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Abstract

In theory, a comparison of two experimental effects requires a statistical test on their difference. In practice, this comparison is often based on an incorrect procedure involving two separate tests in which researchers conclude that effects differ when one effect is significant (P < 0.05) but the other is not (P > 0.05). We reviewed 513 behavioral, systems and cognitive neuroscience articles in five top-ranking journals (Science, Nature, Nature Neuroscience, Neuron and The Journal of Neuroscience) and found that 78 used the correct procedure and 79 used the incorrect procedure. An additional analysis suggests that incorrect analyses of interactions are even more common in cellular and molecular neuroscience. We discuss scenarios in which the erroneous procedure is particularly beguiling.

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Using confidence intervals in within-subject designs.

Geoffrey Loftus, Michael Masson (1994)

We argue that to best comprehend many data sets, plotting judiciously selected sample statistics with associated confidence intervals can usefully supplement, or even replace, standard hypothesis-testing procedures. We note that most social science statistics textbooks limit discussion of confidence intervals to their use in between-subject designs. Our central purpose in this article is to describe how to compute an analogous confidence interval that can be used in within-subject designs. This confidence interval rests on the reasoning that because between-subject variance typically plays no role in statistical analyses of within-subject designs, it can legitimately be ignored; hence, an appropriate confidence interval can be based on the standard within-subject error term-that is, on the variability due to the subject × condition interaction. Computation of such a confidence interval is simple and is embodied in Equation 2 on p. 482 of this article. This confidence interval has two useful properties. First, it is based on the same error term as is the corresponding analysis of variance, and hence leads to comparable conclusions. Second, it is related by a known factor (√2) to a confidence interval of the difference between sample means; accordingly, it can be used to infer the faith one can put in some pattern of sample means as a reflection of the underlying pattern of population means. These two properties correspond to analogous properties of the more widely used between-subject confidence interval.

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Error bars in experimental biology

Geoff Cumming, Fiona Fidler, David Vaux (2007)

Error bars commonly appear in figures in publications, but experimental biologists are often unsure how they should be used and interpreted. In this article we illustrate some basic features of error bars and explain how they can help communicate data and assist correct interpretation. Error bars may show confidence intervals, standard errors, standard deviations, or other quantities. Different types of error bars give quite different information, and so figure legends must make clear what error bars represent. We suggest eight simple rules to assist with effective use and interpretation of error bars.