St at is t ic s 270 Lec t ure 1

Today

• Course outline

• Introductory to statistics

• Some Definitions

• Descriptive statistics

In t roduc t ion

• What is statistics?

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

• Done to answer questions of interest.

Ex am ple (Pain Reduc t ion and Reik i )

• 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.

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

Ex am ple (Saving for Ret i rem ent )

• 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?

Som e Def in i t ions

• 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

Som e Def in i t ions

• 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 Var iab les

• 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.

Desc r ip t ive St at is t ic s

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

• Two basic methods: graphical and numerical.

Graphic a l Desc r ip t ions of Dat a

• 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 Char t s

• 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

80

100

Ca

t. 1

Ca

t. 2

Ca

t. 3

Co u n to r %

Ex am ple(ret i rem ent sav ings)

• 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:

R e s p o n s e C o u n t

L o t t e r y 4 0 0 0

S a v e a n d i n v e s t 3 0 0 0

D o n o t k n o w 1 4 0 0

I n h e r i t M o n e y 1 2 0 0

L a w s u i t o r i n s u r a n c e c l a i m 4 0 0

Retirement Savings Example

0

1000

2000

3000

4000

5000

Lotery Save Do notknow

Inherit Lawsuit

Response

Co

un

ts

Bar Chart for Ret. Savings Example

05

1015202530354045

Lotery Save Do notknow

Inherit Law suit

Response

Pe

rce

nt

Bar Chart for Ret. Savings Example

-500

500

1500

2500

3500

4500

Lote

rySav

e

Do no

t kno

w

Inhe

rit

Lawsu

it

Response

Cou

nt

Pie Char t s

• 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

East

10%

W est

25%

North

45%

South

20% East

W est

North

South

Lottery40%

Save 30%

Don't Know14%

Inherit12%

Lawsuit4%

LotterySave Don't KnowInheritLawsuit

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