statistics 270 lecture 1. today course outline introductory to statistics some definitions...
TRANSCRIPT
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Statistics 270 Lecture 1
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Today
• Course outline
• Introductory to statistics
• Some Definitions
• Descriptive statistics
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Introduction
• What is statistics?
• Discipline which deals with the collection, organization and interpretation of data.
• Done to answer questions of interest.
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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?
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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?
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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
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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
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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:
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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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Descriptive Statistics
• Want to describe or summarize data in a clear and concise way.
• Two basic methods: graphical and numerical.
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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.
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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
80
100
Ca
t. 1
Ca
t. 2
Ca
t. 3
Countor %
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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
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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
Co
un
t
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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
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Lottery40%
Save 30%
Don't Know14%
Inherit12%
Lawsuit4%
Lottery
Save
Don't Know
Inherit
Lawsuit