Statistics 270 Lecture 1 - Simon Fraser...
Transcript of Statistics 270 Lecture 1 - Simon Fraser...
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St at is t ic s 270 Lec t ure 1
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Today
• Course outline
• Introductory to statistics
• Some Definitions
• Descriptive statistics
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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.
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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?
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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?
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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
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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
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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:
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• 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.
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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.
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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.
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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 %
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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
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Retirement Savings Example
0
1000
2000
3000
4000
5000
Lotery Save Do notknow
Inherit Lawsuit
Response
Co
un
ts
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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
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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
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Lottery40%
Save 30%
Don't Know14%
Inherit12%
Lawsuit4%
LotterySave Don't KnowInheritLawsuit
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