Frequency Distributions

  • frequency distribution tables help organize variable values so you can:

    • see patterns

    • detect outlier values

  • compress data into a grouped frequency table

    • combine nearby items into score “bins” that represent a range of values

grouped frequency table

  • bins are exclusive, equal-sized, and exhaustive

    • exclusive: each item fits in no more than one bin

    • equal-sized: each bin has the same range

    • exhaustive: every item fits in a bin

  • raw frequency tables reflect sample size

    • this can be useful is you want to see sample sizes

    • but this can make it hard to compare across studies with different sample sizes

  • relative frequency tables express frequency in proportions or percentages

    • proportion is frequency over total measurements

  • cumulative frequency counts accumulated scores across bins

    • useful for counting scores below or above a threshold value

    • cumulative frequencies can slo be counted in relative proportion or percentages

jamovi output for frequency of breakfast and traits in the "breakfast" data set

  • a histogram is a graphical depiction of a frequency table by plotting how often different values occur

  • expectations:

    • x-axis has possible values (bins from frequency table)

      • typically need to reflect bins of values for quantitative variables

    • bins should be equal-sized, exclusive and without gaps, and exhaustive of all possible scores

    • y-axis reflects frequency (raw count or relative using proportion or percentage)

    • increment of values on the y-axis should be equal-sized

  • using histograms to describe the shape of a variable’s distribution

  • there are common distribution shapes that occur in nature

    • normal distribution: a symmetrical distribution of data with a single peak and a bell shape

    • skewed distribution: many observations clumped on one end, with a “tail” of extreme values on the other (skewed) end

    • bi-modal: two peaks