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Chapter 4

73-100 Chapter Notes - Chapter 4: Marginal Distribution, Contingency Table, Bar Chart

Course Code
MSCI 1000
Peter Miller

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CHAPTER 4 Displaying and Describing Categorical Data
Make a picture
- display data ! help see what you are not likely to see in table ! help plan approach to
- shows important features, patterns and relationships
- reveals extraordinary (or possible wrong) data
- best way to report data to others
Frequency Tables – shows number of cases (ex. website visits) for each category and records
totals and category names (ex. provinces)
- describe the distribution of a categorical variable – name possible categories and tell how
frequently each occurs.
Relative frequency table – displays percentages, rather than the counts, of each of the value in
each category
- The area principle – the area occupied by a part of the graph should correspond to the
magnitude of the value it represents
- Bar charts – displays the distribution of a categorical variable, showing the counts for each
category next to each other for easy comparison
- more accurate visual impression of the distribution
- common base, freestanding, spaces in-between
- horizontal or vertical
- Relative frequency bar chart – replacing counts with percentages, draws attention to
- Pie Charts – severe perceptual problems, hard to interpret – try not to use them!
Categorical Data Condition – that the data are counts or percentages of individuals in
- make sure categories don’t overlap
** best perception of – positions of common scale (ex. plot or bar graph), comparing 2 separate
images with same scale, length
worst perception – volume, colour, angles, area
Contingency tables – shows how individuals are distributed along each variable, depending on
(contingent on), the value of the other variable
- marginal distribution – in a contingency table, the distribution of either variable alone.
The counts or percentages are the totals found n the margins (usually the right-most column
or bottom row) of the table.
- each cell – gives the count for a combination of values of the two variables
- total percentage, row percentage, column percentage
Conditional distribution – shows the distribution of one variable for just those cases that satisfy
a condition on another
Independent variable – when the distribution of one variable is the same for all categories of
another, in a contingency table (no association between the variables)
Segmented Bar Charts – treats each bar as the “whole and divides it proportionally into
segments corresponding to the percentage in each group
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