This is harder to explain to a lay audience because it in an inferential statistic.Ī qualitative explanation is that the SEM shows the accuracy of the mean computation. In the second graph, the length of the error bars is the standard error of the mean (SEM). Use the standard error for the error bars For that, you need one of the other statistics. The disadvantage is that the graph does not display the accuracy of the mean computation. The main advantage of this graph is that a "standard deviation" is a term that is familiar to a lay audience. If the data at each time point are normally distributed, then (1) about 64% of the data have values within the extent of the error bars, and (2) almost all the data lie within three times the extent of the error bars. The standard deviation is a measure of the variation in the data. This is the easiest graph to explain because the standard deviation is directly related to the data. In the first graph, the length of the error bars is the standard deviation at each time point. Use the standard deviations for the error bars %PlotMeanAndVariation (limitstat=CLM, label= Mean and CLM ) %PlotMeanAndVariation (limitstat= STDERR, label= Mean +/- SEM ) %PlotMeanAndVariation (limitstat=STDDEV, label= Mean +/- Std Dev ) Yaxis label= "&label" values= ( 75 to 82 ) grid Vline t / response=y stat= mean limitstat= &limitstat markers Title "VLINE Statement: LIMITSTAT = &limitstat" %macro PlotMeanAndVariation (limitstat=, label= ) The following statements create the three line plots with error bars: Several interpretations use the 68-95-99.7 rule for normally distributed data. Let's plot all three options for the error bars on the same scale, then discuss how to interpret each graph. Visualize and interpret the choices of error bars The SD, SEM, and CLMWidth columns are the lengths of the error bars when you use the STDDEV, STDERR, and CLM options (respectively) to the LIMITSTAT= option on the VLINE statement in PROC SGPLOT. ![]() ![]() (The multiplier depends on N For these data, it ranges from 2.03 to 2.06.)Īs shown in the next section, the values in The CLMWidth value is a little more than twice the SEM value. The table shows the standard deviation (SD) and the sample size (N) for each time point. Output out=MeanOut N= N stderr=SEM stddev=SD lclm=LCLM uclm=UCLM ĬLMWidth = (UCLM-LCLM )/ 2 /* half-width of CLM interval */ run * Optional: Compute SD, SEM, and half-width of CLM (not needed for plotting) */ proc means data=Sim noprint You can use PROC MEANS and a short DATA step to display the relevant statistics that show how these three statistics are related: Then the multiplier is a quantile of the t distribution with N-1 degrees of freedom, often denoted by t* 1-α/2, N-1. In general, suppose the significance level is α and you are interested in 100(1-α)% confidence limits. For large samples, the multiple for a 95% confidence interval is approximately 1.96. The width of CLM is a multiple of the SEM. ![]() That is, the standard error of the mean is the standard deviation divided by the square root of the sample size. The SEM and width of the CLM are multiples of the standard deviation, where the multiplier depends on the sample size: These statistics are all based on the sample standard deviation (SD). Relationships between sample standard deviation, SEM, and CLMīefore I show how to plot and interpret the various error bars, I want to review the relationships between the sample standard deviation, the standard error of the mean (SEM), and the (half) width of the confidence interval for the mean (CLM). But what statistic should you use for the heights of the error bars? What is the best way to show the variation in the response variable? A simpler display is a plot of the mean for each time point and error bars that indicate the variation in the data. A line connects the means of the responses at each time point.Ī box plot might not be appropriate if your audience is not statistically savvy. The boxes use the interquartile range and whiskers to indicate the spread of the data. The box plot shows the schematic distribution of the data at each time point. Y = rand ( "Normal", mu, sigma ) /* Y ~ N(mu, sigma) */ output Array mu _temporary_ ( 80 78 78 79 ) /* mean */ array sigma _temporary_ ( 1 2 2 3 ) /* std dev */ array N _temporary_ ( 36 32 28 25 ) /* sample size */ call streaminit ( 12345 )
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