Module stikpetP.other.thumb_pearson_r

Functions

def th_pearson_r(r, qual='bartz')

Rules Of Thumb For Pearson Correlation Coefficient

This function will give a qualification (classification) to a given correlation coefficient

Parameters

r : the correlation coefficient

 

qual : {"bartz", "agnes", "brydges", "cohen", "disha", "funder", "hopkins", "lovakov", "rafter", "rea", "rosenthal", "rumsey", "gignac", "hemphill"}, optional

the rule of thumb to be used. Default is "bartz".

Returns

pandas.DataFrame

A dataframe with the following columns:

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

Notes

The following rules-of-thumb can be used:

"agnes" => Agnes (2011)

|r|	Interpretation
0.00 < 0.20	negligible
0.20 < 0.40	low
0.40 < 0.60	moderate
0.60 < 0.80	marked
0.80 or more	high

"bartz" => Bartz (1988, p. 199)

|r|	Interpretation
0.00 < 0.20	very low
0.20 < 0.40	low
0.40 < 0.60	moderate
0.60 < 0.80	strong
0.80 or more	very high

"brydges" => Brydges (2019, p. 5) = "gignac" => Gignac and Szodorai (2016, p. 75) = "hemphill" => Hemphill (2003, p. 78)

|r|	Interpretation
0.00 < 0.10	negligible
0.10 < 0.20	small
0.20 < 0.30	medium
0.30 or more	large

"cohen" => Cohen (1988, p. 82)

|r|	Interpretation
0.00 < 0.20	negligible
0.20 < 0.50	small
0.50 < 0.80	medium
0.80 or more	large

"disha" => Disha (2016)

|r|	Interpretation
0.00 < 0.10	markedly low and negligible
0.10 < 0.30	very low
0.30 < 0.50	low
0.50 < 0.70	moderate
0.70 < 0.90	high
0.90 or more	very high

"funder" => Funder and Ozer (2019, p. 166)

|r|	Interpretation
0.00 < 0.05	negligible
0.05 < 0.10	very small
0.10 < 0.20	small
0.20 < 0.30	medium
0.30 < 0.40	large
0.40 or more	very large

"hopkins" => Hopkins (1997, as cited in Warmbrod 2001)

|r|	Interpretation
0.00 < 0.10	trivial
0.10 < 0.30	low
0.30 < 0.50	moderate
0.50 < 0.70	high
0.70 < 0.90	very large
0.90 or more	nearly perfect

"lovakov" => Lovakov and Agadullina (2021, p. 514)

|r|	Interpretation
0.00 < 0.12	negligible
0.12 < 0.24	small
0.24 < 0.41	medium
0.41 or more	large

"rafter" => Rafter et al. (2003, p. 194)

|r|	Interpretation
0.00 < 0.25	weak
0.25 < 0.75	moderate
0.75 or more	strong

"rea" => Rea and Parker (2014, pp. 229, 271)

|r|	Interpretation
0.00 < 0.10	negligible
0.10 < 0.30	low
0.30 < 0.60	moderate
0.60 < 0.75	strong
0.75 or more	very strong

"rosenthal" => Rosenthal (1996, p. 45)

|r|	Interpretation
0.00 < 0.10	negligible
0.10 < 0.30	small
0.30 < 0.50	medium
0.50 < 0.70	large
0.70 or more	very large

"rumsey" => Rumsey (2011, p. 284)

|r|	Interpretation
0.00 < 0.30	negligible
0.30 < 0.50	weak
0.50 < 0.70	moderate
0.70 or more	strong

See Also

Before using this function you need to obtain a Cramer v value: * [r_rosenthal](../correlations/cor_rosenthal.html#r_rosenthal) to determine a Rosenthal correlation coefficient

References

Agnes. (2011, April 16). Correlation – Correlation coefficient, r. Finance Training Course. https://financetrainingcourse.com/education/2011/04/correlation-correlation-coefficient-r/

Bartz, A. E. (1988). Basic statistical concepts (3rd ed.). Macmillan.

Brydges, C. R. (2019). Effect size guidelines, sample size calculations, and statistical power in gerontology. Innovation in Aging, 3(4), 1–8. doi:10.1093/geroni/igz036

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). L. Erlbaum Associates.

