These notes capture the key concepts, discussions, and important information from the class sessions. They are intended to provide a comprehensive summary of the material covered, including lecture highlights, significant topics, and any additional insights provided by the instructor.
Chapter 10
Graphs, Good and Bad
● Clear graphical displays →
○ Easier for decision makers to decide how to allocate resources for prevention or intervention
● Tables and graphs →
○ Helps us see what the data says
○ But, not all do so accurately or clearly
● In this chapter:
○ Basic methods for displaying data
○ How to assess the quality of graphics
Types of Variables (REVIEW)
● Categorical variable
○ Places an individual into one of several groups or categories
■ E.g., gender, occupation, education level
● Quantitative variable
○ Takes numerical values for which arithmetic operations such as adding and averaging make sense
■ E.g., height in centimeters, SAT scores
Pie Charts and Bar Graphs
● Example: Level of education
○ A categorical variable
○ Six possible values:
■ Less than high school, high
school graduate, some
college, associate’s degree,
bachelor's degree, advanced
degree
○ To graph this? A pie chart, maybe
● Pie charts depict how a whole is divided into parts
● To make one:
○ Draw a circle which represents the whole
○ Wedges represent the parts
■ The angle spanned by each wedge = the relative proportion of that part
● Advantages of pie charts
○ Forces us to see that the parts do make a whole
○ However, it is much easier for our eyes to compare heights → harder to compare relative
proportions of wedges
○ Hence, bar graphs
● Bars show a category
● Height show the number for that category
○ E.g., count/frequency or percentage
● Notes on bar graphs
○ Each bar will always have the same
width and space between the bars
○ Can be either vertical or horizontal
● Advantages of bar graphs
○ Easy to make comparisons of size across
categories
○ Natural ordering of the variabel (if any)
, ■ E.g., education level (increasing left to right)
■ Order can be displayed along axis
● No obvious way to do this in a pie chart
● Comparisons
○ Both show the distribution (either counts or percentages) of a categorical variable
■ Pie chart
● Percentage for each category (rather than the count)
● Only works if you have all the categories (the percentages must add up to
100%)
■ Bar graph
● Not restricted to 100%
● Can also show count, not just percentage
● Easily compare the size of categories that are not parts of one whole
Beware the pictogram
● Bar graphs
○ Differ in height only!
■ Width of each bar is the same
■ The area (width x height) varies only the
proportion to height → our eyes receive the
right impression
○ However
■ Bar graphs are a bit bland, artistically speaking
■ Tempting to replace the bars with pictures for
greater eye appeal
■ Avoid this!!
Change over time: Line graphs
● Time series (for quantitative variables)
○ Measured at intervals over time
○ Make a line graph
● Line graph
○ Each observation plotted at the
time it was measured
○ Time on the horizontal axis (x)
○ Variable of interest on the vertical
axis (y)
○ Connect the data points by lines
● Advice
○ Use equally spaced time intervals
■ Reduces distortion
○ Separate lines for separate
categories
■ Options
● Color and line
type (solid, dashed, dotted, dash-dot)
● How to describe the line chart
○ Look for an overall pattern
○ Trend
■ A long-term upward or downward movement over time
, ○ More on what to look for
■ Look for striking deviations from the overall pattern
○ Seasonal variation
■ A pattern that repeats itself at known regular intervals
Watch those scales!
● Graphs
○ Very powerful effect on people
○ Can also be used to mislead
● Advice
○ Look closely at the scales marked off on the axes
● Using raw values v percentages
○ Raw values
■ Can be misleading in line graphs
○ Percentage increase from the previous period
■ Often better
Stats in summary
● To see what data says, start with graphs
● The choice of graph depends on the type of data
○ Do you have a categorical variable, such as level of education or occupation, which puts
individuals into a category?
○ Or do you have a quantitative variable measured in meaningful numerical units?
● Check data presented in a table for roundoff errors
● The distribution of a variable tells us what values it takes and how often it takes those values
● To display the distribution of a categorical variable, use a pie chart or a bar graph
○ Pie charts always show the parts of some whole…
■ But bar graphs can compare any set of numbers measured in the same units
○ Bar graphs are better for comparisons
■ Bar graphs can be displayed vertically or horizontally
● To show how a quantitative variable changed over time, use a line graph that plots values of the variable
(vertical scale) against time (horizontal scale)
● If you have values of the variable for different categories, use a separate line for each category
● Look for trends and seasonal variation in a line graph, and ask whether the data have been seasonally
adjusted
● Graphs can mislead
● Avoid pictograms that replace the bars of a bar graph with pictures whose height and width both change
● Look at the scales of a line graph to see if they have been stretched or squeezed to create a particular
impression
● Avoid clutter that makes the data hard to see
Chapter 11
Displaying data
● The nature of your variable dictates how you can display the data
○ Categorical variables
■ Measuring frequency of group membership in a category
■ Ex: gender, favorite music genre
■ Pie charts and bar graphs
○ Quantitative variables
■ Many numerical values
■ Measuring the frequency of each numerical value
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