There are several problems here. The confidence interval is not represented explicitly; rather the upper bound of the confidence interval can be seen, but the lower bound is not shown. This style of graph commonly uses a minimum value of zero, as shown in the example here. This is essentially an arbitrary choice, as the value of zero need not be relevant in the context of the measurements taken.
But note the effect of setting the minimum to zero; it's potentially quite comforting. The error in this graph looks smaller than in the other graphs. This problem has a simple solution shown in the first graph but it is not used as often as it should be. Statistical Consulting Centre Graphs for statistical analysis Error bars on graphs. In the first graph, the length of the error bars is the standard deviation at each time point. This is the easiest graph to explain because the standard deviation is directly related to the data.
The standard deviation is a measure of the variation in the data. The main advantage of this graph is that a "standard deviation" is a term that is familiar to a lay audience.
The disadvantage is that the graph does not display the accuracy of the mean computation. For that, you need one of the other statistics. In the second graph, the length of the error bars is the standard error of the mean SEM.
This is harder to explain to a lay audience because it in an inferential statistic. A qualitative explanation is that the SEM shows the accuracy of the mean computation.
A quantitative explanation requires using advanced concepts such as "the sampling distribution of the statistic" and "repeating the experiment many times. Recall that the sampling distribution of the mean can be understood in terms of repeatedly drawing random samples from the population and computing the mean for each sample. The standard error is defined as the standard deviation of the distribution of the sample means.
The exact meaning of the SEM might be difficult to explain to a lay audience, but the qualitative explanation is often sufficient. This graph also displays the accuracy of the mean, but these intervals are about twice as long as the intervals for the SEM.
The confidence interval for the mean is hard to explain to a lay audience. There is no probability involved! The error bars convey the variation in the data and the accuracy of the mean estimate.
Which one you use depends on the sophistication of your audience and the message that you are trying to convey. My recommendation? Despite the fact that confidence intervals can be misinterpreted, I think that the CLM is the best choice for the size of the error bars the third graph. If I am presenting to a statistical audience, the audience understands the CLMs. For a less sophisticated audience, I do not dwell on the probabilistic interpretation of the CLM but merely say that the error bars "indicate the accuracy of the mean.
As explained previously, each choice has advantages and disadvantages. What choice do you make and why? The Data Visualisation Catalogue. Description Although not a chart outright, Error Bars function as a graphical enhancement that visualises the variability of the plotted data on a Cartesian graph. Functions Ranges. Error Bars can be applied to: Area Graph. Bar Chart. Line Graph.
Multi-set Bar Chart. Span Chart. Need to access this page offline?
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