Graphing Data

The Basics X axisAbscissa Y axis Ordinate About ¾ of the length of the X axis Start at 0

Graphs of Frequency Distributions The Frequency Polygon The Histogram The Bar Graph The Stem-and-Leaf Plot

The Frequency Polygon Xf To convert a frequency distribution table into a frequency polygon: 1.Put your X values on the X axis (the abscissa). 2.Find the highest frequency and use it to determine the highest value for the Y axis. 3.For each X value go up and make a dot at the corresponding frequency. 4.Connect the dots.

The Frequency Polygon

The Histogram Follow the same steps for creating a frequency polygon. Instead of connecting the dots, draw a bar extending from each dot down to the X axis. A histogram is not the same as a bar graph, there should be no gaps between the bars in a histogram (there should be no gaps in the data).

The Histogram

Grouped Frequency Distributions We can group the previous data into a smaller number of categories and produce simpler graphs Use the midpoint of the category for your dot XMPf

Grouped Frequency Polygon

Grouped Frequency Histogram

Relative Frequency Polygon BPMMPf%age % % % % % % % % % Use the following formula to find out what percentage of scores falls in each category: Use the percentage on your Y axis instead of the frequency.

Relative Frequency Polygon

Relative Frequency Histogram

Notice:

So what’s the point? Graphs of relative frequency allow us to compare groups (samples) of unequal size. Much of statistical analysis involves comparing groups, so this is a useful transformation.

Activity #1 A researcher is interested in seeing if college graduates are less satisfied with a ditch-digging job than non- graduates. Because of the small number of college graduates digging ditches, the researcher could not get as many college graduate participants. Below are the scores on a job satisfaction survey for each group (possible values are 0 – 30, 30 being the most satisfied): College: 11, 3, 5, 12, 18, 6, 4, 1, 2, 6, 2, 17, 12, 10, 8, 3, 9, 9 No College: 19, 3, 15, 11, 13, 12, 12, 9, 2, 6, 21, 15, 11, 8, 6, 25, 17, 1, 14, 15, 9, 7, 20, 4, 2, 19, 7, 12

Activity #1 College: 11, 3, 5, 12, 18, 6, 4, 1, 2, 6, 2, 17, 12, 10, 8, 3, 9, 9 No College: 19, 3, 15, 11, 13, 12, 12, 9, 2, 6, 21, 15, 11, 8, 6, 25, 17, 1, 14, 15, 9, 7, 20, 4, 2, 19, 7, 12 1.Create a frequency distribution table with about 10 categories (for each group) 2.Convert the frequency to relative frequency (percentage) 3.Construct a relative frequency polygon for each group on the same graph (see p. 43 for an example) 4.Put your name on your paper.

Cumulative Frequency Polygon BPMfCum f Create a column for cumulative frequency and make the Cum f value equal to the frequency plus the previous Cum f value (see ch. 3 for a review) 2.Plot the resulting values just as you did for a frequency distribution polygon

Cumulative Frequency Polygon

Cumulative Percentage Polygon 1.Using cumulative frequency data, calculate the cumulative percentage data. 2.Make your Y axis go to 100% 3.Plot the data as normal. BPMfCum fCum %age 57000% 58111% 59011% 60232% 61143% 62485% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %

Cumulative Percentage Polygon

The Normal Curve

Skewed Curves

Bar Graph Used when you have nominal data. Just like a frequency distribution diagram, it displays the frequency of occurrences in each category. But the category order is arbitrary.

Example The number of each of 5 different kinds of soda sold by a vendor at a football stadium. Sodaf Coke498 Diet Coke387 Sprite254 Root Beer278 Mr. Pibb193

Bar Graph

Line Graphs Line graphs are useful for plotting data across sessions (very common in behavior analysis). The mean or some other summary measure from each session is sometimes used instead of raw scores (X). The line between points implies continuity, so make sure that your data can be interpreted in this way.

Example Rats are trained to perform a chain of behavior and then divided into two groups: drug and placebo. The average number of chains performed each minute is plotted across sessions. SessionDrugPlacebo

Line Graph Example

Venn Diagrams Not in your book, but make sure you understand the basics.

Example Classes Dorm Sports Freda’s Friends

Goal of Making Graphs

What not to do…

What’s wrong with this graph?

Activity #2 Work with a group and fix these 3 graphs:

Homework Prepare for Quiz 4 Read Chapter 5 Finish Chapter 4 Homework (check WebCT/website)