# Data comparison graphs

Command: | Graphs Data comparison graphs |

## Description

Creates graphs for the comparison between 2 sets of data.

The graph can be composed from different elements: *Bars*, *Horizontal lines*, *Markers* and or *Connecting lines* for mean or median, with choice of different *error bars* for mean (95% CI, 1 SEM, 1 SD, 2 SD, 3 SD, range) or median (95% CI, 25-75 percentiles, 10-90 percentiles, 5-95 percentiles, 2.5-97.5 percentiles, 1-99 percentiles, range), *Box-and-whisker plot* or *Notched box-and-whisker plot*, *Violin plot*, and/or *Dot plot* (display all data).

## Required input

You can select the graph type in the dialog box that appears after you click **Data comparison graphs** on the Graphs menu:

Several elements can be selected to compose the graph, and some of these can be combined.

**Bars**,**Horizontal lines**,**Markers**and/or**Connecting lines**for*means*or*medians*.**Error bars**: the following error bars are available if at least one of the graph types*Bars*,*Horizontal lines*,*Markers*and/or*Connecting lines*is selected: If*mean*is selected: (none), or 95% CI for the mean, 1 SD, 2 SD, 3 SD, 1 SEM, and range.- Note that 2 SEM is not in this list: when the number of cases is large, mean ± 2 SEM corresponds to the 95% confidence interval (CI) for the mean. When the number of cases is small, then the 95% CI interval is calculated as mean ± t * SEM, where t is taken from a t-table with DF=n−1 and area A=95%) (see also SEM).
- Although 1 SEM gives the more narower error bar, this option is not recommended since the resulting error bar may be highly misleading, especially when the number of cases in the groups is different. Preferably the 95% CI for the mean is used for providing a valid graphical comparison of means (Pocock, 1984), or use 2 SD as an indication for the variability of the data.

*median*is selected: (none), or 95% CI for the median, 25-75 percentiles, 10-90 percentiles, 5-95 percentiles, 2.5-97.5 percentiles, 1-99 percentiles, and range- When the number of cases is small, it is possible that the 95% CI for the median is not defined and that it will not be displayed in the graph.
- When you use percentile ranges, take into account the number of observations: you need at least 100 observations for 1-99 percentiles, at least 20 for 5-95 percentiles, at least 10 for 10-90 percentile and at least 4 for 25-75
^{th}percentiles.

**Box-and-Whisker plot**(Tukey, 1977) or**Notched box-and-whisker plot**(McGill et al., 1978). A Notched box-and-whisker plot is a variation of the box-and-whisker plot in which confidence intervals for the medians are shown by means of notches surrounding the medians. If the notches about two medians do not overlap, the medians are significantly different at a ± 95% confidence level. For a detailed description of a Box-and-Whisker plot and Notched Box-and-Whisker plot, see Construction of a Box-and-Whisker plot.**Violin plot**. The violin plot (Hintze & Nelson, 1998) shows the density trace of the data. It is recommended to combine the violon plot with a box-and-whisker plot (select both options).- When you select
**Dots (plot all data**, all observations will be displayed in the graph.

The *box-and-whisker plot *in combination with *dot plot* has the advantage of displaying a statistical summary of the data (range, quartiles and median), without concealing the data.

If the data require a logarithmic transformation, select the Logarithmic transformation option.

## Examples

Dual box-and-whisker plot:

Notched box-and-whisker plots:

Combined box-and-whisker and dot plot:

## Literature

- Altman DG (1991) Practical statistics for medical research. London: Chapman and Hall.
- Hintze JL, Nelson RD (1998) Violin Plots: A Box Plot-Density Trace Synergism. The American Statistician 52:181-184.
- McGill R, Tukey JW, Larsen WA (1978) Variations of box plots. The American Statistician, 32, 12-16.
- Tukey JW (1977) Exploratory data analysis. Reading, Mass: Addison-Wesley Publishing Company.

## See also

## Recommended book

## Exploratory Data Analysis

John W. Tukey

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