To better understand the display of our data,
we should add error bars to our repeated measures bar chart. The top of the bar in a bar chart
represents the mean,
but we know that the mean is an estimate,
and it's likely to be off by a little or maybe a lot. I has some error built in.
Now the error bar looks like a little I beam that sticks out from the main bar, and
it measures how much error is around the mean, and that tells us how reliably the mean
represents the rest of our data.
So let's figure out what's going on with those little things
sticking out of the bar.
The top of that big yellow bar usually
represents the mean score for that variable. Now the mean is the best estimate, the most representative score.
The mean is very precise, but we cannot be confident that it is exactly right. In fact,
we're pretty sure that it will always be off a little, and
we need to know how much.
Error bars help clarify the accuracy of the mean by showing an error estimate.
We balanced precision with confidence when scores and our variable are similar to each other. The mean
represents the other scores very well.
A mean with a small error bar tells us that the mean is a very accurate predictor.
The smaller the error bar, the better the estimate of the mean.
Large error bars indicate
unreliable measurements. In this cartoon, the value with the large error bar is being told "Sorry,
we just can't trust you," because his mean estimate is so unreliable.
We have three options in SPSS for what estimate the error bars display.
A 95% confidence interval.
The error bars show the range of scores for the mean, and we are very confident, 95%, that the
real mean is within that range.
The error bar could also display the standard deviation for that variable, the average amount of variability in the data.
An error bar could also show the standard error of the mean. All of these options are available in the element properties
dialog box.
Continuing with our previous example,
we will recreate the same bar chart, this time adding error bars that show the 95% confidence interval.
The 95% confidence interval is a range of possible mean values that will contain the true mean
95%t of the time. It is not as precise as an individual single mean,
but the range of scores is more accurate in that it is much more likely to contain the true mean.
We are still using the data set Clickers.sav.
Go to Graphs > Chart Builder
You notice that the settings from the previous bar chart are still in place.
Don't change anything. Let's just look at the element properties window
You'll notice here that the statistic being represented by the yellow bar is the mean.
If you do not see the mean you can change it here.
But when the mean is selected, then there will be an option for "Display error bars" Click that box.
By default the confidence interval is set to 95%.
Make sure that the bar style is set to bar and
feel free to play around with other settings to see how they change the appearance of the graph. When you're ready, click Apply and then
click OK.
The resulting bar chart looks just like the first one, except now we see the error bars have been added.
Now look at that, error bar for Round 1. It is much larger than for Round 2 or 3.
That means that there is much more variability around that mean.
Combined with the taller bar for Round 1,
I suspect we might have some outliers in Round 1. They are artificially inflating the mean and
also increasing the variability, or error, around the mean. We should look more closely at Round 1 using a histogram.