BUS7010 Quant Prep Statistics in Business and Economics

BUS7010 Quant PrepStatistics in Business and Economics

Week 5Dr. Jenne Meyer

Discovering Statistics

Field of statistics regarded as dry, too antiseptic and unfeeling

Dispel this misapprehension by sharing these data stories with you

Individual people speaking from behind the numbers

Example 1.1: The reasons Katrina survivors did not evacuate

Hurricane Katrina was the costliest and one of the deadliest hurricanes in American history. Damages exceeded $50 billion and fatalities exceeded 1300, according to the National Oceanic and Atmospheric Administration. In September 2005, a survey was conducted of a group of hurricane survivors who had later been moved to shelters in the Greater Houston area. The respondents who did not evacuate were asked what was their most important reason for not evacuating.

Example 1.1 continued

Katrina survivors’ reasons for not evacuating.

Example 1.1 continued

Katrina survivors’ most important reasons for not evacuating

Example The ballot that changed history

Look at the accompanying illustration. Do you find this 2000 presidential election ballot confusing? There is evidence that many Palm Beach County, Florida, residents did find the ballot confusing.

Example The ballot that changed historyAccording to the Palm Beach Post,

confused voters marked more than one choice on the “butterfly ballot.”

Gore likely lost 6607 votes because of these ballots.

Example The ballot that changed historyEvidence that many confused Palm Beach County voters chose Reform Party candidate Pat Buchanan by mistake.

What Is Statistics?

Informal meaning of statistic-number that describes a person, a group, or a set of items. According to a recent survey, 54% of the

men surveyed responded that they believed in aliens, and 33% of the women did.

How else are we exposed to statistics?

Definition of Statistics?

Statistics is the art and science of collecting, analyzing, presenting, and interpreting data.

Relevance of statistics to today’s college student A business major interested in diversifying

her portfolio to stocks based on their price/earnings ratio.

A psychology major interested in whether there are differences in therapeutic outcomes between traditional counseling methods and a new cognitive approach.

An education major interested in whether listening to a Mozart sonata before taking an exam can significantly improve a grade.

Case Study - Does Friday the 13th Change Human Behavior?

How would researchers go about studying whether superstitions change the way people behave? What kind of evidence would support the hypothesis that Friday the 13th causes a change in human behavior?

Case Study - Does Friday the 13th Change Human Behavior?

T. J. Scanlon and his co-researchers thought that if there were fewer vehicles on the road on Friday the 13th than on the previous Friday, this would be evidence that some people were playing it safe on Friday the 13th and staying off the roads.

What they deemed important is the effect of such a superstition on human behavior and how to measure such an effect as a change in behavior.

Case Study - Does Friday the 13th Change Human Behavior?

Phase 1 Data collection.

Select method to collect the data.

Obtained data kept by the British Department of Transport on the traffic flow through certain junctions of the M25 motorway in England.

Case Study - Does Friday the 13th Change Human Behavior?

Phase 2 Data analysis.

Determine ways to analyze the data.

Compared the number of vehicles passing through certain junctions on the M25 motorway on Friday the 13th and the previous Friday during 1990, 1991, and 1992.

Case Study - Does Friday the 13th Change Human Behavior?

Table 1.3 Traffic through M25 junctions, 1990–1992

Case Study - Does Friday the 13th Change Human Behavior?

Case Study - Does Friday the 13th Change Human Behavior?

Phase 3 Data presentation Presentation of the results importantResearchers found a highly

respectable journal, the British Medical Journal, in which to publish their findings.

Other methods: delivering a talk at a conference, writing up a report for one’s supervisor, or presenting a class project.

Case Study - Does Friday the 13th Change Human Behavior?

Phase 4 Data interpretationResults should be understandable to

non-statisticians. In this case, researchers chose

decrease in number of vehicles as the criterion on which to base support for their hypothesis that people changed their behavior on Friday the 13th.

Consistent decrease in traffic on Friday the 13th supports hypothesis.

Descriptive Statistics

Refers to methods for summarizing and organizing the information in a data set.

We use numbers (such as counts and percents) and graphics to describe the data set, as a first step in data analysis.

Elements, Variables, and ObservationsAn element is a specific entity for

which information is collected.

A variable is a characteristic of an element, which can assume different values for different elements.

An observation is the set of values of the variables for a given element.

Qualitative Variable

Is a variable that does not have a numeric value but is classified into categories.

Qualitative variables are also called categorical variables, because they

can be grouped into categories.

Quantitative Variable

A quantitative variable is a variable that takes numeric values.

Quantitative variables can be classified as either discrete or continuous.

