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Dataplot Vol 2 Vol 1

HEDGES G

Name:
    HEDGES G (LET)
    BIAS CORRECTED HEDGES G (LET)
    COHENS D (LET)
    GLASS G (LET)
Type:
    Let Subcommand
Purpose:
    Compute the Hedge's g (or the bias corrected Hedge's g) statistic for two response variables.
Description:
    The Hedge's g statistic is used to measure the effect size for the difference between means. The formula is

      \( g = \frac{\bar{y}_{1} - \bar{y}_{2}} {s_{p}} \)

    with \( \bar{y}_{1} \), \( \bar{y}_{2} \), and \( s_{p} \) denoting the mean of sample 1, the mean of sample 2, and the pooled standard deviation, respectively.

    The formula for the pooled standard deviation is

      \( s_{p} = \sqrt{\frac{(n_{1} - 1) s_{1}^{2} + (n_{2} - 1) s_{2}^{2}} {(n_{1} - 1) + (n_{2} - 1)}} \)

    with \( s_{1} \) and \( n_{1} \) denoting the standard deviation and number of observations for sample 1, respectively, and \( s_{2} \) and \( n_{2} \) denoting the standard deviation and number of observations for sample 2, respectively.

    The Hedge's g statistic expresses the difference of the means in units of the pooled standard deviation.

    For small samples, the following bias correction is recommended

      \( \frac{n-3}{n-2.25} \sqrt{\frac{n-2}{n}} \)

    where \( n = n_{1} + n_{2} \). This bias correction is typically recommended when n < 50.

    Hedge's g is similar to the Cohen's d statistic and the Glass g statistic. The difference is what is used for the estimate of the pooled standard deviation. The Hedge's g uses a sample size weighted pooled standard deviation while Cohen's d uses

      \( s_{p} = \sqrt{\frac{s_{1}^{2} + s_{2}^{2}} {2}} \)

    These statistic are typically used to compare an experimental sample to a control sample. The Glass g statistic uses the standard deviation of the control sample rather than the pooled standard deviation. His argument for this is that experimental samples with very different standard deviations can result in significant differences in the g statistic for equivalent differences in the mean. So the Glass g statistic measures the difference in means in units of the control sample standard deviation.

    Hedge's g, Cohen's d, and Glass's g are interpreted in the same way. Cohen recommended the following rule of thumb

      0.2 => small effect
      0.5 => medium effect
      0.8 => large effect

    However, Cohen did suggest caution for this rule of thumb as the meaning of small, medium and large may vary depending on the context of a particular study.

    The Hedge's g statistic is generally preferred to Cohen's d statistic. It has better small sample properties and has better propoerties when the sample sizes are signigicantly different. For large samples where \( n_{1} \) and \( n_{2} \) are similar, the two statistics should be almost the same. The Glass g statistic may be preferred when the standard deviations are quite different.

    In many cases, there are multiple experimental groups being compared to the control. This could be either a separate control sample for each experiment (e.g., we are comparing effect sizes from different experiments) or a common control (e.g., different laboratories are measuring identical material and are being compared to a reference measurement). In these cases, you can compute the Hedge's g (or Glass's g or Cohen's d) for each experiment relative to its control group. You can then obtain an "overall" value of the statistic by averaging these individual statistics.

Syntax 1:
    LET <par> = HEDGES G <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 computed Hedge's g statistic is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    This syntax computes Hedge's g statistic without the bias correction.

Syntax 2:
    LET <par> = BIAS CORRECTED HEDGES G <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 computed bias corrected Hedge's g statistic is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    This syntax computes the Hedge's g statistic with the bias correction.

Syntax 3:
    LET <par> = GLASS G <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 computed Glass's g statistic is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    This syntax computes Glass's g statistic.

    The <y2> variable will be treated as the "control" sample. That is, the standard deviation of <y2> will be used as the pooled standard deviation.

Syntax 4:
    LET <par> = COHEN D <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 computed Cohen's d statistic is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    This syntax computes Cohen's d statistic.

