Quantitative Representation - Statistics - Lecture Slides, Slides of Statistics

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Descriptive Statistics:

Quantitative Representation

n Crosstabulation and Scatter Diagram

Exploratory Data Analysis

 The techniques of exploratory data analysis consist of simple arithmetic and easy-to-draw pictures that can be used to summarize data quickly.

Crosstabulation

 The left and top margin labels define the classes for the two variables.

 Crosstabulation can be used when:

• one variable is qualitative and the other is quantitative,
• both variables are qualitative, or
• both variables are quantitative.

 A crosstabulation is a tabular summary of data for two variables.

Price Range Colonial Log Split A-Frame Total

< $200,

$200,

45

Total 30 20 35 15 100

Home Style

Crosstabulation

 Example: Finger Lakes Homes

quantitative variable

categorical variable

The number of Finger Lakes homes sold for each style and price for the past two years is shown below.

Price Range Colonial Log Split A-Frame Total

< $200,

$200,

45

Total 30 20 35 15 100

Home Style

Crosstabulation

Frequency distribution for the price range variable

Frequency distribution for the home style variable

 Example: Finger Lakes Homes

Crosstabulation: Row or Column

Percentages

Converting the entries in the table into row

percentages or column percentages can

provide additional insight about the

relationship between the two variables.

Price Range (^) Colonial Log Split A-Frame

< $200,

$200,

Home Style

Total 100 100 100 100

(Colonial and > $200K)/(All Colonial) x 100 = (12/30) x 100

Crosstabulation: Column Percentages

 Example: Finger Lakes Homes

Crosstabulation: Simpson’s Paradox

 In some cases the conclusions based upon an aggregated crosstabulation can be completely reversed if we look at the unaggregated data. The reversal of conclusions based on aggregate and unaggregated data is called Simpson’s paradox.

 We must be careful in drawing conclusions about the relationship between the two variables in the aggregated crosstabulation.

 Data in two or more crosstabulations are often aggregated to produce a summary crosstabulation.

Scatter Diagram

A Positive Relationship

x

y

Scatter Diagram

A Negative Relationship

x

y

Scatter Diagram

Example: Panthers Football Team

x = Number of Interceptions

y = Number of Points Scored

The Panthers football team is interested in investigating the relationship, if any, between interceptions made and points scored.

Scatter Diagram

y

x

Number of Interceptions

Number of Points Scored

Scatter Diagram for the Panthers

0

5

10

15

20

25

30

35

0 1 2 3 4 Number of Interceptions

Number of Points Scored.

Scatter Diagram and Trendline

Tabular and Graphical Methods

Categorical Data Quantitative Data

Tabular Methods

Tabular Methods

Graphical Methods

Graphical Methods

• Frequency Distribution
• Rel. Freq. Dist.
• Percent Freq. Distribution
• Crosstabulation
  • Bar Chart
  • Pie Chart
    • Frequency Distribution
    • Rel. Freq. Dist.
    • % Freq. Dist.
    • Cum. Freq. Dist.
    • Cum. Rel. Freq. Distribution
    • Cum. % Freq. Distribution
    • Crosstabulation
      • Dot Plot
      • Histogram
      • Ogive
      • Stem-and- Leaf Display
      • Scatter Diagram

Data