p-value interpretation and how to write analysis
For example, suppose that a vaccine study produced a P value of 0.04. This P value indicates that if the vaccine had no effect, you’d obtain the observed difference or more in 4% of studies due to random sampling error.
There are several reasons why P values can’t be the error rate.
One commonly used significance level is 0.05. If the investor finds that the p-value is less than 0.05, then there is evidence against the null hypothesis. As a result, the investor would reject the null hypothesis and accept the alternative hypothesis. The smaller the p-value, the greater the evidence against the null hypothesis. Thus, if the investor finds that the p-value is 0.001, there is strong evidence against the null hypothesis, and the investor can confidently conclude the portfolio’s returns and the S&P 500’s returns are not be equivalent.
P-values are calculated using p-value tables or spreadsheets/statistical software. Because different researchers use different levels of significance when examining a question, a reader may sometimes have difficulty comparing results from two different tests. P-values provide a solution to this problem.
A p-value less than 0.05 (typically в‰¤ 0.05) is statistically significant. It indicates strong evidence against the null hypothesis, as there is less than a 5% probability the null is correct (and the results are random). Therefore, we reject the null hypothesis, and accept the alternative hypothesis.
By Saul McLeod, published 2019
The P value means the probability, for a given statistical model that, when the null hypothesis is true, the statistical summary would be equal to or more extreme than the actual observed results . Therefore, P values only indicate how incompatible the data are with a specific statistical model (usually with a null-hypothesis). The smaller the P value, the greater statistical incompatibility of the data with the null hypothesis. What is important is that P values do not focus on the study hypothesis but on the null hypothesis.
Department of Anesthesiology and Pain Medicine, Seoul National University Bundang Hospital, Seongnam, Korea.
A colleague just shared your blog with me and after 2 posts I’m hooked. I will read more today.
I use ttest and pvalues in the domain of web and app A/B testing and I’ve read everything I could find online but I still wasn’t sure I understood.
I built an A/A simulator in python and I got a lot more statistically significant results than 5% so I’m confused.
Just for clarity I call an A/A test a randomise observation where both series use the same success rate in %.
Even after reading your article alpha and pvalue are still somehow overlapping for me. I’ll keep reading your article to further clarify.
Let’s return to Frequentist approach because there’s another side of things that isn’t obvious. In contrast with the earlier example for an individual study, the Frequentist approach talks about the Type I errors not for an individual study but for a class of studies that use the same significance level. A result is statistically significant when the p-value is less than the significance level. The significance level equals the Type I Error for all studies that use a particular significance level. For example, 5% of all studies that use a significance level of 0.05 should be false positives. Of course, when you see significant test results, you don’t know for sure which ones are real effects and which ones are false discoveries.