Disha, M. (2016, November 3). Correlation: Meaning, types and its computation. Your Article Library. https://www.yourarticlelibrary.com/statistics-2/correlation-meaning-types-and-its-computation-statistics/92001

Funder, D. C., & Ozer, D. J. (2019). Evaluating effect size in psychological research: Sense and nonsense. Advances in Methods and Practices in Psychological Science, 2(2), 156–168. doi:10.1177/2515245919847202

Gignac, G. E., & Szodorai, E. T. (2016). Effect size guidelines for individual differences researchers. Personality and Individual Differences, 102, 74–78. doi:10.1016/j.paid.2016.06.069

Hemphill, J. F. (2003). Interpreting the magnitudes of correlation coefficients. American Psychologist, 58(1), 78–79. doi:10.1037/0003-066X.58.1.78

Hopkins, W. G. (2006, August 7). New view of statistics: Effect magnitudes. http://www.sportsci.org/resource/stats/effectmag.html

Lovakov, A., & Agadullina, E. R. (2021). Empirically derived guidelines for effect size interpretation in social psychology. European Journal of Social Psychology, 51(3), 485–504. doi:10.1002/ejsp.2752

Rafter, J. A., Abell, M. L., & Braselton, J. P. (2003). Statistics with Maple. Academic Press.

Rea, L. M., & Parker, R. A. (2014). Designing and conducting survey research: A comprehensive guide (4th ed.). Jossey-Bass, a Wiley brand.

Rosenthal, J. A. (1996). Qualitative descriptors of strength of association and effect size. Journal of Social Service Research, 21(4), 37–59. doi:10.1300/J079v21n04_02

Rumsey, D. J. (2011). Statistics for dummies (2nd ed.). Wiley.

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

>>> es = 0.6
>>> th_pearson_r(es)
  classification             reference
0         strong  Bartz (1988, p. 199)

Expand source code

def th_pearson_r(r, qual="bartz"):
    '''
    Rules of Thumb for Pearson Correlation Coefficient
    --------------------------------------------------
     
    This function will give a qualification (classification) to a given correlation coefficient
    
    Parameters
    ----------
    r : the correlation coefficient
    qual : {"bartz", "agnes", "brydges", "cohen", "disha", "funder", "hopkins", "lovakov", "rafter", "rea", "rosenthal", "rumsey", "gignac", "hemphill"}, optional 
        the rule of thumb to be used. Default is "bartz". 
        
    Returns
    -------
    pandas.DataFrame
        A dataframe with the following columns:
    
        * *classification*, the qualification of the effect size
        * *reference*, a reference for the rule of thumb used
   
    Notes
    -----
    The following rules-of-thumb can be used:
    
    "agnes" => Agnes (2011)
    
    |\\|r\\|| Interpretation|
    |---|----------|
    |0.00 < 0.20 | negligible |
    |0.20 < 0.40 | low |
    |0.40 < 0.60 | moderate |
    |0.60 < 0.80 | marked |
    |0.80 or more | high |
    
    "bartz" => Bartz (1988, p. 199)
    
    |\\|r\\|| Interpretation|
    |---|----------|
    |0.00 < 0.20 | very low |
    |0.20 < 0.40 | low |
    |0.40 < 0.60 | moderate |
    |0.60 < 0.80 | strong |
    |0.80 or more | very high |
    
    "brydges" => Brydges (2019, p. 5) =
    "gignac" => Gignac and Szodorai (2016, p. 75) =
    "hemphill" => Hemphill (2003, p. 78)
    
    |\\|r\\|| Interpretation|
    |---|----------|
    |0.00 < 0.10 | negligible |
    |0.10 < 0.20 | small |
    |0.20 < 0.30 | medium |
    |0.30 or more | large |
    
    "cohen" => Cohen (1988, p. 82)
    
    |\\|r\\|| Interpretation|
    |---|----------|
    |0.00 < 0.20 | negligible |
    |0.20 < 0.50 | small |
    |0.50 < 0.80 | medium |
    |0.80 or more | large |
    
    "disha" => Disha (2016)
    
    |\\|r\\|| Interpretation|
    |---|----------|
    |0.00 < 0.10 | markedly low and negligible |
    |0.10 < 0.30 | very low |
    |0.30 < 0.50 | low |
    |0.50 < 0.70 | moderate |
    |0.70 < 0.90 | high |
    |0.90 or more | very high |
    
    "funder" => Funder and Ozer (2019, p. 166)
    
    |\\|r\\|| Interpretation|
    |---|----------|
    |0.00 < 0.05 | negligible |
    |0.05 < 0.10 | very small |
    |0.10 < 0.20 | small |
    |0.20 < 0.30 | medium |
    |0.30 < 0.40 | large |
    |0.40 or more | very large |
    
    "hopkins" => Hopkins (1997, as cited in Warmbrod 2001)
    
    |\\|r\\|| Interpretation|
    |---|----------|
    |0.00 < 0.10 | trivial |
    |0.10 < 0.30 | low |
    |0.30 < 0.50 | moderate |
    |0.50 < 0.70 | high |
    |0.70 < 0.90 | very large |
    |0.90 or more | nearly perfect |
    
