variables 9/12/2013. readings chapter 2 measuring and describing variables (pollock) (pp.32-33)...
TRANSCRIPT
Variables
9/12/2013
Readings
• Chapter 2 Measuring and Describing Variables (Pollock) (pp.32-33)
• Chapter 2 Descriptive Statistics (Pollock Workbook)
Exam 1 9/19
• Exam 1 9/19
• In class exam. You do not need an exam book
• You can use a basic calculator
OPPORTUNITIES TO DISCUSS COURSE CONTENT
Office Hours For the Week
• When– Monday and Friday 10-12:00– Tuesday 8-12– And by appointment
Course Learning Objectives
1. Students will learn the basics of research design and be able to critically analyze the advantages and disadvantages of different types of design.
2. Students Will be able to interpret and explain empirical data.
Variables
Variables
• Measured Concepts
• We need to operationalize concepts to test hypotheses
• Concept- Conceptual Definition- Operational-Definition- Operationalization- Variable
Four Categories of Variables
Categorical
Nominal• Name
• And provide value
Ordinal• Name
• Provide value
• And Order
CONTINUOUS VARIABLES
What makes them unique
• The values matter
• Your variable includes all possible values, not just the one’s that you assign.
• Name, order, and the distances between values matter.
Interval Level Variables
• The values matter at this level
• The distances matter
• The zero is arbitrary
Examples of Interval Scales
Ratio Variables
• The Full properties of numbers.
• Its measurement on Steroids
• A zero means the absence of a property
• Classify, order, set units of distance
Examples
Energy Use
Nominal, Ordinal, Ratio
Crime By Region
DESCRIPTIVE STATISTICS
Descriptive Statistics
• These simply describe the attributes of a single variable.
• You cannot test here (you need two variables)
• Why do them?
Categories of Descriptive Statistics
Measures of Central Tendency• The most common, the
middle, the average
• Mean, Median and Mode
Measures of Dispersion• How wide is our range of
data, how close to the middle are the values distributed
• Range, Variance, Standard Deviation
Frequency Distributions• This Provides counts and percentages (relative
frequencies) of the values for a given variable
• Computing a relative Frequency
• The Cumulative Percent is percentage of observations less than or equal to the category
• St. Edward’s Data
Lets Look at this one again
The Largest Hispanic Groups in America: Pie Charts
Immigration- Column/Bar Charts
The Mode
• the most frequent observation of the variable in a distribution
• Which category is most common
• There can be more than 1
Examples
• What are the Modes here?
1. 110,105.100.100.100.100.99.982. 110.105.105.105.100.95.95.95.90
Advantages and Disadvantages
• Advantages of the Mode
• Disadvantages of the Mode
Where Parties Should Go in A Normal Distribution
They Move To the Center, why?
What About A Bimodal Distribution?
Party Polarization
A polymodal System
THE MEDIAN
The Median
• It only tells us one thing– 50% above, 50% below
• the value that lies in the middle of the data when arranged in ascending order.
Examples
• The University of Texas
• The 78704 Zip Code
About the Median
• Characteristics and problems of the median
• The middle observation = (N+1)/2
• Three Examples – (133,113,112,95,94) – (27,12,78,104,45,34) – (105,102,101,92,91,80)
Locating the Median
Finding the Median
• location of median case (1747+1)/2 = 874 • Where Does that case fall?
– Case 1 through 534 = has value of 0 – Case 535 through 1747 = has value of 1
• Case 874 is more than 535 and less than 1747 • THE MEDIAN IS 1, the category is voted
You can also look here for where 50% falls
Lets Try Again
The Answer• location of median case
(1454+1)/2 = 727.5• Where Does that case
fall? Cases 1 through 74 = has value of 1 Cases 75 through 502= has value of 2Cases 503 through 1454= as a value of 3
• Case 727.5 is more than 503
THE MEDIAN IS 3, the category is not at all scientific
The 50% falls in here
Median Voter Theory
THE MEAN
The Mean
• What is it
• How do you compute it?
About the Mean
• Characteristics of the Mean
• Problems of the Mean
An Example
Name Income
Skipper 50.00
Gilligan 150.00
Mary Ann 150.00
Professor 400.00
Mrs. Howell 500.00
Mr. Howell 1000.00
Ginger 3000.00
Picking the Right Measure
Measure Level of AnalysisMode Nominal, Ordinal, Ratio, IntervalMedian Ordinal, Ratio, Interval
Mean Ratio, interval (sometimes ordinal, but super statistics nerds will say no)