Statistics on Less Likely
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Recent content in Statistics on Less LikelyHugo -- gohugo.ioWed, 02 Jan 2019 00:00:00 +0000When Can We Say That Something Doesn’t Work?
https://lesslikely.com/statistics/evidence-of-absence/
Wed, 02 Jan 2019 00:00:00 +0000https://lesslikely.com/statistics/evidence-of-absence/People don’t want to waste their time on things that don’t work. To avoid wasting time, many may want to assess the scientific evidence. They may first look at the basic science (if it can be studied at such a level) and ask, “does this thing have a clear molecular/biological mechanism,” or they may ask, “does it have a theoretical foundation?”
Next, the person may look at the human evidence (if there is any) and ask if it worked in a clinical trial or epidemiological data.Book Review: Fisher, Neyman, and the Creation of Classical Statistics
https://lesslikely.com/statistics/classical-lehmann/
Sun, 30 Dec 2018 00:00:00 +0000https://lesslikely.com/statistics/classical-lehmann/Erich Lehmann’s last book, which was published after his death, is on the history of classical statistics and its creators. Specifically, how his mentor Jerzy Neyman and his adversary Ronald Fisher helped lay the foundations for the methods that are used today in several fields.
This post is intended to be a general review/summary of the book, which I recommend to everyone and anyone who is interested in statistics and science.P-Values Are Tough And S-Values Can Help
https://lesslikely.com/statistics/s-values/
Sun, 11 Nov 2018 00:00:00 +0000https://lesslikely.com/statistics/s-values/The P-value doesn’t have many fans. There are those who don’t understand it, often treating it as a measure it’s not, whether that’s a posterior probability, the probability of getting results due to chance alone, or some other bizarre/incorrect interpretation. [1–3]
Then there are those who dislike it for reasons such as believing that the concept is too difficult to understand or because they see it as a noisy statistic that provides something we’re not interested in.We May Not Understand Control Groups
https://lesslikely.com/statistics/control-group-effects/
Sun, 28 Oct 2018 00:00:00 +0000https://lesslikely.com/statistics/control-group-effects/It’s well known that randomized trials are some of the most efficient ways to make causal inferences and to determine how much something (an intervention) differs from the comparator (some sort of control). Random assignment helps make these goals easier by minimizing selection bias and making the distribution of prognostic factors between groups random (not balanced). [1]
Discussions (similar to the one above) praising the efficiency of randomized trials are widespread, however, few of these discussions take a close look at some of the common assumptions that individuals hold regarding randomized trials.Misplaced Confidence in Observed Power
https://lesslikely.com/statistics/misplaced-power/
Sun, 30 Sep 2018 00:00:00 +0000https://lesslikely.com/statistics/misplaced-power/Two months ago, a study came out in JAMA which compared the effectiveness of the antidepressant escitalopram to placebo for long-term major adverse cardiac events (MACE).
The authors explained in the methods section of their paper how they calculated their sample size and what differences they were looking for between groups.
First, they used some previously published data to get an idea for incidence rates,
“Because previous studies in this field have shown conflicting results, there was no appropriate reference for power calculation within the designated sample size.The Bradford Hill Criteria Don't Hold Up
https://lesslikely.com/statistics/bradford-hill-criteria-dont-hold/
Thu, 06 Sep 2018 00:00:00 +0000https://lesslikely.com/statistics/bradford-hill-criteria-dont-hold/In 1965, the epidemiologist, Austin Bradford Hill, who helped link smoking to lung cancer, gave a speech where he presented his viewpoints/criteria on how we can arrive at causation from correlation.
This lecture was a bit of a game changer at the time given that the tobacco industry was employing statisticians, medical doctors, and even popular science writers to push the idea that the relationship between smoking and lung cancer was merely a correlation, not a causal one.Misuse of Standard Error in Clinical Trials
https://lesslikely.com/statistics/standard-error-clinical-trials/
Tue, 07 Aug 2018 00:00:00 +0000https://lesslikely.com/statistics/standard-error-clinical-trials/Reporting effect sizes with their accompanying standard errors are necessary because it lets the reader interpret the magnitude of the treatment effect and the amount of uncertainty in that estimate. It is magnitudes better than not providing any effect sizes at all and only focusing on statements of statistical significance.
