Module stikpetP.effect_sizes.eff_size_cont_coeff

Functions

def es_cont_coeff(chi2, n, adj=None, r=None, c=None)

(Pearson) Contingency Coefficient

Determines the Pearson Contingency Coefficient value.

Parameters

chi2 : float

chi-square value

n : int

the sample size

adj : {None, "sakoda", "br"}, optional

method to adjust the coefficient with.

r : int, optional

number of rows (categories), only needed if adj="sakoda"

c : int, optional

number of rows (categories), only needed if adj="sakoda"

Returns

es : the coefficient value

 

Notes

The formula used is (Pearson, 1904, p. 9): $$C = \sqrt{\frac{\chi^2}{n + \chi^2}}$$

The Sakoda adjustment will use (Sakoda, 1977, p. 778): $$C_{adj} = \frac{C}{C_{max}}$$

With: $$C_{max} = \sqrt{\frac{m - 1}{m}}$$ $$m = \min\left(r, c\right)$$

The Blaikie-Roberts adjustment uses (Blaikie, 1969, p. 19): $$C_{adj} = \frac{C}{C_{max}}$$

With: $$C_{max} = \sqrt[4]{\frac{r - 1}{r}\times\frac{c - 1}{c}}$$

Blaikie refers to his mentor Roberts for this (Blaikie, 2003, p. 115)

References

Blaikie, N. W. H. (1969). Religion, social status, and community involvement: A study in Christchurch. The Australian and New Zealand Journal of Sociology, 5(1), 14–31. doi:10.1177/144078336900500102

Blaikie, N. W. H. (2003). Analyzing quantitative data: From description to explanation. Sage Publications Ltd.

Pearson, K. (1904). Contributions to the Mathematical Theory of Evolution. XIII. On the theory of contingency and its relation to association and normal correlation. Dulau and Co.

Sakoda, J. M. (1977). Measures of Association for Multivariate Contingency Tables. In Proceedings of the Social Statistics Section of the American Statistical Association: Vol. Part III (pp. 777–780).

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

Expand source code

def es_cont_coeff(chi2, n, adj=None, r=None, c=None):
    '''
    (Pearson) Contingency Coefficient
    ---------------------------------
    
    Determines the Pearson Contingency Coefficient value.
    
    Parameters
    ----------
    chi2 : float
        chi-square value
    n : int
        the sample size
    adj : {None, "sakoda", "br"}, optional
        method to adjust the coefficient with.
    r : int, optional
        number of rows (categories), only needed if adj="sakoda"
    c : int, optional
        number of rows (categories), only needed if adj="sakoda"
        
    Returns
    -------
    es: the coefficient value
    
    Notes
    -----
    The formula used is (Pearson, 1904, p. 9):
    $$C = \\sqrt{\\frac{\\chi^2}{n + \\chi^2}}$$
    
    The Sakoda adjustment will use (Sakoda, 1977, p. 778):
    $$C_{adj} = \\frac{C}{C_{max}}$$
    
    With:
    $$C_{max} = \\sqrt{\\frac{m - 1}{m}}$$
    $$m = \\min\left(r, c\\right)$$

    The Blaikie-Roberts adjustment uses (Blaikie, 1969, p. 19):
    $$C_{adj} = \\frac{C}{C_{max}}$$
    
    With:
    $$C_{max} = \\sqrt[4]{\\frac{r - 1}{r}\\times\\frac{c - 1}{c}}$$

    Blaikie refers to his mentor Roberts for this (Blaikie, 2003, p. 115)
    
    References
    ----------
    Blaikie, N. W. H. (1969). Religion, social status, and community involvement: A study in Christchurch. *The Australian and New Zealand Journal of Sociology, 5*(1), 14–31. doi:10.1177/144078336900500102

    Blaikie, N. W. H. (2003). *Analyzing quantitative data: From description to explanation*. Sage Publications Ltd.
    
    Pearson, K. (1904). *Contributions to the Mathematical Theory of Evolution. XIII. On the theory of contingency and its relation to association and normal correlation*. Dulau and Co.
    
    Sakoda, J. M. (1977). *Measures of Association for Multivariate Contingency Tables*. In Proceedings of the Social Statistics Section of the American Statistical Association: Vol. Part III (pp. 777–780).
    
    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
    
    '''
    es = (chi2/(n + chi2))**0.5
    
    if adj=="sakoda":
        m = r
        if (c < r):
            m = c        
        cmax = ((m - 1)/m)**0.5
        es = es/cmax
    elif adj=="br":
        cmax = ((r - 1)/r * (c - 1)/c)**(0.25)
        es = es/cmax
    return es