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.

Decimal places

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?

  • A standard deviation (SD) is used to describe individual variability.
  • A standard error (SE or better SEM) is used to describe the variability of means.
  • A confidence interval (CI) is used to indicate the range within which we can be reasonably sure the true mean lies.
  • In all three cases it is important to know the numbers in each group.
  • Rather than using a ± it is better to use a designation such as “Mean = 10.1 (SD 1.5, n=8)” or “Mean = 10.1 (SE 1.5, n=8)” so that there can be no confusion between standard error and standard deviation.
  • When two means are being compared, the size of the difference between them should be quoted, with a confidence interval.
  • The difference could also be expressed as the Standardised Effect Size, SES (The difference divided by the pooled SD). However this is biased upwards if “n” is very low (say less than 10).  The SES measures the response in standard deviation units and can be used to compare different characters.

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).

Tables

These should be clear and easy to read

  • Heading and footnotes should clearly indicate  content without having to read text
  • Where summary statistics are presented “n”, the means/medians and some measure of reliability should be given
  • Where possible numbers to be compared should be in the same column
  • Consider whether a plot show the results more effectively?

Graphical methods

Plots should be simple, informative and easy to read. Bar plots are used extensively and when properly used can be useful.

plot8However, 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.

 

Error bars

plot3

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.   plot9 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.

plot1plot2

 

 

 

 

 

 

 

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

plot4plot5

 

 

 

 

 

 

 

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.

 

Home
Top