-values alongside other metrics, such as effect sizes and domain knowledge, to make informed decisions about model performance and feature relevance in machine learning experiments.

The interpretation of a p-value is not as common or straightforward as in traditional statistical hypothesis testing. P-value is an important metric in the process of feature selection. In feature selection, we try to find out the best subset of the independent variables to build the model.

Proper use of p-values involves recognizing them as indicators of data compatibility with a hypothesis, not absolute measures of truth. Establish a significance level, commonly 0.05, as a threshold to decide whether to reject or fail to reject the null hypothesis. Rejection occurs when the p-value is below the chosen threshold. Importantly, not rejecting the null hypothesis doesn't mean accepting the alternative hypothesis; it signifies having insufficient evidence to doubt the null hypothesis. Consider context, sample size, effect size, and confidence intervals alongside p-values for a comprehensive understanding of your results, as they offer more nuanced insights than p-values alone.

Suppose you are conducting a study to investigate whether a new drug is effective in reducing blood pressure. You have two groups: a treatment group receiving and a control group. Your null hypothesis (H0) is that there is no difference in blood pressure between the treatment and control groups, while your alternative hypothesis (H1) is that there is a difference. After collecting and analyzing the data, you calculate a p-value of 0.03. Now, to properly use the p-value, you need to consider your predefined significance level, often denoted as alpha. Since your calculated p-value (0.03) is less than your significance level (0.05), you reject the null hypothesis.

The p-value evaluates the probability of observing results as extreme as those obtained, assuming the null hypothesis is true. If the p-value falls below the chosen significance level, it suggests that the observed results are unlikely due to chance alone, leading to rejection of the null hypothesis. However, it's widely believed that the significance level is always fixed at 0.05 (as is mostly done in cases of a 95% confidence level), which is not the case. Significance levels can be adjusted based on specific requirements or confidence levels. For instance, a lower significance level like 0.01 may offer more precise results, while a higher level like 0.1 may provide wider confidence intervals.

Reporting the effect size is a good practice. Using metrics like Cohen's d for a two sample t-test makes the results more reliable.

If you get a high p-value, your results could quickly happen by random chance, even if there's no real improvement. You need more evidence to ditch the old model. However, a low p-value means your results are pretty unusual if the 'no difference' assumption were valid, giving you reason to suspect your new model might genuinely be an improvement. It's important to remember that p-values don't definitively prove or disprove anything – they deal with probabilities, not certainties. Scientists often pick a cutoff point (like 0.05) to determine if they should call a result "statistically significant ."Ultimately, p-values are just one tool and shouldn't be the only factor in making decisions about your machine-learning models.

Remember that p-values do not provide evidence in favor of the alternative hypothesis or the null hypothesis. They merely indicate the strength of evidence against the null hypothesis based on the observed data. Avoid interpreting p-values as measures of effect size or the probability of the null hypothesis being true.

A critical technical insight to keep in mind when reporting p-values is the problem of "p-hacking" or "data dredging." This refers to the practice of performing multiple comparisons or testing multiple hypotheses without properly adjusting for these multiple comparisons. The danger of p-hacking lies in its ability to produce statistically significant results purely by chance. When researchers conduct a large number of tests, the likelihood of finding at least one statistically significant result due to random variation increases, even if there is no real effect present. This can lead to false positives, where results appear to be significant when they are not, potentially misleading researchers and the public about the findings of a study.

A common mistake is to think that p-values directly translate into the probability to replicate a result with a different sample. (replicability). This is not the case. A statistical test with p=.05 means that a replication with the same sample size will be as likely to have a result with p>.05 as p<.05.

P-hacking (repeating an experiment until you get a statistically significant result or selecting a sample that produces a statistically significant result) must be avoided. Also, the significance level must not be changed after conducting an experiment to get a statistically significant result.

While p-values provide valuable information, they should not be the sole determinant of your conclusion. Consider the context of the study, the sample size, effect size, and confidence intervals. These factors can provide more nuanced insights into the practical significance and reliability of your findings.

p-hacking to manipulate p-values is prevalent and other stats are used to obscure reproducibilty and is a prevalent issue in research. Be aware that even mundane papers that helps build foundational research is an important and often undervalued contribution. Be transparent, reevaluate and publish. It's the journey that helps you understand.

Although p-values are important for either rejecting or accepting the null hypothesis, it is crucial to remember that they merely indicate the absence or lack of evidence in support of a hypothesis. P-values do not evaluate the magnitude of the effect; to do so, an effect measure is needed, such as risk difference, odds ratio, hazard ratio, etc., depending on the type of study being conducted.

P-value is a threshold for the probability of Type I error and it is associated with the cost of altering a current situation (null hypothesis). Type II error is linked to the cost of missed opportunities, that is, no reject the null hypothesis being false. The challenge in evaluating the probability of Type II error lies in the fact that within the context of the alternative hypothesis, we deal with a probability distribution whose parameters are unknown.