# Are descriptive statistics sometimes more useful than tests of significance?

How does the biology community currently feel with regards to publishing descriptive and effect size statistics rather than significance stats? Almost every journal article I read in the cell biology field almost always reports things like P values and stats tests to report statistical significance, but should effect sizes be more important to a biologist? Do we even care if something is statistically significant if the effect size is negligible? Rather than crunch for significance, could one get away with showing things like confidence intervals, eta^2, Cohen's d, and r values instead over P values? P values tell you the odds that if you assume the null hypothesis is true, then the observation you're making are only 5%(assuming of course P<0.05). However, this can lead to the logical fallacy as noted by Aristotle--theory A predicts that changing X will cause Y. An experimenter thus performs experiments to manipulate X and sees changes in Y, therefore he/she concludes theory A is supported, which is however completely wrong. Theories B, C, D, E....... could all also predict that X changes Y and may even be better at it. Even if you conclude that your findings "support" theory A, it's still weak because you haven't ruled out all of the other possibilities.

So in order to avoid statistical significance relative to null hypothesis that has all sorts of pitfalls, can one just use descriptive and effect size statistics just as effectively, if not more so?

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I wonder how much of this is because biologists have been taught statistical significance and haven't been taught to use effect size. In my introductory stats class in college, we never got beyond linear regression (yes, it was sad, but at least I learned R), and that was more stats than most people knew. I learned about effect size simply because of a well-informed PI whose background was not in biology. I, personally, would favor the use of descriptive and effect size statistics in combination with significance statistics, i.e. these are significantly different, by this much. – dd3 Mar 12 '13 at 5:05
Agree with @dd3. You can try and talk about effect size and such, but then when the infamous third reviewer whines about p values you gotta play the game... To be honest most biologists I know (many of whom are very good at biology, nothing to say there) only have a very basic -and often slightly wrong- understanding of statistics. I can tell you I always have a hard time convincing people to use things like generalized mixed models or such. Most people will just say: I'll do a t-test or an ANOVA instead... – nico Mar 12 '13 at 7:17
On a related note: xkcd.com/882 – Alan Boyd Mar 12 '13 at 7:55
@GPI For a better answer this should really be on stats.stackexchange.com - you are asking biologists when you could be asking statisticians, generally they know more about stats than us biologists! Personally I think each case is different so this question is also a bit difficult to answer, but my approach tends to be: do the stats, report the statistical significance and some descriptive statistics, but discuss the scientific significance - stat & sci significance are not perfectly correlated (p>0.005) ;) – rg255 Mar 12 '13 at 8:27
I think this is a valid question to as Biology because the standards of publication are different between fields of study. I'm sure any statistician will have problems with biological literature. You may have found an important, and biological effect which you can describe qualitatively. When it comes time to publish, if you cannot show the different quantitatively (and likely with a stats test), you limit yourself to publishing in a lower-tier journal. – user560 Mar 12 '13 at 22:13

I'm not a statistician, but I think the comments have got it right. There is never a reason to omit P values, statistical power or some other measure that you have done something that is not a random outcome.

For the sake of reference lets define the terms you reference: Eta squared is a ratio of the variances of two sets of measurements Cohen's d is a measure of the difference between two means.
R value or Pearson Correlation describes the linearity of two numbers, usually one of them being a measurement and the second being an experimental variable.

These numbers as you say are descriptive, but they could be created by throwing coins and writing them up. With small numbers of measurements, and a large enough range of possibilities, its possible to get terribly large numbers here.

Biology, medicine, social science and economics are really susceptible to this. You go into the field and measure butterfly wings or do surveys of people's opinions, or try to guess who is going to win the election and its quite expensive to do more measurements.

If you are measuring something hard to determine because accuracy is important such as a close election race or that is really complicated such as which genes convey a susceptibility to type 2 diabetes (a problem which remains unsolved because so many genes play a role) you need large numbers of responses. Yet each study that comes out gets some answer, but if you want to believe it these numbers should convince no one in most cases.

Microarray data and RNASeq data analysis for instance often suffer from this problem. The measurements are all statistically significant but each one costs hundreds or even thousands of dollars. Most experiments do a minimal three measurements to understand the variance in each measurement and then do 2 to 8 actual measurements. That's not going to so revealing when working with a system with thousands of genes in it. one bad sample with slightly different culture conditions can ruin the experiment.

Our butterfly biologist may measure 100 butterflies and stop when the P values are 0.05 or 0.001 - its a lot of work camping out and setting nets. The truth is that 5% is a number that can happen at random a lot. Even a 0.1% error will happen in one in ten such experiments. In thousands of experiments published that means that 10% of them have a mistake. Not so great.

It gets worse though - not only significance, but bias needs consideration. Because biologists and most other scientists don't understand statistics, the assumptions that we use when we calculate a P value are often inappropriate and don't give honest estimates of the chance that this is a random phenomenon.

If good looking result is chosen specifically to show to prove the point or some data are thrown out because they simply don't look good, or if a hypothesis is chosen in a biased way simply to fit an unreliable set of data.

Or the statistical assumptions of the calculation might simply be so inappropriate that to really cite them is an out and out lie. An everyday example of this is to do a BLAST search. The E-value calculations, if read as a P value would be wrong, even though they are mathematically correct - two strings that show a 10% identity will have a small E value - 10^-8 for instance, but this is only the chance two strings of these lengths will have so many letters in common. Anyone who plays with BLAST will quickly throw out anything that has less than 30% identity unless they are desperate, even though the E-values are infinitesimal.

John Ioannidis has made this subject his focus and has published widely on this topic. A good place to start is his commentary "Why Most Published Research Findings Are False".

There is increasing concern that most current published research findings are false. The probability that a research claim is true may depend on study power and bias, the number of other studies on the same question, and, importantly, the ratio of true to no relationships among the relationships probed in each scientific field. In this framework, a research finding is less likely to be true when the studies conducted in a field are smaller; when effect sizes are smaller; when there is a greater number and lesser preselection of tested relationships; where there is greater flexibility in designs, definitions, outcomes, and analytical modes; when there is greater financial and other interest and prejudice; and when more teams are involved in a scientific field in chase of statistical significance. Simulations show that for most study designs and settings, it is more likely for a research claim to be false than true. Moreover, for many current scientific fields, claimed research findings may often be simply accurate measures of the prevailing bias. In this essay, I discuss the implications of these problems for the conduct and interpretation of research.

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Very interesting response thank you. Does anyone in the community use Bayesian statistics rather than classical statistics as well to analyze their data? My understanding is that a Bayesian analysis will actually tell you the probability that YOUR hypothesis is correct based on data. Are journals accepting of Bayesian stats? It seems like a Bayesian analysis would also address the questions of false positives/negatives quite effectively. – GPI Mar 12 '13 at 14:57
There is lots of bioinformatics work with bayesian statistics. Use of Bayes rule by itself is not free us from the need to estimate statistical power of the probabilities used in the analysis though... – shigeta Mar 13 '13 at 4:08
Of course reading BLAST e-values as p-values is wrong. e-values give the number of hits of this quality you would expect to find by chance, given the size of the hit and the size of the database (and the composition of the sequences in question, low complexity etc). They do not give the probability of finding such a hit. They are not even similar to p-values and should never be confused. – terdon Mar 13 '13 at 15:03
so you are saying they are never confused? they are probabilities even though they are not p values. I'm open to other examples that can be used, but couldn't come up with one while writing. – shigeta Mar 13 '13 at 15:43