6. Presentation and reporting of data

Presentation depends on the data collected and what the authors wants to emphasise. For example, to present the mean when one has done a non-parametric test is not meaningful, though a median is (consider using boxplots). The mean is a valid descriptive representation of the location parameter if the distribution is symmetric. The best way to summarise descriptively and represent graphically a given data set depends on both the empirical distribution of the data and the purpose of the statistics and graphs. There are excellent references on this topic such as those by Cleveland (1993) and Tufte (2001), whereas the classic book by Tukey (1977) has a decidedly statistical slant.

Standard error or Standard deviation - the latter is a measurement of the variability of the observed data around the mean; the former indicates uncertainty around a calculated mean.  We believe that the standard deviation is the better metric to convey characteristics of the data because the standard error, which is a function of sample size, can be made arbitrarily small by including more observations.

Presentation of data might be overlaid with statistics one has applied, such as regression lines or mean separation letters. If data were transformed for the analysis, data on the original scale should be presented, but any means fit from a statistical model back-transformed to the original scale (even though this will create curves in a “straight” line model, like a linear regression). Back-transformed confidence intervals on means should replace standard error bars.