Module stikpetP.measures.meas_mode

Functions

def me_mode(data, allEq='none')

Mode

The mode is a measure of central tendency and defined as “the abscissa corresponding to the ordinate of maximum frequency” (Pearson, 1895, p. 345). A more modern definition would be “the most common value obtained in a set of observations” (Weisstein, 2002).

The word mode might even come from the French word 'mode' which means fashion. Fashion is what most people wear, so the mode is the option most people chose.

If one category has the highest frequency this category will be the modal category and if two or more categories have the same highest frequency each of them will be the mode. If there is only one mode the set is sometimes called unimodal, if there are two it is called bimodal, with three trimodal, etc. For two or more, thse term multimodal can also be used.

An advantage of the mode over many other measures of central tendency (like the median and mean), is that it can be determined for already nominal data types.

A video on the mode is available here.

This function is shown in this YouTube video and the measure is also described at PeterStatistics.com

Parameters

data : list or pandas series

the scores to determine the mode from

allEq : {"none", "all"}, optional

indicator on what to do if maximum frequency is equal for more than one category. Default is "none".

Returns

A dataframe with:

 

• mode, the mode(s)
• mode freq., frequency of the mode

Notes

One small controversy exists if all categories have the same frequency. In this case none of them has a higher occurence than the others, so none of them would be the mode (see for example Spiegel & Stephens, 2008, p. 64, Larson & Farber, 2014, p. 69). This is used when allEq="none" and the default.

On a rare occasion someone might argue that if all categories have the same frequency, then all categories are part of the mode since they all have the highest frequency. This is used when allEq="all".

Before, After and Alternatives

Before this an impression using a frequency table or a visualisation might be helpful: * tab_frequency * vi_bar_simple for Simple Bar Chart * vi_cleveland_dot_plot for Cleveland Dot Plot * vi_dot_plot for Dot Plot * vi_pareto_chart for Pareto Chart * vi_pie for Pie Chart

After this you might want some variation measure: * me_qv for Measures of Qualitative Variation

or perform a test: * ts_pearson_gof for Pearson Chi-Square Goodness-of-Fit Test * ts_freeman_tukey_gof for Freeman-Tukey Test of Goodness-of-Fit * ts_freeman_tukey_read for Freeman-Tukey-Read Test of Goodness-of-Fit * ts_g_gof for G (Likelihood Ratio) Goodness-of-Fit Test * ts_mod_log_likelihood_gof for Mod-Log Likelihood Test of Goodness-of-Fit * ts_multinomial_gof for Multinomial Goodness-of-Fit Test * ts_neyman_gof for Neyman Test of Goodness-of-Fit * ts_powerdivergence_gof for Power Divergence GoF Test

If you are looking to determine the mode of binned data use: * me_mode_bin for the mode with binned data

References

Larson, R., & Farber, E. (2014). Elementary statistics: Picturing the world (6th ed.). Pearson.

Pearson, K. (1895). Contributions to the mathematical theory of evolution. II. Skew variation in homogeneous material. Philosophical Transactions of the Royal Society of London. (A.), 186, 343–414. https://doi.org/10.1098/rsta.1895.0010

Spiegel, M. R., & Stephens, L. J. (2008). Schaum’s outline of theory and problems of statistics (4th ed.). McGraw-Hill.

Weisstein, E. W. (2002). CRC concise encyclopedia of mathematics (2nd ed.). Chapman & Hall/CRC.

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: pandas series

>>> import pandas as pd
>>> df1 = pd.read_csv('https://peterstatistics.com/Packages/ExampleData/GSS2012a.csv', sep=',', low_memory=False, storage_options={'User-Agent': 'Mozilla/5.0'})
>>> ex1 = df1['mar1']
>>> me_mode(ex1)
        mode  mode freq.
0  [MARRIED]         972

Example 2: a list

>>> ex2 = ["MARRIED", "DIVORCED", "MARRIED", "SEPARATED", "DIVORCED", "NEVER MARRIED", "DIVORCED", "DIVORCED", "NEVER MARRIED", "MARRIED", "MARRIED", "MARRIED", "SEPARATED", "DIVORCED", "NEVER MARRIED", "NEVER MARRIED", "DIVORCED", "DIVORCED", "MARRIED"]
>>> me_mode(ex2)
         mode  mode freq.
0  [DIVORCED]           7

