1. Graphing Data

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

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

4. The Frequency Polygon Xf 570 581 590 602 611 624 634 643 657 662 679 687 698 708 7111 7214 7313 7412 756 769 776 784 796 802 813 821 830 840 852 860 871 880 890 900 910 920 931 940 950 960 970 981 990 1001 1010 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.

5. The Frequency Polygon

6. 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).

7. The Histogram

8. 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 57-61594 62-666420 67-716943 72-767454 77-817921 82-86843 87-91891 92-96941 97-101992

9. Grouped Frequency Polygon

10. Grouped Frequency Histogram

11. Relative Frequency Polygon BPMMPf%age 57-615943% 62-66642013% 67-71694329% 72-76745436% 77-81792114% 82-868432% 87-918911% 92-969411% 97-1019921% 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.

12. Relative Frequency Polygon

13. Relative Frequency Histogram

14. Notice:

15. 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.

16. 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

17. 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.

18. Cumulative Frequency Polygon BPMfCum f 5700 5811 5901 6023 6114 6248 63412 64315 65722 66224 67933 68740 69848 70856 711167 721481 731394 7412106 756112 769121 776127 784131 796137 802139 813142 821143 830143 840143 852145 860145 871146 880146 890146 900146 910146 920146 931147 940147 950147 960147 970147 981148 990148 1001149 1010149 1.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

19. Cumulative Frequency Polygon

20. 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% 634128% 6431510% 6572215% 6622416% 6793322% 6874027% 6984832% 7085638% 71116745% 72148154% 73139463% 741210671% 75611275% 76912181% 77612785% 78413188% 79613792% 80213993% 81314295% 82114396% 83014396% 84014396% 85214597% 86014597% 87114698% 88014698% 89014698% 90014698% 91014698% 92014698% 93114799% 94014799% 95014799% 96014799% 97014799% 98114899% 99014899% 1001149100% 1010149100%

21. Cumulative Percentage Polygon

22. The Normal Curve

23. Skewed Curves

24. 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.

25. 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

26. Bar Graph

27. 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.

28. 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 11412 21715 31614 41916 52116 62217 72316 82518 92417 102419

29. Line Graph Example

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

31. Example Classes Dorm Sports Freda’s Friends

32. Goal of Making Graphs

33. What not to do…

39. What’s wrong with this graph?

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

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