Skewness and Curves

10/1/2013

Readings

• Chapter 2 Measuring and Describing Variables (Pollock) (pp.37-44)

• Chapter 6. Foundations of Statistical Inference (128-133) (Pollock)

• Chapter 3 Transforming Variables (Pollock Workbook)

OPPORTUNITIES TO DISCUSS COURSE CONTENT

Office Hours For the Week

• When– Wedesday10-12– Thursday 8-12– And by appointment

Homework

• Chapter 2 – Question 1: A, B, C, D, E– Question 2: B, D, E (this requires a printout)– Question 3: A, B, D– Question 5: A, B, C, D– Question 7: A, B, C, D– Question 8: A, B, C

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.

MEASURES OF DISPERSION

The Normal/Bell Shaped curve

• Symmetrical around the mean

• It has 1 hump, it is located in the middle, so the mean, median, and mode are all the same!

Why we use the normal curve

• To determine skewness

• The Normal Distribution curve is the basis for hypothesis/significance testing

What is skewness?

• an asymmetrical distribution.

• Skewness is also a measure of symmetry,

• Most often, the median is used as a measure of central tendency when data sets are skewed.

A distribution is said to be skewed if the magnitude of (Skewness value/ St. Error of Skew) is greater than 2 (in absolute

value)

World Urban Population

STATISTICAL SIGNIFICANCE

Testing

• Causality

• Statistical Significance

• Practical Significance

Statistical Significance

• A result is called statistically significant if it is unlikely to have occurred by chance

• You use these to establish parameters, so that you can state probability that a parameter falls within a specified range called the confidence interval (chance or not).

• Practical significance says if a variable is important or useful for real-world. Practical significance is putting statistics into words that people can use and understand.

Curves & Significance Testing

What this Tells us

• Roughly 68% of the scores in a sample fall within one standard deviation of the mean

• Roughly 95% of the scores fall 2 standard deviations from the mean (the exact # for 95% is 1.96 s.d)

• Roughly 99% of the scores in the sample fall within three standard deviations of the mean

A Practice Example• Assuming a normal curve compute

the age (value) – For someone who is +1 s.d, from the

mean

– what number is -1 s.d. from the mean

• With this is assumption of normality, what % of cases should roughly fall within this range (+/-1 S.D.)

• What about 2 Standard Deviations, what percent should fall in this range?

Life Expectancy in Latin America and Caribbean

• Compute the estimated values for Average Life Expectancy for +/- 2 standard deviations from the mean.

• With this is assumption of normality, what % of cases should fall within this range (+/-2 s.d).

If you find this amusing or annoying, you get the concept

STANDARD DEVIATION AND CHARTS IN SPSS

Standard Deviation (open GSS)

For Ratio Variables

Step 1

Step 2

Step 3

Step 4

Testing for Skewness

In the Descriptive Command In the Frequencies Command

Click Here

Simple Bar Charts

• In SPSS• OPEN GSS 2008 • Analyze – Descriptive Statistics

• Frequencies

PRINTING OUTPUTS

SPSS Printing

• SPSS outputs can be very large

• Much of the information is useless

• Please be smart in printing outputs

Step 1: Change your settings

Change from portrait to landscape

Step 2: Highlight only the output you want

Step 3: Click on “selected output”

Step 4: Choose ok

Research Design

What is a Research Design

• It is a plan for research

• It guides the researcher through all aspects of the study

What it Includes: Your Unit of Analysis

• Unit of Analysis

• What is it that you are trying to study?

• What kind of data will you need

What it includes: Variables

• The Variables

– Dependent (only 1)

– The Independent(s) (additive)

• How you intend to measure each (operational definitions)

What it Includes: Hypotheses

• What is your null hypotheses for each relationship .

• What are your alternate hypotheses (for each relationship)

• Make sure these hypothesis are “good”

What it includes: Statistical Analysis

• What statistics you plan to use

• And Why

The Goal of A Research Design is to create a study that can demonstrate causality

INTERNAL VALIDITY OF DESIGNWorking for Causality

Internal Validity

• Setting up Research Designs Properly

• Having control over the experiment. Especially the independent variable.

• This can be threatened

Threat 1:History

• You cannot account for all previous knowledge and events

• You cannot control for all potential independent variables

An Example

Threat 2: Maturation

• We get older

• We get wiser

• We get tired (short term)

• These are natural changes

Threat 3: Experimental Mortality

• Participants leave the research study

• The world changes

• Those who remain, may not be like the target group

Threat 4: Selection Bias

• Choosing the wrong sample

• Picking Respondents to favor your results

• Excluding cases or respondents that do not fit your goals

• Using volunteers!

Threat 5: Instrumentation

A Bad Measure Changing a Measure to Fit your Needs

Threat 6: Design Contamination

• People intentionally or unintentionally act differently

• “Instrument Reactivity”

• We Guess the test, we share information

Hawthorne Effect

Which of these are Most Common?

• History

• Maturation

• Selection

• Contamination is the worst!