Example 3: Multi-Mode

>>> ex3a = [1, 1, 2, 3, 3, 4, 5, 6, 6]
>>> me_mode(ex3a)
              mode  mode freq.
0  [1.0, 3.0, 6.0]           2
>>> ex3b = ["MARRIED", "DIVORCED", "MARRIED", "DIVORCED", "DIVORCED", "NEVER MARRIED", "MARRIED"]
>>> me_mode(ex3b)
                  mode  mode freq.
0  [MARRIED, DIVORCED]           3

Example 4: All Equal

>>> ex4a = [1, 1, 2, 2, 3, 3, 6, 6]
>>> me_mode(ex4a)
        mode mode freq.
0  [no mode]         na
>>> ex4b = [1, 1, 2, 2, 3, 3, 6, 6]
>>> me_mode(ex4b, allEq="all")
                   mode  mode freq.
0  [1.0, 2.0, 3.0, 6.0]           2

Expand source code

def me_mode(data, allEq="none"):
    '''
    Mode
    ----    
    The mode is a measure of central tendency and defined as “the abscissa corresponding to the ordinate of maximum frequency” (Pearson, 1895, p. 345). A more modern definition would be “the most common value obtained in a set of observations” (Weisstein, 2002). 
    
    The word mode might even come from the French word 'mode' which means fashion. Fashion is what most people wear, so the mode is the option most people chose.
    
    If one category has the highest frequency this category will be the modal category and if two or more categories have the same highest frequency each of them will be the mode. If there is only one mode the set is sometimes called unimodal, if there are two it is called bimodal, with three trimodal, etc. For two or more, thse term multimodal can also be used.
    
    An advantage of the mode over many other measures of central tendency (like the median and mean), is that it can be determined for already nominal data types. 
    
    A video on the mode is available [here](https://youtu.be/oPpTE8qt2go).

    This function is shown in this [YouTube video](https://youtu.be/3MEz6OJI4rE) and the measure is also described at [PeterStatistics.com](https://peterstatistics.com/Terms/Measures/Mode.html)

    Parameters
    ----------
    data : list or pandas series
        the scores to determine the mode from
        
    allEq : {"none", "all"}, optional 
        indicator on what to do if maximum frequency is equal for more than one category. Default is "none".
    
    Returns
    -------
    A dataframe with:
    
    * *mode*, the mode(s)
    * *mode freq.*, frequency of the mode
    
    Notes
    -----
    One small controversy exists if all categories have the same frequency. In this case none of them has a higher occurence than the others, so none of them would be the mode (see for example Spiegel & Stephens, 2008, p. 64, Larson & Farber, 2014, p. 69). This is used when *allEq="none"* and the default.
    
    On a rare occasion someone might argue that if all categories have the same frequency, then all categories are part of the mode since they all have the highest frequency. This is used when *allEq="all"*.
        
    Before, After and Alternatives
    ------------------------------
    Before this an impression using a frequency table or a visualisation might be helpful:
    * [tab_frequency](../other/table_frequency.html#tab_frequency)
    * [vi_bar_simple](../visualisations/vis_bar_simple.html#vi_bar_simple) for Simple Bar Chart
    * [vi_cleveland_dot_plot](../visualisations/vis_cleveland_dot_plot.html#vi_cleveland_dot_plot) for Cleveland Dot Plot
    * [vi_dot_plot](../visualisations/vis_dot_plot.html#vi_dot_plot) for Dot Plot
    * [vi_pareto_chart](../visualisations/vis_pareto_chart.html#vi_pareto_chart) for Pareto Chart
    * [vi_pie](../visualisations/vis_pie.html#vi_pie) for Pie Chart
    
