A p -value is the probability of the observed, or more extreme, data, under the assumption that the null-hypothesis is true. The goal of this blog post is to understand what this means, and perhaps more importantly, what this doesn’t mean. People often misunderstand p -values, but with a little help and some dedicated effort, we should be able explain these misconceptions.

If I ever make a follow up to my current MOOC, I will call it ‘Improving Your Statistical Questions’. The more I learn about how people use statistics, the more I believe the main problem is not how people interpret the numbers they get from statistical tests. The real issue is which statistical questions researchers ask from their data. Our statistics education turns a blind eye to training people how to ask a good question.

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The replication crisis is over. Sure, not everyone has gotten the memo (either about it having started, or about it having ended) but the majority of scientists agree that there were (slightly) too many findings from the past that cannot easily be replicated. The underlying reasons are clear: publication bias, flexibility in the data analysis, low power, and not enough rewards for replication studies.

I was listening to a recent Radiolab episode on blame and guilt, where the guest Robert Sapolsky mentioned a famous study on judges handing out harsher sentences before lunch than after lunch. The idea is that their mental resources deplete over time, and they stop thinking carefully about their decision – until having a bite replenishes their resources.

Does science offer a way to learn what is true about our world? According to the perspective in philosophy of science known as scientific realism , the answer is ‘yes’. Scientific realism is the idea that successful scientific theories that have made novel predictions give us a good reason to believe these theories make statements about the world that are at least partially true.

When designing a study, you need to justify the sample size you aim to collect. If one of your goals is to observe a p -values lower than the alpha level you decided upon (e.g., 0.05), one justification for the sample size can be a power analysis. A power analysis tells you the probability of observing a statistically significant effect, based on a specific sample size, alpha level, and true effect size.

The Dutch toilet cleaner ‘WC-EEND’ (literally: 'Toilet Duck') aired a famous commercial in 1989 that had the slogan ‘We from WC-EEND advise… WC-EEND’. It is now a common saying in The Netherlands whenever someone gives an opinion that is clearly aligned with their self-interest. In this blog, I will examine the hypothesis that blogs are, on average, of higher quality than journal articles.

One of the challenges of trying to get people to improve their statistical inferences is access to good software. After 32 years, SPSS still does not give a Cohen’s d effect size when researchers perform a t-test.

In the latest exuberant celebration of how Bayes Factors will save science, Ravenzwaaij and Ioannidis write: “our study offers through simulations yet another demonstration of the unfortunate effect of p-values on statistical inferences.” Uh oh – what have these evil p -values been up to this time?

Greenland and colleagues (Greenland et al., 2016) published a list with 25 common misinterpretations of statistical concepts such as power, confidence intervals, and, in points 1-10, p-values. Here I’ll explain how 50% of these problems are resolved by using equivalence tests in addition to null-hypothesis significance tests.