    "lovakov" => Lovakov and Agadullina (2021, p. 514)
    
    |\\|r\\|| Interpretation|
    |---|----------|
    |0.00 < 0.12 | negligible |
    |0.12 < 0.24 | small |
    |0.24 < 0.41 | medium |
    |0.41 or more | large |
    
    "rafter" => Rafter et al. (2003, p. 194)
    
    |\\|r\\|| Interpretation|
    |---|----------|
    |0.00 < 0.25 | weak |
    |0.25 < 0.75 | moderate |
    |0.75 or more | strong |
    
    "rea" => Rea and Parker (2014, pp. 229, 271)
    
    |\\|r\\|| Interpretation|
    |---|----------|
    |0.00 < 0.10 | negligible |
    |0.10 < 0.30 | low |
    |0.30 < 0.60 | moderate |
    |0.60 < 0.75 | strong |
    |0.75 or more | very strong |
    
    "rosenthal" => Rosenthal (1996, p. 45)
    
    |\\|r\\|| Interpretation|
    |---|----------|
    |0.00 < 0.10 | negligible |
    |0.10 < 0.30 | small |
    |0.30 < 0.50 | medium |
    |0.50 < 0.70 | large |
    |0.70 or more | very large |
    
    "rumsey" => Rumsey (2011, p. 284)
    
    |\\|r\\|| Interpretation|
    |---|----------|
    |0.00 < 0.30 | negligible |
    |0.30 < 0.50 | weak |
    |0.50 < 0.70 | moderate |
    |0.70 or more | strong |
    
    
    See Also
    --------
    Before using this function you need to obtain a Cramer v value:
    * [r_rosenthal](../correlations/cor_rosenthal.html#r_rosenthal) to determine a Rosenthal correlation coefficient
    
    References
    ----------
    Agnes. (2011, April 16). Correlation – Correlation coefficient, r. Finance Training Course. https://financetrainingcourse.com/education/2011/04/correlation-correlation-coefficient-r/
    
    Bartz, A. E. (1988). *Basic statistical concepts* (3rd ed.). Macmillan.
    
    Brydges, C. R. (2019). Effect size guidelines, sample size calculations, and statistical power in gerontology. *Innovation in Aging, 3*(4), 1–8. doi:10.1093/geroni/igz036
    
    Cohen, J. (1988). *Statistical power analysis for the behavioral sciences* (2nd ed.). L. Erlbaum Associates.
    
    Disha, M. (2016, November 3). Correlation: Meaning, types and its computation. Your Article Library. https://www.yourarticlelibrary.com/statistics-2/correlation-meaning-types-and-its-computation-statistics/92001
    
    Funder, D. C., & Ozer, D. J. (2019). Evaluating effect size in psychological research: Sense and nonsense. *Advances in Methods and Practices in Psychological Science, 2*(2), 156–168. doi:10.1177/2515245919847202
    
    Gignac, G. E., & Szodorai, E. T. (2016). Effect size guidelines for individual differences researchers. *Personality and Individual Differences, 102*, 74–78. doi:10.1016/j.paid.2016.06.069
    
    Hemphill, J. F. (2003). Interpreting the magnitudes of correlation coefficients. *American Psychologist, 58*(1), 78–79. doi:10.1037/0003-066X.58.1.78
    
    Hopkins, W. G. (2006, August 7). New view of statistics: Effect magnitudes. http://www.sportsci.org/resource/stats/effectmag.html
    
    Lovakov, A., & Agadullina, E. R. (2021). Empirically derived guidelines for effect size interpretation in social psychology. *European Journal of Social Psychology, 51*(3), 485–504. doi:10.1002/ejsp.2752
    
    Rafter, J. A., Abell, M. L., & Braselton, J. P. (2003). *Statistics with Maple*. Academic Press.
    
    Rea, L. M., & Parker, R. A. (2014). *Designing and conducting survey research: A comprehensive guide* (4th ed.). Jossey-Bass, a Wiley brand.
    
    Rosenthal, J. A. (1996). Qualitative descriptors of strength of association and effect size. *Journal of Social Service Research, 21*(4), 37–59. doi:10.1300/J079v21n04_02
    
    Rumsey, D. J. (2011). *Statistics for dummies* (2nd ed.). Wiley.