    After this you might want some variation measure:
    * [me_qv](../measures/meas_qv.html#me_qv) for Measures of Qualitative Variation

    or perform a test:
    * [ts_pearson_gof](../tests/test_pearson_gof.html#ts_pearson_gof) for Pearson Chi-Square Goodness-of-Fit Test
    * [ts_freeman_tukey_gof](../tests/test_freeman_tukey_gof.html#ts_freeman_tukey_gof) for Freeman-Tukey Test of Goodness-of-Fit
    * [ts_freeman_tukey_read](../tests/test_freeman_tukey_read.html#ts_freeman_tukey_read) for Freeman-Tukey-Read Test of Goodness-of-Fit
    * [ts_g_gof](../tests/test_g_gof.html#ts_g_gof) for G (Likelihood Ratio) Goodness-of-Fit Test
    * [ts_mod_log_likelihood_gof](../tests/test_mod_log_likelihood_gof.html#ts_mod_log_likelihood_gof) for Mod-Log Likelihood Test of Goodness-of-Fit
    * [ts_multinomial_gof](../tests/test_multinomial_gof.html#ts_multinomial_gof) for Multinomial Goodness-of-Fit Test
    * [ts_neyman_gof](../tests/test_neyman_gof.html#ts_neyman_gof) for Neyman Test of Goodness-of-Fit
    * [ts_powerdivergence_gof](../tests/test_powerdivergence_gof.html#ts_powerdivergence_gof) for Power Divergence GoF Test
    
    If you are looking to determine the mode of binned data use:
    * [me_mode_bin](../measures/meas_mode_bin.html#me_mode_bin) for the mode with binned data
    
    References
    ----------
    Larson, R., & Farber, E. (2014). *Elementary statistics: Picturing the world* (6th ed.). Pearson.
    
    Pearson, K. (1895). Contributions to the mathematical theory of evolution. II. Skew variation in homogeneous material. *Philosophical Transactions of the Royal Society of London. (A.), 186*, 343–414. https://doi.org/10.1098/rsta.1895.0010
    
    Spiegel, M. R., & Stephens, L. J. (2008). *Schaum’s outline of theory and problems of statistics* (4th ed.). McGraw-Hill.
    
    Weisstein, E. W. (2002). *CRC concise encyclopedia of mathematics* (2nd ed.). Chapman & Hall/CRC.
    
    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: pandas series
    >>> import pandas as pd
    >>> df1 = pd.read_csv('https://peterstatistics.com/Packages/ExampleData/GSS2012a.csv', sep=',', low_memory=False, storage_options={'User-Agent': 'Mozilla/5.0'})
    >>> ex1 = df1['mar1']
    >>> me_mode(ex1)
            mode  mode freq.
    0  [MARRIED]         972
    
    Example 2: a list
    >>> ex2 = ["MARRIED", "DIVORCED", "MARRIED", "SEPARATED", "DIVORCED", "NEVER MARRIED", "DIVORCED", "DIVORCED", "NEVER MARRIED", "MARRIED", "MARRIED", "MARRIED", "SEPARATED", "DIVORCED", "NEVER MARRIED", "NEVER MARRIED", "DIVORCED", "DIVORCED", "MARRIED"]
    >>> me_mode(ex2)
             mode  mode freq.
    0  [DIVORCED]           7
    
    Example 3: Multi-Mode
    >>> ex3a = [1, 1, 2, 3, 3, 4, 5, 6, 6]
    >>> me_mode(ex3a)
                  mode  mode freq.
    0  [1.0, 3.0, 6.0]           2
    >>> ex3b = ["MARRIED", "DIVORCED", "MARRIED", "DIVORCED", "DIVORCED", "NEVER MARRIED", "MARRIED"]
    >>> me_mode(ex3b)
                      mode  mode freq.
    0  [MARRIED, DIVORCED]           3

    Example 4: All Equal
    >>> ex4a = [1, 1, 2, 2, 3, 3, 6, 6]
    >>> me_mode(ex4a)
            mode mode freq.
    0  [no mode]         na
    >>> ex4b = [1, 1, 2, 2, 3, 3, 6, 6]
    >>> me_mode(ex4b, allEq="all")
                       mode  mode freq.
    0  [1.0, 2.0, 3.0, 6.0]           2
        
    '''
    
    if type(data) == list:
        data = pd.Series(data)
    
    freq = data.value_counts()
    maxCount = freq.max()
    modes = []
    for i in range(len(freq)):
        if freq.values[i]==maxCount:
            modes = np.append(modes, freq.index[i])
    
    if len(modes)==len(freq) and allEq=="none":
        modes = ['no mode']
        maxCount = "na"
    
    res = pd.DataFrame(list([[modes, maxCount]]), columns = ["mode", "mode freq."])
        
    return res