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Dataplot Vol 2 Vol 1

SIGNAL TO NOISE RATIO

Name:
    SIGNAL TO NOISE RATIO (LET)
Type:
    Let Subcommand
Purpose:
    Compute the signal to noise ratio of a variable.
Description:
    The sample signal to noise ratio (SNR) is defined as the ratio of the mean to the standard deviation:

      \( \mbox{SNR} = \frac{\bar{x}}{s} \)

    where s is the sample standard deviation and \( \bar{x} \) is the sample mean.

    This is the reciprocal of the coefficient of variation:

      \( \mbox{cv} = \frac{s}{\bar{x}} \)

    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.

Syntax 1:
    LET <par> = SIGNAL TO NOISE RATIO <y>
                            <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.
Syntax 2:
    LET <par> = SIGNAL TO NOISE RATIO <y1> <y2>
                            <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.
Examples:
    LET SNR = SIGNAL TO NOISE RATIO Y1
    LET SNR = SIGNAL TO NOISE RATIO Y1 SUBSET TAG > 2

    LET SNRDIFF = DIFFERENCE OF SIGNAL TO NOISE RATIO Y1 Y2

Note:
    Dataplot statistics can be used in a number of commands. For details, enter

Default:
    None
Synonyms:
    SNR is a synonym for SIGNAL TO NOISE
Related Commands: Applications:
    Data Analysis
Implementation Date:
    2017/01
    2017/03: Added DIFFERENCE OF SIGNAL TO NOISE
Program 1:
     
    . 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
        
    plot generated by sample program
                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
        
    plot generated by sample program
                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   |        186.670894
        
Program 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 X
    
    
                Cross 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

    plot generated by sample program

    CHAR X ALL LINE BLANK ALL BOOTSTRAP DIFFERENCE OF SNR PLOT Y1 Y2 X plot generated by sample program

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Date created: 03/06/2017
Last updated: 06/30/2017

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