Examples:
    LET A = HEDGES G Y1 Y2
    LET A = BIAS CORRECTED HEDGES G Y1 Y2
    LET A = BIAS CORRECTED HEDGES G Y1 Y2 SUBSET Y1 > 0
    LET A = GLASS G Y1 Y2
    LET A = COHENS D Y1 Y2
Note:
    This statistic can be used in a large number of plots and commands. For details, enter

Default:
    None
Synonyms:
    None
Related Commands: Applications:
    Data Analysis
Implementation Date:
    2017/07
Program:
     
    SKIP 25
    READ IRIS.DAT Y1 TO Y4 X
    .
    LET A = HEDGES G Y1 Y2
    TABULATE HEDGES G Y1 Y2 X
    .
    LABEL CASE ASIS
    TITLE CASE ASIS
    Y1LABEL Hedge's G Statistic
    X1LABEL Group
    TITLE Hedge's G Statistic for IRIS.DAT
    X1TIC MARK OFFSET 0.5 0.5
    TIC MARK OFFSET UNITS DATA
    CHAR X
    LINE BLANK
    HEDGES G PLOT Y1 Y2 X
    .
    Y1LABEL Hedge's G Statistic
    X1LABEL Group
    TITLE Bootstrap of Hedge's G Statistic for IRIS.DAT
    CHAR X ALL
    LINE BLANK ALL
    BOOTSTRAP SAMPLES 1000
    BOOTSTRAP HEDGES G PLOT Y1 Y2 X 
        
    The following output is generated
                Cross Tabulate HEDGES G
     
    (Response Variables: Y1       Y2      )
    ---------------------------------------------
           X          |          HEDGES G
    ---------------------------------------------
      0.1000000E+01   |     0.4311260E+01
      0.2000000E+01   |     0.7412040E+01
      0.3000000E+01   |     0.7168413E+01
        
    plot generated by sample program
                Bootstrap Analysis for the HEDGES G
     
    Response Variable One: Y1
    Response Variable Two: Y2
    Group ID Variable One (X       ):          1.000000
     
    Number of Bootstrap Samples:             1000
    Number of Observations:                  50
    Mean of Bootstrap Samples:                 4.389604
    Standard Deviation of Bootstrap Samples:  0.4288846
    Median of Bootstrap Samples:               4.335823
    MAD of Bootstrap Samples:                 0.2615915
    Minimum of Bootstrap Samples:              3.342993
    Maximum of Bootstrap Samples:              6.389001
     
     
     
    Percent Points of the Bootstrap Samples
    -----------------------------------
      Percent Point               Value
    -----------------------------------
                0.1    =   3.343002
                0.5    =   3.511410
                1.0    =   3.546756
                2.5    =   3.687836
                5.0    =   3.798257
               10.0    =   3.910058
               20.0    =   4.037920
               50.0    =   4.335823
               80.0    =   4.705708
               90.0    =   4.947669
               95.0    =   5.174219
               97.5    =   5.409715
               99.0    =   5.681841
               99.5    =   5.823756
               99.9    =   6.388623
     
     
                Percentile Confidence Interval for Statistic
     
    ------------------------------------------
      Confidence          Lower          Upper
     Coefficient          Limit          Limit
    ------------------------------------------
           50.00   4.087805       4.619201
           75.00   3.934208       4.869211
           90.00   3.798257       5.174219
           95.00   3.687836       5.409715
           99.00   3.511410       5.823756
           99.90   3.342993       6.389001
    ------------------------------------------
     
     
    Response Variable One: Y1
    Response Variable Two: Y2
    Group ID Variable One (X       ):          2.000000
     
    Number of Bootstrap Samples:             1000
    Number of Observations:                  50
    Mean of Bootstrap Samples:                 7.537408
    Standard Deviation of Bootstrap Samples:  0.5465833
    Median of Bootstrap Samples:               7.499111
    MAD of Bootstrap Samples:                 0.3508403
    Minimum of Bootstrap Samples:              6.092766
    Maximum of Bootstrap Samples:              9.751977
     
     
     
    Percent Points of the Bootstrap Samples
    -----------------------------------
      Percent Point               Value
    -----------------------------------
                0.1    =   6.092945
                0.5    =   6.287894
                1.0    =   6.397113
                2.5    =   6.541644
                5.0    =   6.668351
               10.0    =   6.842498
               20.0    =   7.102805
               50.0    =   7.499111
               80.0    =   7.976231
               90.0    =   8.257037
               95.0    =   8.490531
               97.5    =   8.726730
               99.0    =   8.898412
               99.5    =   9.116481
               99.9    =   9.751736
     
     
                Percentile Confidence Interval for Statistic
     
    ------------------------------------------
      Confidence          Lower          Upper
     Coefficient          Limit          Limit
    ------------------------------------------
           50.00   7.171687       7.894311
           75.00   6.920084       8.177537
           90.00   6.668351       8.490531
           95.00   6.541644       8.726730
           99.00   6.287894       9.116481
           99.90   6.092766       9.751977
    ------------------------------------------
     
     
    Response Variable One: Y1
    Response Variable Two: Y2
    Group ID Variable One (X       ):          3.000000
     
    Number of Bootstrap Samples:             1000
    Number of Observations:                  50
    Mean of Bootstrap Samples:                 7.338842
    Standard Deviation of Bootstrap Samples:  0.6960418
    Median of Bootstrap Samples:               7.310299
    MAD of Bootstrap Samples:                 0.4584347
    Minimum of Bootstrap Samples:              5.688356
    Maximum of Bootstrap Samples:              11.27284
     
     
     
    Percent Points of the Bootstrap Samples
    -----------------------------------
      Percent Point               Value
    -----------------------------------
                0.1    =   5.688367
                0.5    =   5.747268
                1.0    =   5.929775
                2.5    =   6.122410
                5.0    =   6.271287
               10.0    =   6.488546
               20.0    =   6.749534
               50.0    =   7.310299
               80.0    =   7.873042
               90.0    =   8.208357
               95.0    =   8.487544
               97.5    =   8.823580
               99.0    =   9.252583
               99.5    =   9.609171
               99.9    =   11.27161
     
     
                Percentile Confidence Interval for Statistic
     
    ------------------------------------------
      Confidence          Lower          Upper
     Coefficient          Limit          Limit
    ------------------------------------------
           50.00   6.862967       7.771134
           75.00   6.543979       8.090032
           90.00   6.271287       8.487544
           95.00   6.122410       8.823580
           99.00   5.747268       9.609171
           99.90   5.688356       11.27284
    ------------------------------------------
     
     
    Response Variable One: Y1
    Response Variable Two: Y2
    Group ID Variable One (All Data):
     
    Number of Bootstrap Samples:             1000
    Number of Observations:                  150
    Mean of Bootstrap Samples:                 6.421951
    Standard Deviation of Bootstrap Samples:   1.547468
    Median of Bootstrap Samples:               7.007179
    MAD of Bootstrap Samples:                 0.8567694
    Minimum of Bootstrap Samples:              3.342993
    Maximum of Bootstrap Samples:              11.27284
     
     
     
    Percent Points of the Bootstrap Samples
    -----------------------------------
      Percent Point               Value
    -----------------------------------
                0.1    =   3.409331
                0.5    =   3.625963
                1.0    =   3.741478
                2.5    =   3.852497
                5.0    =   3.968823
               10.0    =   4.131668
               20.0    =   4.447991
               50.0    =   7.007179
               80.0    =   7.739732
               90.0    =   8.062719
               95.0    =   8.351421
               97.5    =   8.614502
               99.0    =   8.894499
               99.5    =   9.203490
               99.9    =   9.751902
     
     
                Percentile Confidence Interval for Statistic
     
    ------------------------------------------
      Confidence          Lower          Upper
     Coefficient          Limit          Limit
    ------------------------------------------
           50.00   4.617406       7.610766
           75.00   4.210556       7.962787
           90.00   3.968823       8.351421
           95.00   3.852497       8.614502
           99.00   3.625963       9.203490
           99.90   3.347339       10.65474
    ------------------------------------------
        
    plot generated by sample program

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Date created: 07/26/2017
Last updated: 07/26/2017

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