
SIGNAL TO NOISE RATIOName:
where s is the sample standard deviation and \( \bar{x} \) is the sample mean. This is the reciprocal of the coefficient of variation:
That is, it shows the variability, as defined by the standard deviation, relative to the mean. This definition of signal to noise ratio should typically only be used for data measured on a ratio scale. That is, the data should be continuous and have a meaningful zero. Measurement data in the physical sciences and engineering are often on a ratio scale. As an example, temperatures measured on a Kelvin scale are on a ratio scale while temperaturs measured on a Celcius or Farenheit scale are interval scales rather than ratio scales. Given a set of temperature measurements, the signal to noise ratio on the Celcius scale will be different than the signal to noise ratio on the Farenheit scale. Note that this is only one specific definition of the signal to noise ratio. There are numerous other definitions in common usage that are not described here.
<SUBSET/EXCEPT/FOR qualification> where <y> is a response variable; <par> is a parameter where the signal to noise ratio value is saved; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
<SUBSET/EXCEPT/FOR qualification> where <y1> is the first response variable; <y2> is the second response variable; <par> is a parameter where the difference of the signal to noise ratios is saved; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET SNR = SIGNAL TO NOISE RATIO Y1 SUBSET TAG > 2
LET SNRDIFF = DIFFERENCE OF SIGNAL TO NOISE RATIO Y1 Y2
2017/03: Added DIFFERENCE OF SIGNAL TO NOISE . Step 1: Create the data . skip 25 read zarr13.dat y skip 0 set write decimals 6 . let snr = signal to noise ratio y let snr = round(snr,3) . . Step 2: Define plot control . title case asis title offset 2 label case asis . y1label Signal to Noise Ratio x1label Bootstrap Sample title Bootstrap of Signal to Noise Ratio for ZARR13.DAT . bootstrap samples 2000 bootstrap snr plot y . let bmean = round(bmean,3) let bsd = round(bsd,3) let b025 = round(b025,3) let b975 = round(b975,3) justification center move 50 6 text Sample SNR: ^snr, Mean of Bootstrap Samples: ^bmean, SD of Bootstrap Samples: ^bsd move 50 3.5 text 2.5 Percentile: ^B025, 97.5 Percentile: ^B975 Bootstrap Analysis for the SIGNAL TO NOISE RATIO Response Variable One: Y Number of Bootstrap Samples: 2000 Number of Observations: 195 Mean of Bootstrap Samples: 408.853631 Standard Deviation of Bootstrap Samples: 20.848402 Median of Bootstrap Samples: 408.357777 MAD of Bootstrap Samples: 13.975891 Minimum of Bootstrap Samples: 338.189159 Maximum of Bootstrap Samples: 495.148676 Percent Points of the Bootstrap Samples  Percent Point Value  0.1 = 343.651065 0.5 = 356.530068 1.0 = 359.826113 2.5 = 370.473897 5.0 = 375.194264 10.0 = 383.055240 20.0 = 391.574737 50.0 = 408.357777 80.0 = 426.735022 90.0 = 435.852705 95.0 = 444.095509 97.5 = 450.198916 99.0 = 457.431107 99.5 = 463.567638 99.9 = 491.749619 Percentile Confidence Interval for Statistic  Confidence Lower Upper Coefficient Limit Limit  50.00 394.902643 422.849973 75.00 385.428649 433.131995 90.00 375.194264 444.095509 95.00 370.473897 450.198916 99.00 356.530068 463.567638 99.90 338.191889 495.146977 Program 2: . Step 1: Create the data . skip 25 read gear.dat y x skip 0 set write decimals 6 . . Step 2: Define plot control . title case asis title offset 2 label case asis . y1label Signal to Noise Ratio x1label Group title Signal to Noise Ratio for GEAR.DAT let ngroup = unique x xlimits 1 ngroup major x1tic mark number ngroup minor x1tic mark number 0 tic mark offset units data x1tic mark offset 0.5 0.5 y1tic mark offset 5 0 . character X line blank . set statistic plot reference line average snr plot y x . tabulate snr y x Cross Tabulate SIGNAL TO NOISE RATIO (Response Variables: Y )  X  SIGNAL TO NOISE  1.000000  229.629318 2.000000  191.529564 3.000000  250.244129 4.000000  259.081016 5.000000  130.883795 6.000000  101.031588 7.000000  127.133680 8.000000  275.815765 9.000000  241.257602 10.000000  186.670894Program 3: SKIP 25 READ IRIS.DAT Y1 TO Y4 X . LET A = DIFFERENCE OF SNR Y1 Y2 SET WRITE DECIMALS 4 TABULATE DIFFERENCE OF SNR Y1 Y2 XCross Tabulate DIFFERENCE OF SNR (Response Variables: Y1 Y2 )  X  DIFFERENCE OF S  1.0000  5.1585 2.0000  2.6727 3.0000  1.1387. XTIC OFFSET 0.2 0.2 X1LABEL GROUP ID Y1LABEL DIFFERENCE OF SNR CHAR X LINE BLANK DIFFERENCE OF SNR PLOT Y1 Y2 X  
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Date created: 03/06/2017 