Graphing Data - How To Calculate Error Bars

When turning numerical data into graphical form (e.g. bar graphs), you sometimes find that the data is much easier to interpret when changes observed in test conditions are presented as fold changes relative to the control, which is set to “1”. In doing this, you might wonder how you would go about calculating the error bars. In the following, I will detail how I go about calculating error bars for relative fold changes:

Below is an example data set with three control and three experimental replicates:

C1. 3.55

C2. 3.82

C3. 3.13

E1. 5.21

E2. 6.74

E3. 5.68

Take the average and you will have:

à C-AVG=3.50     E-AVG=5.88

Next, calculate the relative fold change by dividing by the control average:

à C-AVG=3.50/3.50   E-AVG=5.88/3.50  à  C-RelAVG=1   E-RelAVG=1.68

For the error bars, calculate the SEM:

C-SEM=0.20   E-SEM=0.45

Next calculate the SEM for the relative fold change values by dividing the SEMs with the control average:

à C-SEM=0.20/3.50            E-SEM=0.45/3.50  à  C-RelSEM=0.06   E-RelSEM=0.13

Below is an illustration of the data presented without setting the data relative to the control:

  

Here is the data set relative to the control: