Agresti/Franklin Statistics, 1 of 33 Enrollment Fall 2005 (all students) ClassificationMenWomenTotal...

Agresti/Franklin Statistics, 1 of 33

Enrollment Fall 2005 (all students)

Classification Men Women Total

Undergraduate1,533(52%)

1,416(48%)

2,949

Professional* 17 22 39

Graduate 1,285 698 1,983

Master 505 276 781

Doctoral 780 422 1,202

Total2 2,835 2,136 4,971


Geographic Origin3 (Fall 2005)

Undergraduates* Graduates Total

Master Doctoral

Texas1,532

(51.3%)474 482 2,488

Other U.S.1,320

(44.2%)157 178 1,655

International96

(3.2%)123 521 740

Not Designated40

(1.3%)27 21 88

Total 2,988 781 1,202 4,971


Student Demographics (Fall 2005)

Undergrad Grad

# % Master % Doctoral %

Architecture 126 4% 74 9% 1 1%

Engineering 751 25% 36 5% 464 39%

Humanities 559 19% 16 2% 175 14%

Management -- 0% 471 60% -- 0%

Music 128 4% 123 16% 39 3%

Natural Sciences 704 23% 29 4% 346 29%

Social Sciences 693 23% -- 0% 135 11%

Interdisciplinary 21 1% -- 0% 42 3%

Continuing Studies -- 0% 32 4% -- 0%

Unclassified 6 1% -- 0% -- 0%

Total 2,988 781 1,202 100%


Chapter 1Statistics: The Art and Science of

Learning from Data

Learn ….

What Statistics Is

Why Statistics Is Important


Chapter 1

Learn…

How Data is Collected

How Data is Used to Make

Predictions


Section 1.1

How Can You Investigate using Data?


Health Study

Does a low-carbohydrate diet result in significant weight loss?


Market Analysis

Are people more likely to stop at a Starbucks if they’ve seen a recent TV advertisement for their coffee?


Heart Health

Does regular aspirin intake reduce deaths from heart attacks?


Cancer Research

Are smokers more likely than non-smokers to develop lung cancer?


To search for answers to these questions, we…

Design experiments

Conduct surveys

Gather data


Statistics is the art and science of:

Designing studies Analyzing data Translating data into knowledge and

understanding of the world


Example from the National Opinion Center at the University of Chicago:

General Social Survey (GSS) provides data about the American public

Survey of about 2000 adult Americans


Example from GSS: Do you believe in life after death?


Three Main Aspects of Statistics

Design

Description

Inference


Design

How to conduct the experiment

How to select the people for the survey


Description

Summarize the raw data

Present the data in a useful format


Inference

Make decisions or predictions based on the data.


Example: Harvard Medical School study of Aspirin and Heart attacks

Study participants were divided into two groups• Group 1: assigned to take aspirin

• Group 2: assigned to take a placebo



Results: the percentage of each group that had heart attacks during the study:

0.9% for those taking aspirin 1.7% for those taking placebo



Can you conclude that it is beneficial for people to take aspiring regularly?



Section 1.2

We Learn About Populations Using Samples


Subjects

The entities that we measure in a study

Subjects could be individuals, schools, countries, days,…


Population and Sample

Population: All subjects of interest

Sample: Subset of the population for whom we have data


Geographic Origin (Fall 2005)

Undergraduates* Graduates Total

Master Doctoral

Texas1,532

(51.3%)474 482 2,488

Other U.S.1,320

(44.2%)157 178 1,655

International96

(3.2%)123 521 740

Not Designated40

(1.3%)27 21 88

Total 2,988 781 1,202 4,971


Enrollment Fall 2005

Classification Men Women Total

Undergraduate1,533(52%)

1,416(48%)

2,949

Professional* 17 22 39

Graduate 1,285 698 1,983

Master 505 276 781

Doctoral 780 422 1,202

Total2 2,835 2,136 4,971


Majors (Fall 2005)Undergrad Grad

# % Master % Doctoral %

Architecture 126 4% 74 9% 1 1%

Engineering 751 25% 36 5% 464 39%

Humanities 559 19% 16 2% 175 14%

Management -- 0% 471 60% -- 0%

Music 128 4% 123 16% 39 3%

Natural Sciences 704 23% 29 4% 346 29%

Social Sciences 693 23% -- 0% 135 11%

Interdisciplinary 21 1% -- 0% 42 3%

Continuing Studies

-- 0% 32 4% -- 0%

Unclassified 6 1% -- 0% -- 0%

Total 2,988 781 1,202 100%


Example Format

• Picture the Scenario

• Question to Explore

• Think it Through

• Insight

• Practice the concept


Example: The Sample and the Population for an Exit Poll

In California in 2003, a special election was held to consider whether Governor Gray Davis should be recalled from office.

An exit poll sampled 3160 of the 8 million people who voted.


What’s the sample and the

population for this exit poll?

The population was the 8 million people who voted in the election.

The sample was the 3160 voters who were interviewed in the exit poll.

Example: The Sample and the Population for an Exit PollExample: The Sample and the Population for an Exit Poll


Descriptive Statistics

Methods for summarizing data

Summaries usually consist of graphs and numerical summaries of the data


Types of U.S. Households


Inference

Methods of making decisions or predictions about a populations based on sample information.