Discrete or Continuous Variables A discrete variable can take either a

finite or a countable number of values.

Each value can be graphed as a separate point on a number line, with space between each point.

A continuous variable can take infinitely many values, forming an interval on the number line, with no space between the points.

Levels of Measurement Nominal – names, labels, or categories. No

natural or obvious ordering of nominal data (such as high to low)

Ordinal – arranged in a particular order, no arithmetic can be performed on ordinal data, ie poor, satisfactory, good, or best.

Interval – Same as ordinal data, has the extra property that subtraction may be carried out on interval data, “no natural zero”, high temperatures in the city of Pompey’s Pillar, Montana for the month of December.

Ratio – similar to interval data, division may be carried out, natural zero exists, example salaries of college professors.

Inferential Statistics - How Do We Get There from Here?

Descriptive methods of data analysis are widespread and quite informative.

The modern field of statistics involves much more than simply summarizing a data set.

A sample is a subset of a population.

Statistical inference

Learning about the characteristics of a population by studying those characteristics in a subset of the population (that is, in a sample)

Why Sample?

Why Sample…

TimeCostDestructive nature of samplingAccess to sampleSampling is good enough

Normal Distribution of Sample

Attributes or characteristics of the population are generally normally distributed.

For instance, when attributes such as height and weight are considered, most people will be clustered around the mean, leaving only a small number at the extremes who are either very tall or very short

Key Questions for Sampling What is the relevant target population of

focus to the study? What exactly are the parameters we are

interested in investigating? What kind of a sampling frame is

available? What is the sample size needed? What costs are attached to the sampling

design? How much time is available to collect the

data from the sample?

Sampling Methods

Simple random sample Systematic sampling (every nth one) Stratified random sampling (random

samples from segments) Cluster sampling (random clusters) Area sampling Convenience sampling Quotas

Types of questions:

Administrative – self identifying, usually comes from the company

Classification – demographic infoTarget questions Structured – closed-ended Unstructured – open-ended

Review types of Data Collection Methods Surveys (paper, online, in person,

mail in) InterviewsFocus GroupsEthnographyObservationCase studyContent analysisOmnibus survey **

Question Content CriteriaShould this question be asked? Is the questions of proper scope and

coverage?Can the participant adequately

answer this question as asked?Will the participant willingly answer

this question, as asked?

Common Wording ProblemsVague or ambiguous terminologyTechnical terminologyHypothetical questions – must be

reasonable for meaningful answersLeading questions (Would you agree

the government’s policies on healthcare are unfair?), would you agree, do you agree questions…

Value judgments – do not express your views

Context effects – be aware of the impact of surrounding questions on your target item (drinking last week and health behaviors)

Double-barreled questions – ask one question only

Hidden assumptions – (when did you stop drinking and driving?)

Social desirability – respondents like to present themselves in a positive manner – would you say no to charitable giving?

Sensitive issues/questions – (death, sex, religion)

Cultural/Lingua Wording ProblemsGM took a step back when it tried to

market the NOVA in Central and South America. In Spanish, “No va” means “it doesn’t go.”

Pepsi’s “Come Alive With the Pepsi Generation,” when translated into Chinese, means “Pepsi brings Your Ancestors From the Grave.”

Frank Perdue’s chicken slogan, “It takes a strong man to make a tender chicken” translates in Spanish to, “It takes an aroused man to make a chicken affectionate.”

When American Airlines wanted to advertise its new leather first-class seats to Mexico, its “Fly in Leather” campaign would have literally translated to “Fly Naked” in Spanish.

The “Got Milk?” in Spanish would translate to “Are you lactating?”

Types of Info Gleaned:

DemographicBehavioralAttitudes and opinionsKnowledge Intentions, expectations, and

aspirations

Experimental Studies

Conducted when a survey or sampling methods cannot be used.

Researchers investigate how varying the predictor variable affects the response variable

A predictor variable (or explanatory variable)is a characteristic purported to explain differences in the response variable.

Treatment - predictor variable that takes the form of a purposeful intervention

Designing an Experimental StudyThree main factors:

Control

Randomization

Replication

Observational Studies

Used when an experimental study is not possible for ethical reasons

Observes whether the subjects’ differences in the predictor variable are associated with differences in the response variable

No attempt to manipulate the variables

Example 1.15 - Secondhand smoking and illness in children

A 2006 Surgeon General’s report found that “the evidence is sufficient to infer a causal relationship” between secondhand tobacco smoke exposure from parental smoking and respiratory illnesses in infants and children. Was this report based on an experimental study or an observational study?

Example 1.15 continued

Solution

Unethical to force the parents of a treatment group to smoke tobacco

The study must have been an observational one