GRAPHICAL DESCRIPTIVE STATISTICS FOR QUALITATIVE, TIME SERIES AND RELATIONAL DATA

1. GRAPHICAL DESCRIPTIVE STATISTICS FOR QUALITATIVE, TIME SERIES AND RELATIONAL DATA

2. Reasons To Collect Data • Obtain Input to a Research Study • Measure Performance • Assist in Formulating Decision Alternatives • Satisfy Curiosity • Knowledge for the Sake of Knowledge

3. Random Variables • Random variables are phenomena or characteristics that are not known in advance • Data are observations of random variables

4. TYPES OF DATA • Qualitative • Result to a survey question is non-numeric • Categorical Data • Ordinal (Ranked) Data • Quantitative • Result to a survey question is a number • Ratio Data – Has an “absolute 0” point, e.g. age • Interval – 0 is simply another number – e.g. degrees Fahrenheit

5. Graphical TechniquesQualitative Data • Pie Charts • Bar Charts

6. Plot of Frequency Distributions • Objective is to develop a frequency distribution table • Hand Count • Excel Approach • COUNTIF command

7. Pie Charts • Determine the relative frequency for each category • Apportion sectors (wedges) of a 360 degree circle proportionately

8. Example Frequency Distribution of Origin of Car Manufacturer Frequency American 16 Asian 20 European 4 Relative Frequency .40 .50 .10

9. Pie Chart

10. Bar Charts • Bars show the frequency or relative frequency of the observations • Consider the same example

11. Frequency Bar Chart

12. Relative Frequency Bar Chart

13. EXCELPie Charts • Example -- 66 people surveyed and asked the color of their car -- Their choices: • Red • Blue • Black • White • Other • These are recorded in cells A2 to A67 of a spreadsheet

14. Record responses recorded in column A Determining Frequency DistributionsStep 1 – Record Responses in a Column

15. Type Categories in Column B Step 2 – Type Categories in another Column

16. =COUNTIF( ) $A$2:$A$67, B2 Where data is located (Drag down) What it should match (Relative Address) Drag down to C3:C6 Step 3 – Use COUNTIF to Determine Frequencies

17. 3. Select this sub-type 1. Go to Chart Wizard 2. Select Pie Click Next Creating a Pie Chart

18. Highlight Cells B1through C6 First Column – Labels Second Column -- Frequencies Click Next Creating a Pie Chart - 2

19. 1. Put in an appropriate title 2. Click Legend Tab Creating a Pie Chart - 3

20. 1. Uncheck Show legend 2. Click Data Labels Tab Creating a Pie Chart - 4

21. Put bullet in Show label and percent Click Finish Creating a Pie Chart - 5

22. Completed Pie Chart

23. Editing Options • Enlarge • Put Labels Inside Wedges • Change Colors • Add Text • Etc.

24. EXCELBar Charts • What we call Bar Charts, Excel calls Column Charts • The steps are similar • If you already have a pie chart, you can convert it to a bar chart as shown on the next slide:

25. Right Mouse Click on graph • Select Chart Type 3. Select Column Creating a Bar Chart From a Pie Chart

26. Resulting Bar Chart

27. Line Charts for Time Series Data • Time series -- Values vs. time • Dow Jones vs. Day • Sales vs. Quarter • Population vs. Year • Typically depicted as line charts • In Excel if you already have a bar chart you can convert it to a line chart using the method on the last slide • Otherwise we do the following

28. 1. Go to Chart Wizard 2. Select Line Click Next Example -- Sales at Epencil.com

29. 2. Click Series Tab 1. Enter Cells with With Sales Figures B2:B8

30. 1. Enter Chart Title 2. Enter Years Cells A2:A8 Click Next

31. 3. Click Legend Tab 1. Enter a label for X-axis 2. Enter a label for Y-axis Note: In this dialogue box, there are many editing features

32. 1. Uncheck Show legend 2. Click Finish

33. Can now edit figure: Resize Delete Gray Background Delete Lines Etc.

34. Scatter Diagrams -- Showing Relationships Between Variables • A scatter diagram shows the relationship between two quantitative variables as a plot of a series of points (observations) • (Grade vs. Study time) • (Sales vs. Advertising $) • (Production vs. Resources) • Types of relations that can be detected • Linear (Positive or Negative) • Least Squares Line -- “Best” line through points • Nonlinear • No Relation

35. Example • Sales of Pencils at Epencil vs. Advertising $ spent during the week

36. 1. Click Chart Wizard 2. Select Scatter Click Next

37. 2. Click Series Tab 1. Enter data columns for both X and Y with the column for X first. Do not include the labels.

38. Enter Chart Title Click Next

39. 1. Uncheck Show legend 2. Click Titles Tab In this dialogue box there are many editing features

40. 1. Enter X-axis Label 2. Enter Y-axis Label Click Finish

41. Can now edit figure: Resize Delete Gray Background Delete Lines Etc.

42. Determining Trend • We can have Excel put the best straight line or other curve (parabola, etc.) through these points so that we can easily observe trend

43. 1. Right mouse click on any data point so that squares appear in the data points 3. Select Type (Usually Linear) 2. Select Add Trendline from the Popup Menu

44. Trendline added

45. How to Lie With Statistics • Graphs can be used to accurately portray data • However, sometimes a graph can be distorted in such a way as to skew the information it conveys • Examples • Fatter or different shaped bars • Stretched or condensed axes • No indication of a “break” on the axis • Unlabeled axes

46. Review • How to construct by hand and by Excel • Pie Charts for Qualitative Data • Bar Charts for Qualitative Data • Line Charts for Time Series Data • Scatter Diagrams to Show Relationships Between Variables • How Graphs Can be Deceptive