Standard Deviation vs Standard Error in Scatter Dot Plot

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When make a Scatter Dot Plot together with mean values and Standard Deviation it looks fine. However, if I change to Standard Error the error bars actualy become much smaller than the true Standard Error. Is this a bug or am I doing something wrong. I enclose an illustration of the problem. The data in wave A6 has a Mean Value of 1.485, a Standard Deviation of 0.447 and a Standard Error of 0.075. The Mean Values and Standard Deviation are shown correctly in the left graph but the right graph indicates a Standard Error of 0.0128 (measured with Show Info) rather than 0.075.
Standard deviation is simply the standard deviation of your raw data. The Standard Error is more properly called Standard Error of the Mean; it is stdev/(N-1) where N is the number of data points. If your data follow nice Gaussian statistics, it is an estimate of how well you know the "true" mean value of the supposed underlying distribution from which your data were drawn.

John Weeks
WaveMetrics, Inc.
support@wavemetrics.com

October 18, 2017 at 10:06 am - Permalink
Hi Erik,

I think that's a bug. I use scatter dot plot a lot but I always use s.d. for the error bars, but I can reproduce what you see in IP7.05 on macOS.

John, s.e.m. is stdev/sqrt(n). But even so, the standard error calculated by the scatter dot plot package is out.


•make/o/n=20 dd=10+gnoise(1)
•wavestats dd
  V_npnts= 20; V_numNaNs= 0; V_numINFs= 0; V_avg= 10.2673; 
  V_Sum= 205.346; V_sdev= 1.08918; V_sem= 0.243549; V_rms= 10.322; 
  V_adev= 0.82628; V_skew= -0.0352432; V_kurt= -0.77727; 
  V_minloc= 15; V_maxloc= 12; V_min= 8.30005; V_max= 12.1819; 
  V_minRowLoc= 15; V_maxRowLoc= 12; V_startRow= 0; V_endRow= 19;
// make a scatter dot plot using the GUI
// print the magnitude of error plotted by the package
•print root:Packages:WMScatterDotPlot:Graph0:counts_ddSy[2]-root:Packages:WMScatterDotPlot:Graph0:counts_ddSy[3]
  0.0573254

October 18, 2017 at 12:17 pm - Permalink
Sure enough- the author of the Scatter Dot Plot package made the same mistake I did. I have corrected the error, and attached a fixed procedure file. You will find the procedure file in Igor Pro Folder:WaveMetrics Procedures:Graphing: Simply replace that copy with the one attached.

John Weeks
WaveMetrics, Inc.
support@wavemetrics.com
Scatter Dot Plot.ipf.zip (18.23 KB)

October 18, 2017 at 12:54 pm - Permalink