introduction to statistical concepts. objectives definition of “statistics” descriptive vs....
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INTRODUCTION TO INTRODUCTION TO STATISTICAL CONCEPTSSTATISTICAL CONCEPTS
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Objectives
• Definition of “statistics”
• Descriptive vs. Inferential Statistics
• Types of Descriptive Statistics
• Elements of Inferential Statistics
• Qualitative vs. Quantitative Data
• Data Collection Methods
• Inference errors from nonrandom samples
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SURVEY• A random sample of students taking taking a
statistics class are asked, “What is your age?”
Responses23
27
25
26
22
23 21
24
3045
21
20
2519
35
23
2520
31
26
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DATA
• From this survey we get data:
22 35 21 2623 27 25 2020 19 25 2425 26 23 2123 30 45 31
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INFORMATION
• In reality, data files are often very large– Much larger than this example
• Data is often stored in– Large computer databases– Printed records
• The key question is, “how do we extract useful informationinformation from this data?”
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What is Statistics?
StatisticsStatisticsis a way to get
INFORMATIONINFORMATION from
DATADATA
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Types of Statistics
• Two Types of Statistics
StatisticsStatistics
DescriptiveDescriptive
InferentialInferential
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DESCRIPTIVE STATISTICS
• Graphical Depictions of Data– Histograms (Bar Charts)– Pie Charts – Other Types of Charts/Graphs
• Numerical Descriptions/Measures of Data– Frequencies– Measures of Central Tendency– Measures of Variability
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Inferential Statistics
• Testing hypotheses
• Making inferences from surveys
• Giving ranges for estimates
• Predicting the value of one variable (e.g. sales) for given values of other variables (e.g. advertising dollars)
• Forecasting future values over time
• Quality control
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Basic Statistical Concepts
• PopulationPopulation– A set of items (experimental unitsexperimental units) under study
• Parameter (Variable)Parameter (Variable)– A descriptive measure of the population that is of
interest e.g. the mean (Unknown -- Use Greek letter)
• (Random) Sample(Random) Sample – A (random) subset chosen from the population
• StatisticStatistic– A descriptive measure that is calculated from the
sample, e.g. the sample mean (Use regular letter)
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Purpose of Inferential Statistics Making inferences about a
parameterparameter of a populationpopulation
based on information obtained from a
statisticstatistic of the samplesample
(With a Certain Degree of Confidence)
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Example What is the average age of students taking the introductory statistics class at this university?
• POPULATIONPOPULATION under study – AllAll studentsstudents taking the statistics course at this
university• We may not have access to all records• Even if we did, this population is constantly changing with
adds/drops
• PARAMETERPARAMETER of interest– Average ageAverage age of all students taking the course
• Symbol -- • We can never know for sure without looking at the entire
database
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EXAMPLE (Continued)
• Take a (random) SAMPLESAMPLE– Obtain data from a random subset of the population -- i.e.
randomly select 8 students taking the course and ask, “What is your age?”
– Results might be: 23 22 19 35 21 25 25 26
• Calculate a STATISTICSTATISTIC from the sampled data– The average age of the samplesample of the 8 students (a statistic
computed from the sample) can be calculated. This is notnot the average age of the populationpopulation but is our best estimate of it.
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The Sample Statistic
375.248
2625252130192623x
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CONFIDENCE
• The average of the sample was 24.375• What are the chances that the exact true
average of all (1000(?)) students taking statistics is 24.375?– The chance is effectively 0
– But it is our best single guess (point estimatepoint estimate)
– Pretty sure the average is within the interval 23.375 to 25.375
– Even more sure it is in the interval 21.375 to 27.375
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How Large An Interval?
• How wide does the interval have to be before we are “reasonably sure” the interval contains the true average age of all students taking statistics?
• The answer to this question is one of the basic concepts of inferential statistics
• We will discuss this later in the course
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Computing Arithmetic Statistical Values in this Course
• By hand/tablesBy hand/tables– It is important to know the concepts behind
statistical computations and to be able to calculate basic statistical values by hand or use statistical tables in the analyses
• Computer Computer (EXCEL)(EXCEL)– Computer packages are a valuable aid for
making tedious and/or complex calculations and for generating usable output
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TYPES OF DATA• Qualitative Data
– Observation is nonnumeric• What color is your car?
• Who is your favorite candidate for President?
• How would you rate your instructor?
• Quantitative Data– Observation is numeric
• What is your GPA?
• How far do you live from campus?
• What is your salary?
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Collecting Data
• Data can be extracted from a public sourcepublic source– Wall Street Journal, Orange County Business Journal
• A designed experimentdesigned experiment can be performed– Test cavity prevention – divide subjects into groups
• A surveysurvey can be taken– Presidential poll (phone, mail), TV program (Nielsen)
• Observation studiesObservation studies can be made– Observe output of workers on morning/evening shifts
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Goal of Data Collection
• To obtain a “representative sample” that exhibits the characteristics of the entire population
• Most common approach – taking random random samplessamples where each experimental unit in the population theoretically has the same chance of being selected for the sample
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Nonrandom Sampling Errors
• Selection bias– One subset of experimental units in the population
has either no chance, less of a chance, or more of a chance of being selected than another subset
• Nonresponse bias– When data is unavailable or unattainable for certain
experimental units in the population
• Measurement errors – Inaccuracies in getting/recording data; ambiguous
questions on questionnaires, etc.
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Using Nonrandom Samples
• Unintentionally– Leads to unjustified or false conclusions
• Intentionally– Designed to skew results on purpose– Unethical statistical practice
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REVIEW
• What is statistics?
• What is the difference between descriptive and inferential statistics?
• What are the elements of inferential statistics?
• What are the two types of data?
• What are four ways data are collected?
• What is the importance of using random samples?