Although many authors provide standard errors with the intention of relaying the amount of uncertainty in the model, there are several misconceptions about when the standard error should be reported, and it is often misused.High Statistical Power Can Be Deceiving
https://lesslikely.com/statistics/high-power-and-nonsignificance/
Mon, 23 Jul 2018 00:00:00 +0000https://lesslikely.com/statistics/high-power-and-nonsignificance/Even though many researchers are now acquainted with what power is and why we try to aim for high power in studies, there are still several misconceptions about statistical power floating around.
For example, if a study designed for 95% power fails to find a difference between two groups, does that offer more support for the null hypothesis? Many will answer yes, because they elicit that if such a large study failed to find a difference between two groups, then this provides evidence for no effect.Vitamin E, Mortality, and the Bayesian Gloss
https://lesslikely.com/statistics/bayesian-vitamin-e/
Wed, 20 Jun 2018 00:00:00 +0000https://lesslikely.com/statistics/bayesian-vitamin-e/Bayesian data analysis is beginning to gain traction in several fields. Some of those reasons include that it allows individuals to represent uncertainty using probability distributions and it helps them avoid losing information that’s typically lost with point estimates and dichotomization.
Bayesian inference also allows for relevant background information to be incorporated into a model using a more continuous approach rather than making binary decisions about what to include.Problems with the Number Needed to Treat
https://lesslikely.com/statistics/problems-with-nnt/
Sun, 27 May 2018 00:00:00 +0000https://lesslikely.com/statistics/problems-with-nnt/The number needed to treat (NNT) is a popular statistic used in medicine and its use is even encouraged by groups like Cochrane and CONSORT. Why is it so popular? Most believe that the NNT is more understandable than effect sizes like odds ratios or risk ratios or statistics like the absolute risk reduction. The NNT is also believed to convey more meaningful information.
In this blog post, I am going to discuss:False Positives, FWER, and FDR Explained
https://lesslikely.com/statistics/multiplicity-explained/
Sat, 05 May 2018 00:00:00 +0000https://lesslikely.com/statistics/multiplicity-explained/If you torture your data long enough, they will tell you whatever you want to hear - Mills (1993)
False positives via statistical hypothesis testing are a severe problem in the scientific literature (Ioannidis, 2005). If a statistically significant finding looks real, but it’s not, and we make policy or clinical decisions based on this finding, it can have catastrophic consequences. Unfortunately, many researchers are still unaware exactly why false positives are so prevalent in the scientific literature, so, I’ve decided to explain some of the common reasons for the high prevalence.Meta-Analysis: Choose Your Model Wisely
https://lesslikely.com/statistics/meta-analysis-models/
Thu, 19 Apr 2018 00:00:00 +0000https://lesslikely.com/statistics/meta-analysis-models/Why Do a Meta-Analysis? Meta-Analyses are statistical techniques where we take the treatment effects from several studies and pool them to estimate the overall treatment effect.
This type of analysis is conducted so that we can get a precise estimate of the true treatment effect or estimate the mean of several true treatment effects and to notice how robust the effects are across studies. If the individual study treatment effects tend to vary substantially across the studies (true heterogeneity, separated from random error), then we want to explore the sources of this observed dispersion.Myth: Covariates Need to Be Balanced in RCTs
https://lesslikely.com/statistics/equal-covariates/
Tue, 10 Apr 2018 00:00:00 +0000https://lesslikely.com/statistics/equal-covariates/Before I get into the nitty-gritty, I want to remind everyone why we randomize in the first place. It’s to reduce selection bias and to get rid of systematic variation amongst groups, which allows us to come to more precise and efficient causal inferences. Many critics claim that we can’t make valid causal inferences if there’s an imbalance in covariates between the groups.
Here’s an example. Say, hypothetically, we had two groups, and we wanted to see the effect of a statin on all-cause mortality and compare it to placebo.Four Misconceptions About Statistical Power
https://lesslikely.com/statistics/power-misconceptions/
Sun, 08 Apr 2018 00:00:00 +0000https://lesslikely.com/statistics/power-misconceptions/Statistical power, within the context of hypothesis testing, is the probability of rejecting the test hypothesis at a specified level, given that the alternative hypothesis is true. In simpler words, it’s the probability of finding a statistically significant effect, when there is one.
Here, I address some misconceptions I often see about statistical power.
Misconception: Statistical power can only be increased with larger sample sizes
Truth: Nope. Here are some other things that increase statistical power: