Module stikpetP.other.thumb_cle

Functions

def th_cle(cle, qual='vd', convert='no')

Rules Of Thumb For Common Language Effect Size

This function will give a qualification (classification) for a Common Language Effect Size (/ Vargha-Delaney A / Probability of Superiority)

The measure is also described at PeterStatistics.com

Parameters

cle : float

the common language effect size

qual : {"vd", others via conversion}, optional

rules-of-thumb to use, currently only 'vd' for Vargha-Delaney, otherwise a converted measure.

convert : {"no", "rb", "cohen_d"}, optional string

in case to use a rule-of-thumb from a converted measure. Either "no", "rb" for rank-biserial, or "cohen_d" for Cohen d.

Returns

results : a dataframe with.

• classification, the qualification of the effect size
• reference, a reference for the rule of thumb used

Notes

"vd" => Vargha and Delaney (2000, p. 106)

|0.5 - CLE|	Interpretation
0.00 < 0.06	negligible
0.06 < 0.14	small
0.14 < 0.21	medium
0.21 or more	large

The CLE can be converted to a Rank Biserial Coefficient using: $$r_b = 2\times CLE - 1$$

Rules of thumb from the th_rank_biserial() function could then be used, by setting: convert="rb". Where the qual is any of the options in th_rank_biserial()

This in turn can be converted to Cohen's d using (Marfo & Okyere, 2019, p.4): $$d = 2\times \phi^{-1}\left(-\frac{1}{r_b - 2}\right)$$ Rules of thumb from the th_cohen_d() function could then be used, by setting: convert="cohen_d". Where the qual is any of the options in th_cohen_d()

Before, After and Alternatives

Before this you might want to obtain the measure: * es_common_language_os for the Common Language Effect Size for one-sample * es_common_language_is for the Common Language Effect Size for independent samples

The function uses the convert function and corresponding rules of thumb: * es_convert for the conversions * th_rank_biserial for options for rules of thumb when converting to Rank Biserial * th_cohen_d for options for rules of thumb when converting to Cohen d.

References

Marfo, P., & Okyere, G. A. (2019). The accuracy of effect-size estimates under normals and contaminated normals in meta-analysis. Heliyon, 5(6), e01838. doi:10.1016/j.heliyon.2019.e01838

Vargha, A., & Delaney, H. D. (2000). A critique and improvement of the CL common language effect size statistics of McGraw and Wong. Journal of Educational and Behavioral Statistics, 25(2), 101–132. doi:10.3102/10769986025002101

Author

Made by P. Stikker

Companion website: https://PeterStatistics.com
YouTube channel: https://www.youtube.com/stikpet
Donations: https://www.patreon.com/bePatron?u=19398076

Examples

Example 1: Using Vargha and Delaney rules:

>>> cle = 0.23
>>> th_cle(cle)
  classification                          reference
0          large  Vargha and Delaney (2000, p. 106)

Example 2: Convert to rank-biserial and use Sawilowsky rules:

>>> cle = 0.23
>>> th_cle(cle, qual="sawilowsky", convert="rb")
  classification                  reference
0         medium  Sawilowsky (2009, p. 599)

Expand source code

def th_cle(cle, qual="vd", convert="no"):
    '''
    Rules of Thumb for Common Language Effect Size
    ----------------------------------------------
     
    This function will give a qualification (classification) for a Common Language Effect Size (/ Vargha-Delaney A / Probability of Superiority)

    The measure is also described at [PeterStatistics.com](https://peterstatistics.com/Terms/EffectSizes/CommonLanguageEffectSize.html)
    
    Parameters
    ----------
    cle : float
        the common language effect size
    qual : {"vd", others via conversion}, optional
        rules-of-thumb to use, currently only 'vd' for Vargha-Delaney, otherwise a converted measure.
    convert : {"no", "rb", "cohen_d"}, optional string
        in case to use a rule-of-thumb from a converted measure. Either "no", "rb" for rank-biserial, or "cohen_d" for Cohen d.
    
    Returns
    -------
    results : a dataframe with.
    
    * *classification*, the qualification of the effect size
    * *reference*, a reference for the rule of thumb used
    
    Notes
    -----
        
    "vd" => Vargha and Delaney (2000, p. 106)
    
    |\\|0.5 - CLE\\|| Interpretation|
    |---------------|---------------|
    |0.00 < 0.06    | negligible    |
    |0.06 < 0.14    | small         |
    |0.14 < 0.21    | medium        |
    |0.21 or more   | large         |

    The CLE can be converted to a Rank Biserial Coefficient using:
    $$r_b = 2\\times CLE - 1$$

    Rules of thumb from the **th_rank_biserial()** function could then be used, by setting: *convert="rb"*. Where the *qual* is any of the options in th_rank_biserial()

    This in turn can be converted to Cohen's d using (Marfo & Okyere, 2019, p.4):
    $$d = 2\\times \\phi^{-1}\\left(-\\frac{1}{r_b - 2}\\right)$$
    Rules of thumb from the **th_cohen_d()** function could then be used, by setting: *convert="cohen_d"*. Where the *qual* is any of the options in th_cohen_d()

    Before, After and Alternatives
    ------------------------------
    Before this you might want to obtain the measure:
    * [es_common_language_os](../effect_sizes/eff_size_common_language_os.html#es_common_language_os) for the Common Language Effect Size for one-sample
    * [es_common_language_is](../effect_sizes/eff_size_common_language_is.html#es_common_language_is) for the Common Language Effect Size for independent samples

    The function uses the convert function and corresponding rules of thumb:
    * [es_convert](../effect_sizes/convert_es.html#es_convert) for the conversions
    * [th_rank_biserial](../other/thumb_rank_biserial.html#th_rank_biserial) for options for rules of thumb when converting to Rank Biserial
    * [th_cohen_d](../other/thumb_cohen_d.html#th_cohen_d) for options for rules of thumb when converting to Cohen d.
    
    References
    ----------
    Marfo, P., & Okyere, G. A. (2019). The accuracy of effect-size estimates under normals and contaminated normals in meta-analysis. *Heliyon, 5*(6), e01838. doi:10.1016/j.heliyon.2019.e01838
    
    Vargha, A., & Delaney, H. D. (2000). A critique and improvement of the CL common language effect size statistics of McGraw and Wong. *Journal of Educational and Behavioral Statistics, 25*(2), 101–132. doi:10.3102/10769986025002101
    
    Author
    ------
    Made by P. Stikker
    
    Companion website: https://PeterStatistics.com  
    YouTube channel: https://www.youtube.com/stikpet  
    Donations: https://www.patreon.com/bePatron?u=19398076

    Examples
    --------
    Example 1: Using Vargha and Delaney rules:
    >>> cle = 0.23
    >>> th_cle(cle)
      classification                          reference
    0          large  Vargha and Delaney (2000, p. 106)
    
    Example 2: Convert to rank-biserial and use Sawilowsky rules:
    >>> cle = 0.23
    >>> th_cle(cle, qual="sawilowsky", convert="rb")
      classification                  reference
    0         medium  Sawilowsky (2009, p. 599)
    
    '''

    if convert=="no":
        es = abs(0.5 - cle)
        #Vargha and Delaney (2000, p. 106)
        if (qual=="vd"):
            src = "Vargha and Delaney (2000, p. 106)"
            if (es < 0.06): qual = "negligible"
            elif (es < 0.14): qual = "small"
            elif (es < 0.21): qual = "medium"
            else: qual = "large"
    
            results = pd.DataFrame([[qual, src]], columns=["classification", "reference"])
            
    elif convert=="rb":
        rb = es_convert(cle ,fr="cle", to="rb")
        results = th_rank_biserial(rb, qual=qual)
    
    elif convert=='cohen_d':
        rb = es_convert(cle ,fr="cle", to="rb")
        d = es_convert(rb ,fr="rb", to="cohend")
        results = th_cohen_d(d, qual=qual)
        
    return(results)