Parameter and Statistic

A parameter is a numerical summary of the population

A statistic is a numerical summary of a sample taken from the population


Randomness

Simple Random Sampling: each subject in the population has the same chance of being included in that sample

Randomness is crucial to experimentation


Variability

Measurements vary from person to person

Measurements vary from sample to sample


a. To describe whether a sample has more females or males.

b. To reduce a data file to easily understood summaries.

c. To make predictions about populations using sample data.

d. To predict the sample data we will get when we know the population.

Inferential Statistics are used:


Chapter 2Exploring Data with Graphs and

Numerical Summaries

Learn ….The Different Types of Data

The Use of Graphs to Describe Data

The Numerical Methods of Summarizing Data


Section 2.1

What are the Types of Data?


In Every Statistical Study:

Questions are posed

Characteristics are observed


Characteristics are Variables

A Variable is any characteristic that is recorded for subjects in the study


Variation in Data

The terminology variable highlights the fact that data values vary.


Example: Students in a Statistics Class

Variables:• Age

• GPA

• Major

• Smoking Status

• …


Data values are called observations

Each observation can be:

• Quantitative

• Categorical


Categorical Variable

Each observation belongs to one of a set of categories

Examples:• Gender (Male or Female)

• Religious Affiliation (Catholic, Jewish, …)

• Place of residence (Apt, Condo, …)

• Belief in Life After Death (Yes or No)


Quantitative Variable

Observations take numerical values

Examples:• Age

• Number of siblings

• Annual Income

• Number of years of education completed


Graphs and Numerical Summaries

Describe the main features of a variable

For Quantitative variables: key features are center and spread

For Categorical variables: key feature is the percentage in each of the categories


Quantitative Variables

Discrete Quantitative Variables

and

Continuous Quantitative Variables


Discrete

A quantitative variable is discrete if its possible values form a set of separate numbers such as 0, 1, 2, 3, …


Examples of discrete variables

Number of pets in a household Number of children in a family Number of foreign languages spoken


Continuous

A quantitative variable is continuous if its possible values form an interval


Examples of Continuous Variables

Height Weight Age Amount of time it takes to complete

an assignment


Frequency Table

A method of organizing data

Lists all possible values for a variable along with the number of observations for each value


Example: Shark Attacks



What is the variable?

Is it categorical or quantitative?

How is the proportion for Florida calculated?

How is the % for Florida calculated?



Insights – what the data tells us about shark attacks



Identify the following variable as categorical or quantitative:

Choice of diet (vegetarian or non-vegetarian):

a. Categorical

b. Quantitative


Number of people you have known who have been elected to political office:

a. Categorical

b. Quantitative

Identify the following variable as categorical or quantitative:


Identify the following variable as discrete or continuous:

The number of people in line at a box office to purchase theater tickets:

a. Continuous

b. Discrete


The weight of a dog:

a. Continuous

b. Discrete

Identify the following variable as discrete or continuous:


Section 2.2

How Can We Describe Data Using Graphical Summaries?


Graphs for Categorical Data

Pie Chart: A circle having a “slice of pie” for each category

Bar Graph: A graph that displays a vertical bar for each category


Example: Sources of Electricity Use in the U.S. and Canada


Pie Chart


Bar Chart


Pie Chart vs. Bar Chart

Which graph do you prefer? Why?


Graphs for Quantitative Data

Dot Plot: shows a dot for each observation

Stem-and-Leaf Plot: portrays the individual observations

Histogram: uses bars to portray the data


Example: Sodium and Sugar Amounts in Cereals


Dotplot for Sodium in Cereals

Sodium Data:

0 210 260 125 220 290 210 140 220 200 125 170 250 150 170 70 230 200 290 180


Stem-and-Leaf Plot for Sodium in Cereal

Sodium Data:

0 210

260 125

220 290

210 140

220 200

125 170

250 150

170 70

230 200

290 180


Frequency Table

Sodium Data: 0 210

260 125220 290210 140220 200125 170250 150170 70230 200290 180


Histogram for Sodium in Cereals


Which Graph?

Dot-plot and stem-and-leaf plot:• More useful for small data sets

• Data values are retained

Histogram• More useful for large data sets

• Most compact display

• More flexibility in defining intervals


Shape of a Distribution

Overall pattern• Clusters?

• Outliers?

• Symmetric?

• Skewed?

• Unimodal?

• Bimodal?


Symmetric or Skewed ?


Example: Hours of TV Watching


Identify the minimum and maximum sugar values:

a. 2 and 14 b. 1 and 3

c. 1 and 15 d. 0 and 16


Consider a data set containing IQ scores for the general public:

What shape would you expect a histogram of this data set to have?

a. Symmetric

b. Skewed to the left

c. Skewed to the right

d. Bimodal


Consider a data set of the scores of students on a very easy exam in which most score very well but a few score very poorly:

What shape would you expect a histogram of this data set to have?

a. Symmetric

b. Skewed to the left

c. Skewed to the right

d. Bimodal

Agresti/Franklin Statistics, 1 of 33 Enrollment Fall 2005 (all students) ClassificationMenWomenTotal...

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