Introduction to Biological Sciences lab, first semester

Fig. 13 Sample mean log reductions and 95% confidence intervals from Fig. 2 of Sickbert-Bennett et al. (2005)

The results from the first column of Fig. 12 are presented in graphical form in Fig. 13. The mean log reduction of each agent is graphed as the height of its column. The upper and lower 95% confidence intervals are shown as **error bars** that extend above and below the top of the mean column. These error bars serve the same purpose as the error bars in Figs. 9 - 11 of section 5.4.

It is important to note that in publications error bars do not always represent 95% confidence limits. It is also common for the error bars to represent plus or minus one standard error of the mean ("SE" or "SEM"). Because plus/minus one standard error is smaller than the 95% confidence interval, overlapping error bars indicate that means are not different. However, non-overlapping error bars may or may not be significantly different so some other means must be used to indicate differences. Often letters are used to indicate differing means by labeling significantly different groups with different letters (Fig. 14).

Fig. 2. *Desmanthus* seed production in relation to timing of vole access. Seed production continued to be lower where voles had continual and early-season access in 2003 even after being protected from vole herbivory in 2004. The number of seeds shown for each treatment is the mean of 2003 and 2004; bars represent standard error. Different letters indicate significant differences in access treatment means from repeated-measures ANOVA (Hotelling's *T*^{2}, *P* < 0.05).

Fig. 14 Mean seed production with error bars representing standard error of the mean from Fig. 2 of Sullivan and Howe (2009).

In some cases error bars represent +/- 2 SE and in a few cases where showing the variability of the data is important, error bars may also represent plus or minus one standard deviation. Because of the great variety of interpretations for error bars, it is extremely important to specify in the figure legend what the error bars actually represent.

To create a column chart of sample means having error bars based a statistical analysis, begin by following the instructions in Section 5.4.4 . To graph several sample means, place the data for each sample group in adjacent columns of the spreadsheet and select the block of columns during the Input Range selection step. When the descriptive statistics are generated, the labels for the statistical values will be repeated unnecessarily, so you can delete the labels that separate the columns of results.

Highlight the mean values in the row labeled "Mean". On the Insert ribbon, click on the Insert Column Chart. Select the Clustered Column option. Excel should create a column chart with a column for each sample mean. To label the columns, click on the funnel-shaped icon to the right of the chart. Click on the "Select data…" link at the bottom of the dialog box. Click on the Edit button under Horizontal (Category) Axis Labels. In the Axis Labels selection dialog box, click on the select button and select the column heading cells. Click OK, then OK again.

To further customize the chart, click on the + sign to the upper right of the chart. Deselect Chart Title. Select Axis Title and edit the labels appropriately. Check the Error Bars checkbox, then click on the triangle to the right of the option. Select "More Options…" Under "Error Amount", click the Custom radio button, then click on Specify Value. The Custom Error Bars dialog box will appear. The positive and negative error values are the amounts to be added to and subtracted from the means to specify the upper and lower limits. They are not the actual values of the limits themselves. Since these amounts are included under Confidence Level(95.0%) in the generated Summary Statistics table, you can simply select the cells in that row for both the Positive Error Value and Negative Error Value, then click OK to dismiss the dialog.

If you want the error bars to represent standard error of the mean or standard deviation, you can select cells in those rows rather than the 95% confidence levels.

Because the chart was created in a Microsoft Office product, you should be able to copy and paste it easily to either a Word or PowerPoint document. The default paste option is "Use Destination Theme & Link Data" which means that if you change the spreadsheet, the chart may change in your Word document. To prevent this, you can change the paste option to Picture. The chart will then be stable in your Word document, although it will also become uneditable.

Sickbert-Bennett, E.E., D.J. Weber, M.F. Gergen-Teague, M.D. Sobsey, G.P. Samsa, W.A. Rutala. 2005. Comparative efficacy of hand hygiene agents in the reduction of bacteria and viruses. American Journal of Infection Control 33:67-77. http://dx.doi.org/10.1016/j.ajic.2004.08.005

Sullivan, A.T. and H.F. Howe. 2009. Prairie forb response to timing of vole herbivory. Ecology 90:1346-1355. http://dx.doi.org/10.1890/08-0629.1