    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
    --------
    >>> es = 0.6
    >>> th_pearson_r(es)
      classification             reference
    0         strong  Bartz (1988, p. 199)
    
    '''
    
    # Agnes (2011).
    if (qual=="agnes"):
        ref = "Agnes (2011)"
        if (abs(r) < 0.2):
            qual = "negligable"
        elif (abs(r) < 0.4):
            qual = "low"
        elif (abs(r) < 0.6):
            qual = "moderate"
        elif (abs(r) < 0.8):
            qual = "marked"
        else:
            qual = "high"
            
    # Bartz (1988, p. 199).
    elif (qual=="bartz"):
        ref = "Bartz (1988, p. 199)"
        if (abs(r) < 0.2):
            qual = "very low"
        elif (abs(r) < 0.4):
            qual = "low"
        elif (abs(r) < 0.6):
            qual = "moderate"
        elif (abs(r) < 0.8):
            qual = "strong"
        else:
            qual = "very high"
            
    # Brydges (2019, p. 5); Gignac and Szodorai (2016, p. 75); Hemphill (2003, p. 78).
    elif (qual=="gignac" or qual=="hemphill" or qual=="brydges"):
        ref = "Brydges (2019, p. 5); Gignac and Szodorai (2016, p. 75); Hemphill (2003, p. 78)"
        if (abs(r) < 0.1):
            qual = "negligable"
        elif (abs(r) < 0.2):
            qual = "small"
        elif (abs(r) < 0.3):
            qual = "medium"
        else:
            qual = "large"
            
    # Cohen (1988, p. 82).
    elif (qual=="cohen"):
        ref = "Cohen (1988, p. 82)"
        if (abs(r) < 0.1):
            qual = "negligable"
        elif (abs(r) < 0.3):
            qual = "small"
        elif (abs(r) < 0.5):
            qual = "medium"
        else:
            qual = "large"
    
    # Disha (2016).
    elif (qual=="disha"):
        ref = "Disha (2016)"
        if (abs(r) < 0.1):
            qual = "markedly low and negligible"
        elif (abs(r) < 0.3):
            qual = "very low"
        elif (abs(r) < 0.5):
            qual = "low"
        elif (abs(r) < 0.7):
            qual = "moderate"
        elif (abs(r) < 0.9):
            qual = "high"
        else:
            qual = "very high"
    
    # Funder and Ozer (2019, p. 166).
    elif (qual=="funder"):
        ref = "Funder and Ozer (2019, p. 166)"
        if (abs(r) < 0.05):
            qual = "negligable"
        elif (abs(r) < 0.1):
            qual = "very small"
        elif (abs(r) < 0.2):
            qual = "small"
        elif (abs(r) < 0.3):
            qual = "medium"
        elif (abs(r) < 0.4):
            qual = "large"
        else:
            qual = "very large"
    
    # Hopkins (2006, tbl. 1)
    elif (qual=="hopkins"):
        ref = "Hopkins (2006, tbl. 1)"
        if (abs(r) < 0.1):
            qual = "trivial"
        elif (abs(r) < 0.3):
            qual = "low"
        elif (abs(r) < 0.5):
            qual = "moderate"
        elif (abs(r) < 0.7):
            qual = "high"
        elif (abs(r) < 0.9):
            qual = "very large"
        else:
            qual = "nearly perfect"
          
    #Lovakov and Agadullina (2021, p. 514).
    elif (qual=="lovakov"):
        ref = "Lovakov and Agadullina (2021, p. 514)"
        if (abs(r) < 0.12):
            qual = "negligable"
        elif (abs(r) < 0.24):
            qual = "small"
        elif (abs(r) < 0.41):
            qual = "medium"
        else:
            qual = "large"
    
    # Rafter et al. (2003, p. 194).
    elif (qual=="rafter"):
        ref = "Rafter et al. (2003, p. 194)"
        if (abs(r) < 0.25):
            qual = "weak"
        elif (abs(r) < 0.75):
            qual = "moderate"
        else:
            qual = "strong"
    
    # Rea and Parker (2014, pp. 229, 271)
    elif (qual=="rea"):
        ref = "Rea and Parker (2014, pp. 229, 271)"
        if (abs(r) < 0.1):
            qual = "negligable"
        elif (abs(r) < 0.3):
            qual = "low"
        elif (abs(r) < 0.6):
            qual = "moderate"
        elif (abs(r) < 0.75):
            qual = "strong"
        else:
            qual = "very strong"
    
    # Rosenthal (1996, p. 45).
    elif (qual=="rosenthal"):
        ref = "Rosenthal (1996, p. 45)"
        if (abs(r) < 0.1):
            qual = "negligable"
        elif (abs(r) < 0.3):
            qual = "small"
        elif (abs(r) < 0.5):
            qual = "medium"
        elif (abs(r) < 0.7):
            qual = "large"
        else:
            qual = "very large"
            
    # Rumsey (2011, p. 284).
    elif (qual=="rumsey"):
        ref = "Rumsey (2011, p. 284)"
        if (abs(r) < 0.3):
            qual = "negligable"
        elif (abs(r) < 0.5):
            qual = "weak"
        elif (abs(r) < 0.7):
            qual = "moderate"
        else:
            qual = "strong"
                        
    results = pd.DataFrame([[qual, ref]], columns=["classification", "reference"])
            
    return results