GRAPHICAL DESCRIPTIVE STATISTICS FOR QUALITATIVE, TIME SERIES AND RELATIONAL DATA

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

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

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

Graphical Techniques Qualitative Data Pie Charts Bar Charts

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

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

Example Frequency Distribution of Origin of Car Manufacturer Frequency American16 Asian20 European 4 Relative Frequency

Pie Chart

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

Frequency Bar Chart

Relative Frequency Bar Chart

EXCEL Pie Charts Example 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

Determining Frequency Distributions Step 1 – Record Responses in a Column Record responses recorded in column A

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

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

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

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

Creating a Pie Chart Put in an appropriate title 2. Click Legend Tab

Creating a Pie Chart Uncheck Show legend 2. Click Data Labels Tab

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

Completed Pie Chart

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

EXCEL Bar 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:

Creating a Bar Chart From a Pie Chart 1. 1.Right Mouse Click on graph 2. 2.Select Chart Type 3. Select Column

Resulting Bar Chart

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

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

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

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

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

1. Uncheck Show legend 2. Click Finish

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

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

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

1. Click Chart Wizard 2. Select Scatter Click Next

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

Enter Chart Title Click Next

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

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

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

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

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

Trendline added

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

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