13. Presenting your results
NB. This section should be read in association with section 14 on Guidelines
The aim of your scientific paper or report is to communicate your results as clearly and concisely as possible.
Sufficient information should be provided to enable somebody else to repeat the experiments The ARRIVE and GSP guidelines, given in the next section can be used as a checklist to ensure that nothing has been forgotten.
This section gives some general advice on the presentation of the numerical results.
Means, Medians and standard deviations should normally be given to no more than three significant digits, e.g. 13.3, 0.0124.
Standard deviation, Standard Error or Confidence interval?
When medians are being quoted, the 25 and 75% centiles can be given.
Where means are tabulated, they should be shown in columns rather than rows as this makes it easier to compare them.
If the means have been compared using an analysis of variance, then the assumption will have been made (and tested using residuals plots) that the variation is the same in each group. In this case a pooled standard deviation could be quoted rather than showing separate SDs for each mean.
When an analysis of variance has been used to analyse the results, and F-value should be quoted with numerator and denominator degrees of freedom, as well as a p-value (e.g. F3, 9 = 3.91, p= 0.049).
These should be clear and easy to read
Plots should be simple, informative and easy to read. Bar plots are used extensively and when properly used can be useful.
However, it is debatable whether the one shown on the right is of any value. About all it shows is that in one group there is some product which can just about be measured and in the other group there is more (about 450 pmol). The error bars are minute and can hardly be seen against the black background.
The bar diagram on the left has error bars against a gray background so that they can easily be seen.
One standard error from the mean
If error bars which are +/- one standard error are used then any two means where the bars overlap are not significantly different at whatever probability level has been chosen, but if they don’t overlap that does not mean that they are significantly different
Two standard errors from the mean
If error bars two standard errors either side of the mean are used, then if they don’t overlap the differences are significantly different, but if they do overlap they may still be significantly different.
Error bars are the least significant difference (used in the bar chart above left)
If error bars are used which are the least significant difference (LSD) among means, then if they don’t overlap the differences are significantly different at the chosen level and if they do overlap they are not significantly different. So this would be the most informative of the three choices. The LSD for a 5% significance level and “df” degrees of freedom is shown here, using the pooled SD estimated from the error mean square in an ANOVA.
A couple of alternatives to the bar plot, which are more informative are the “stripchart” and the box and whisker plot.
The strip chart shown on the left shows individual points and the mean with error bars, in this case +/- one standard error either side of the mean. The box and whisker plot has a bar at the median, a box enclosing the inter-quartile range and whiskers showing the range with obvious outliers shown as a single point. Either of these plots could be used instead of a bar plot, and both would be more informative.
Use plots which are appropriate
The plot on the left claims to be a dose-response curve for the effect of an agent on activity. However all the authors have done is test whether the activity at the higher doses differ from the lower doses, and the values are not equally spaced. The plot on the right shows a straight line fit to the data, 95% confidence intervals for the mean (inner dotted lines) at each dose and 95% prediction intervals (outer dotted lines) and the estimated dose-response relationship, which is more informative.