Making the Error Bar Overlap Myth a Reality: Comparative Confidence Intervals

Many interpret error bars to mean that if they do not overlap the difference is statistically “significant”. This overlap rule is really an overlap myth; the rule does not hold true for any conventional type of error bar. There are rules of thumb for estimating P values, but it would be better to show error bars for which the overlap rule holds true. Here I explain how to calculate comparative confidence intervals which, when plotted as error bars, let us judge significance based on overlap or separation. Others have published on these intervals (the mathematical basis goes back to John Tukey) but here I advertise comparative confidence intervals in the hope that more people use them. Judging statistical “significance” by eye would be most useful when making multiple comparisons, so I show how comparative confidence intervals can be used to illustrate the results of Tukey test. I also explain how to use of comparative confidence intervals to illustrate the effects of multiple independent variables and explore the problems posed by heterogeneity of variance and repeated measures. When families of comparative confidence intervals are plotted around means, I show how box-and-whiskers plots make it easy to judge which intervals overlap with which. Comparative confidence intervals have the potential to be used in a wide variety of circumstances, so I describe an easy way to confirm the intervals’ validity. When sample means are being compared to each other, they should be plotted with error bars that indicate comparative confidence intervals, either along with or instead of conventional error bars

AN EXAMINATION OF SELECTIVE FEEDING AND MOLECULAR RECOGNITION IN THE CILIATE, TETRAHYMENA PYRIFORMIS Ehrenberg, 1830

In amoeboid cells, food particles are engulfed only after receptors on the phagocytic cell’s membrane bind to ligands on a particle’s surface. Ciliates also feed via phagocytosis, but instead of enveloping particles the way amoebae do, ciliates take up particles through a complex, permanent, funnel-shaped feeding apparatus. It is unclear whether receptor-ligand interactions are needed to trigger the process. If ciliates were shown to prefer certain particles over others, based on the particles’ surface properties, then receptor-ligand interactions would likely play a role in phagocytosis. The literature includes few reports of such selectivity in ciliates. To further investigate this issue, we chose to study feeding selectivity in the ciliate Tetrahymena pyriformis Ehrenberg, 1830. We fed Tetrahymena mixtures of orange and green fluorescent, 3 μm, latex beads at two concentrations in which one type of bead was coated with bovine serum albumin through passive adsorption (BSA; 8–13 μg protein/mg beads). Authors were unaware of which beads were coated while collecting data. Treatment groups included the results of 12–16 trials. We found no evidence of a preference for either coated or uncoated beads at either concentration (coated vs. not coated, P = 0.131; bead concentration, P = 0.866; interaction, P = 0.294). In contrast, others have reported that T. pyriformis feeds more rapidly on BSA-coated beads than uncoated ones. We also found no trend toward the development of a preference as cells acquired more beads over time. The literature indicates that two species of nanoflagellates develop such a preference. Although we cannot rule out the possibility that Tetrahymena feeds selectively, we did not find convincing evidence of such selectivity when T. pyriformis is given a choice between uncoated beads and those coated with BSA. Our results failed to demonstrate a role for molecular recognition when Tetrahymena engages in phagocytosis