Statistics 270 Lecture 1

Today

• Course outline

• Introductory to statistics

• Some Definitions

• Descriptive statistics

Introduction

• What is statistics?

• Discipline which deals with the collection, organization and interpretation of data.

• Done to answer questions of interest.

Example (Pain Reduction and Reiki)

• Is Reiki an effective pain management tool?

• Reiki treatment is touch therapy used as an alternative to pain medication.

• A pilot study involving 20 volunteers experiencing pain was conducted.

• All treatments were provided by a certified Reiki therapist.

• Pain was measured using before and after the Reiki treatment.

• If study was repeated, would we see the same results?

Example (Saving for Retirement)

• What are the attitudes of low wage earners about saving for retirement?

• Americans earning $35,000 or less were asked how they are likely to accumulate enough money to retire.

• What are the data?

Some Definitions

• Interested in something about a population.

• Population is a collection of individuals.

• Describe individuals with data.

• Data sets contain information/facts relating to individuals.

• A variables are attributes of an individual (e.g., hair color, pain severity, ...).

• Distribution of a variable gives the values the variable can take and how often it takes on each value

Some Definitions

• Can measure individuals a single time (e.g., weight) to get a univariate data set

• Can measure several variables per individual – multi-variate data

• Would like to measure a sample of indivuduals to make inference about the population – inferential statistics

Types of Variables

• Two types of variable:• Quantitative Variables take on numeric values for which

addition and averaging make sense (height, weight, income,…).

• Qualitative Variables: each individual falls into a category (ethnicity, machine works or does not, …).

• Hair color:

• Color preference (red=1, blue=2, green=3):

• Length of time slept:

• Will first focus on descriptive statistics (graphical and numeric).

• Will move on to inferential statistics (test hypotheses).

• In either case, statistical tools are used to describe data and help answer scientific questions.

Descriptive Statistics

• Want to describe or summarize data in a clear and concise way.

• Two basic methods: graphical and numerical.

Graphical Descriptions of Data

• Often, pictures tells entire story of data.

• Have different plots for the different sorts of variables.

• For Qualitative variables, will use bar-plots and pie charts.

Bar Charts

• Variable values are the category labels (typically placed along the x-axis)

• Heights of bar is the count (percentage) of values falling in that category.

• Note bars are the same width!

0

20

40

60

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100

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t. 1

Ca

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Countor %

Example(retirement savings)

• A USA Today (Jan. 4, 2000) poll asked Americans who earn $35,000 or less how they expected to accumulate a $500,000 retirement nest-egg.

• The results are summarized in the frequency table below:

Response Count

Lottery 4000

Save and invest 3000

Do not know 1400

Inherit Money 1200

Lawsuit or insurance claim 400

Retirement Savings Example

0

1000

2000

3000

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5000

Lotery Save Do notknow

Inherit Lawsuit

Response

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ts

Bar Chart for Ret. Savings Example

05

1015202530354045

Lotery Save Do notknow

Inherit Law suit

Response

Pe

rce

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Bar Chart for Ret. Savings Example

-500

500

1500

2500

3500

4500

Lote

rySav

e

Do no

t kno

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Inhe

rit

Lawsu

it

Response

Co

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Pie Charts

• Variable values are the category labels

• Each category must appear on the plot

• Percentage of area of pie covered by pie is relative frequency or percent) of values falling in that category.

• Can easily see percentage for each category

• Note Less flexible than bar chart

East10%

West 25%

North 45%

South20% East

West

North

South

Lottery40%

Save 30%

Don't Know14%

Inherit12%

Lawsuit4%

Lottery

Save

Don't Know

Inherit

Lawsuit