The Statistical Imagination

1. The Statistical Imagination • Chapter 3. Charts and Graphs: A Picture Says a Thousand Words

2. Graphs and Charts: Pictorial Presentation of Data • Graphs and charts provide a direct sense of proportion • With graphics, visible spatial features substitute for abstract numbers

3. Types of Graphs and Levels of Measurement • For nominal/ordinal variables, use pie charts and bar charts • For interval/ratio variables, use histograms and polygons (line graphs)

4. Graphing Guidelines • Choose design on basis of level of measurement, study objectives, and targeted audience • A good graphic simplifies, not complicates • A good graph is self-explanatory • Produce rough drafts and seek advice • Adhere to inclusiveness and exclusiveness • Indicate the source of material

5. Pie Chart • A circle that is dissected or sliced from its center point with each slice representing the proportional frequency of a category of a nominal/ordinal variable • Pie charts are especially useful for conveying a sense of fairness, relative size, or inequality among categories

6. Constructing a Pie Chart • To determine the correct size of a “slice,” multiply a category’s proportional frequency by 360 degrees • Use a protractor to cut the pie • Percentages are placed on the pie chart for the sake of clarity

7. Bar Chart • A series of vertical or horizontal bars with the length of a bar representing the percentage frequency of a category of a nominal/ordinal variable • Bar charts are especially useful for conveying a sense of competition among categories

8. Constructing a Bar Chart • Construct on two axes, the abscissa (horizontal) and the ordinate (vertical) • Categories of a variable are situated on one axis, and markings for percentages on the other • To determine the correct bar size for a category, compute its percentage frequency • To compare several groups, use clustered bar charts

9. Frequency Histogram • A 90-degree plot presenting the scores of an interval/ratio variable along the horizontal axis and the frequency of each score in a column parallel to the vertical axis • Similar to a bar chart except that the columns of a histogram touch to account for real limits and the principle of inclusiveness

10. Constructing a Histogram • Draw the horizontal axis and label for X. Draw the vertical axis and label for frequency of cases • Calculate the real limits of each score of X. The width of each column of the histogram will be the same • Draw the columns with the height of a column representing the frequency of scores for a given real limit span of X

11. Frequency Polygon • A 90-degree plot with interval/ratio scores plotted on the horizontal axis and score frequencies depicted by the heights of dots located above scores and connected by straight lines • Polygons portray a sense of trend or movement • Polygons are especially useful for comparing two or more samples

12. Constructing a Polygon • Draw the horizontal axis and label for the variable X. Draw the vertical axis and label for the frequency or percentage of cases • Place dots above the scores X at the height of the frequency or percentage frequency • Connect the dots with straight lines, closing the ends

13. Polygons for Grouped Data • To draw a polygon with grouped data, use the midpoint of a group’s interval of scores for the dot location • The midpoint of a grouped data category is the point halfway between the upper and lower real limits of the interval of scores in the group

14. An Ogive • An ogive is a cumulative frequency polygon • Like any polygon, ogives are used with interval/ratio variables • The points on the horizontal axis of the polygon are values of the lower real limits of each score

15. A Boxplot • A box-and-whiskers plot conveys an interval/ratio variable’s quartiles as well as maximum and minimum scores • Boxplots are handy for identifying outliers • The “whiskers” identify the minimum and maximum scores aside from any outliers