## unbelievably small P values?

November 18, 2019 at 9:56 am |**sam**| literature, scientific integrity

Check out our newest preprint at arXiv:

If your P value looks too good to be true, it probably is: Communicating reproducibility and variability in cell biology

Lord, S. J.; Velle, K. B.; Mullins, R. D.; Fritz-Laylin, L. K.arXiv2019, 1911.03509. https://arxiv.org/abs/1911.03509

I’ve noticed a promising trend away from bar graphs in the cell biology literature. That’s great, because reporting simply the average and SD or SEM or an entire dataset conceals a lot of information. So it’s nice to see column scatter, beeswarm, violin, and other plots that show the distribution of the data.

But a concerning outcome of this trend is that, when authors decide to plot every measurement or every cell as a separate datapoint, it seems to trick people into thinking that each cell is an independent sample. Clearly, two cells in the same flask treated with a drug are not independent tests of whether the drug works: there are many reasons the cells in that particular flask might be different from those in other flasks. To really test a hypothesis that the drug influences the cells, one must repeat the drug treatment multiple times and check if the observed effect happens repeatably.

I scanned the latest issues of popular cell biology journals and found that over half the papers counted each cell as a separate *N* and calculated *P* values and SEM using that inflated count.

But that’s not to say the the variability cell-to-cell is unimportant! The fact that some cells in a flask react dramatically to a treatment and others carry on just fine might have very important implications in an actual body.

So we proposed “SuperPlots,” which superimpose sample-to-sample summary data on top of the cell-level distribution. This is a simple way to convey both variability of the underlying data and the repeatability of the experiment. It doesn’t really require any complicated plotting or programming skills. On the simplest level, you can simply paste two (or more!) plots in Illustrator and overlay them. Play around with colors and transparency to make it visually appealing, and you’re done! (We also give a tutorial on how we made the plots above in Graphpad Prism.)

Let me know what you think!

UPDATE: We simplified the figure:

Figure 1.Drastically different experimental outcomes can result in the same plots and statistics unless experiment-to-experiment variability is considered.(A)Problematic plots treat N as the number of cells, resulting in tiny error bars and P values. These plots also conceal any systematic run- to-run error, mixing it with cell-to-cell variability. To illustrate this, we simulated three different scenarios that all have identical underlying cell-level values but are clustered differently by experiment:(B)shows highly repeatable, unclustered data,(C)shows day-to-day variability, but a consistent trend in each experiment, and(D)is dominated by one random run. Note that the plots in (A) that treat each cell as its own N fail to distinguish the three scenarios, claiming a significant difference after drug treatment, even when the experiments are not actually repeatable. To correct that, “SuperPlots” superimpose summary statistics from biological replicates consisting of independent experiments on top of data from all cells, and P values were calculated using an N of three, not 300. In this case, the cell-level values were separately pooled for each biological replicate and the mean calculated for each pool; those three means were then used to calculate the average (horizontal bar), standard error of the mean (error bars), and P value. While the dot plots in the “OK” column ensure that the P values are calculated correctly, they still fail to convey the experiment-to-experiment differences. In the SuperPlots, each biological replicate is color-coded: the averages from one experimental run are yellow dots, another independent experiment is represented by gray triangles, and a third experiment is shown as blue squares. This helps convey whether the trend is observed within each experimental run, as well as for the dataset as a whole. The beeswarm SuperPlots in the rightmost column represent each cell with a dot that is color coded according to the biological replicate it came from. The P values represent an unpaired two-tailed t-test (A) and a paired two-tailed t-test for (B-D). For tutorials on making SuperPlots in Prism, R, Python, and Excel, see the supporting information.

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