How to Check for Significance by Adding Error Bars

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When you conduct a scientific experiment, the mean of the random sample that you include in

your experiment could still be different from the mean of the entire population. For instance, if

you measured the height of seven randomly-chosen California sagebrush seedlings, the mean

height for those seven seedlings is likely to be different than the mean height for the entire

population of California sagebrush seedlings. If the results of an experiment are statistically

significant, this means that you are very sure that the difference between two treatments is

real. If the results are not statistically significant, it means that you can’t be sure that your

results aren’t because of random chance.

A confidence interval shows you the range of numbers that the true mean for the entire

population is likely to be between. You can use confidence intervals to determine if your

results are likely to be statistically significant. In ecological research, scientists typically use a

95% confidence interval. This means that the range of numbers inside the confidence interval

will include the true mean for 95% of experiments.

You can use error bars to show the confidence interval of a data set visually on a graph. (Error

bars can also be used to show other ranges, like standard deviation.)

The function to calculate confidence intervals in google sheets is =CONFIDENCE( alpha, STDEV,

popsize). So to calculate the confidence interval (which you will use to create error bars on

your graph), first you will need to determine the alpha, standard deviation, and population size.

CALCULATING THE CONFIDENCE INTERVAL

Step 1: Set up your table.

First, you’ll want to set up the columns and rows in Google Sheets so that it is ready for you to

enter data. Next to the cells where you calculated the average for each plot, label the next four

columns so that they read Alpha, Standard Deviation, Population Size, and Confidence.

Your table should look like this:

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Step 2: Decide on the Alpha

The alpha is the certainty of the interval. If you want a 95% confidence interval (which is

standard for most ecological research projects), the alpha is 0.05.

Type in the alpha value in the column on your Google Sheet labeled “Alpha.”

Step 3: Calculate the Standard Deviation

You will also need to calculate the standard deviation for each of the two treatments. The

standard deviation describes how your data is distributed (i.e., how much each data point is

different from the mean.) To calculate the standard deviation, you can use the function

=STDEV(). Type =STDEV(, then select all of the cells that you want to include. Finally, type ) to

close the formula.

Step 4: Determine the Population size

This is the number of plots included in your sample. If you have soil moisture readings for

seven different plots included in your sample, the population size is 7.

Make sure to enter this into your table as well!

Highlight the cells

that include all of

the data for one

treatment.

This is what the

formula will look

like!

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Step 5: Calculate the Confidence Interval

Finally, you can calculate the confidence interval, using the formula =CONFIDENCE(Alpha,

STDEV, popsize).

For our Adult Shrub example below, the alpha is 0.05, the standard deviation is 4.073, and the

population size is 7. This means the formula would be =CONFIDENCE(0.05,4.073,7).

Now that you have calculated the confidence interval for each of your treatment types, you can

use it to add error bars to your graph! This will allow you to see if the confidence interval for

the different samples overlap, or if there is likely to be a true difference between the two

populations.

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ADDING ERROR BARS TO YOUR BAR GRAPH

Once you’ve calculated the confidence interval for each of the two treatments, then you will

need to create a bar graph again! However, you will be doing a couple of things differently this

time so that you can add error bars for each treatment.

1. First, highlight the cells with the averages.

2. Next, click on the Insert menu at the top of the browser, and then select Chart to create a

graph.

3. Make sure that your graph is a bar graph. If it is the wrong type of graph, in the chart

editor’s Data menu, select the Column Chart option to change to a bar graph.

Step 1: Highlight the

labels and the

averages to use in

creating your graph.

Step 2: Select

Chart from the

Insert menu.

This is the Data

menu.

Under Chart

Type, select

Column Chart.

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4. Just like last time, you will probably have to adjust the scale on the vertical axis (or y-axis) of

your bar graph. In the chart editor, click on Customize menu at the top, and then click on

Vertical Axis. Make sure the minimum value for the axis is set at zero.

5. In the chart editor, click on the Data menu again at the top. Select the option that says

Switch rows/columns. This will make both of the data sets in the graph independent, so

that the two bars show up in different colors: blue and red.

First, select the

Customize menu.

Under the

Vertical Axis

menu, make sure

the Min value is

set to zero (0).

Next, click on

Vertical Axis.

Click on the Data

menu again to

switch back over

to the Data

menu.

Select the box for

Switch rows /

columns. This

will change your

bar graph so that

the two bars are

different colors.

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6. Next, switch back to the Customize menu, and select the Series sub-menu. (You can also

double-click on the blue bar to open the Series sub-menu.)

7. Select the Error Bar option. This will add an error bar to the left bar in your graph. But you

will still need to adjust it to make sure that the confidence interval is correct!

Step 6: Click on

the Customize

menu again, and

then select the

Series sub-menu.

Step 7: Click on

the box to create

an Error bar for

your first

treatment. (In this

case, it is the

Adult Shrub

treatment.)

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8. You’ll need to make sure that the graph is using the correct confidence interval for that

particular data set. Under Type, select Constant. Under Value, enter the confidence

interval for that data set. (In this case for our Adult Shrub treatment, the confidence

interval that we calculated earlier was 3.017.)

9. Finally, under Apply to, switch to No Adult shrub. Repeat steps 6-7 to add an error bar to

the second bar. When you add the value this time, make sure to use the confidence

interval for your No Adult Shrub data set. (In our example, this confidence interval is 1.82.)

This was the

confidence

interval that you

calculated for the

Adult Shrub

treatment.

Click on Type,

and then select

Constant.

Enter the

confidence

interval here

under Value.

Switch over to

the second

treatment under

Apply to.

Just like last time, click

on Type, and then select

Constant.

Then enter the

confidence interval for

the second treatment

under Value.

This is the confidence

interval that you calculated

for the second No Adult

shrub treatment.

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USING ERROR BARS TO DETERMINE IF YOUR FINDINGS ARE LIKELY TO BE SIGNIFICANT

If your error bars don’t overlap at all, then you can claim that your findings are likely to be

highly significant, with a 95% confidence interval.

If the error bars overlap less than 25%, then you can claim that your findings are likely to be

significant, with a 95% confidence interval.

If the error bars overlap more than 25%, then you would say that your findings do not appear

to be significant. This might be because there is no real difference between the populations. It

could also be because your sample size is very small. Since you are only analyzing the data from

seven plots in each treatment, it may be difficult to get significant results.

If you encounter an overlap, you are welcome to contact Crystal Cove Conservancy, and we can

send you the full data set with all 70 plots to analyze. Including more replicates and more data

points may make it more likely that you will get significant results.

If the error bars look close and you can’t tell if they overlap less than 25% or not, please feel

free to reach out to us as well! There are other more complicated statistical analyses that we

can run to determine if your results are statistically significant or not.

The error bars are

overlapping more

than 25% here.

The error bars here

are not overlapping at

all!