chapter one getting started
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Copyright (C) 2006 Houghton Mifflin Company. All rights reserved. 1
Understandable StatisticsEighth Edition
By Brase and BrasePrepared by: Lynn SmithGloucester County College
Chapter OneGetting Started
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Statistics is
The study of how to:• collect• organize• analyze• interpret
numerical information from data
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Individuals and Variables
• Individuals: the people or objects included in the study
• Variable: the characteristic of the individual to be measured or observed
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Quantitative and Qualitative Data
• Quantitative variable has a value or numerical measurement– example: height
• Qualitative variable places an individual in a category or group– example: gender
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Population
Variable is taken from every individual of interest
Example: the data from all individuals who have
climbed Mt. Everest
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Sample
Variable is taken from only some of the individuals of interest
Example: the data from just some of the climbers
of Mt. Everest
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Levels of Measurement
• Nominal
• Ordinal
• Interval
• Ratio
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Nominal Measurement
Applies to data that consists of names, labels or categories.
Example: names of ski resorts
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Ordinal Measurement
Data that may be arranged in order. Differences between data values
either cannot be determined or are meaningless.
Example: class rank
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Interval Measurement
Data that can be arranged in order. Differences between data values
are meaningful.Example: body temperature
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Ratio MeasurementData that can be arranged in order.
Differences between data values and ratios of data values are
meaningful.Example: temperature in degrees
Kelvin
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Branches of Statistics
• Descriptive: methods of organizing, picturing, and summarizing information
• Inferential: methods of using information from a sample to draw conclusions regarding the population
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Simple Random Sample of n measurements are selected in a
manner such that:• every sample of size n has equal chance of
being selected• every member of the population has an
equal chance of being included
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Random sampling:
• drawing cards “from a hat”
• using a random-number table to select a sample
• using a random-number generator
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Example 1 of using a random number table
We want to choose a random sample of 8 shirts out of a shipment of 300. We drop a pin on a random number table on page A13 and it fallson Column 3 row 15. Since we have 300 shirts we regroup the digits into groups of three. The digits are:275, 924, 208, 999, 281, 596, 401, 522, 196, 079, 099, 610, 537, 129,553, 184, ...The shirts we use in our sample are:275, 208, 281, 196, 79, 99, 129, 184.
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Example 2 using a random number table
We want to use a random number table to simulate rolling a die 10times. We drop a pin on the random number table and it lands on column 7 row 3. Since a die has numbers 1 through 6, we will usesingle digits as our possible rolls. The numbers from the table are:2, 9, 2, 8, 1, 1, 8, 5, 4, 4, 5, 2, 4, ...The simulated outcomes are 2, 2, 1, 1, 5, 4, 4, 5, 2, 4.
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Simulation
• A numerical facsimile or representation of a real-world phenomenon
• Random-number table may be used
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Sampling with replacement
A number that is selected for the sample is not removed from the
population.
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Other sampling techniques
• Stratified Sampling
• Systematic Sampling
• Cluster Sampling
• Convenience Sampling
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Stratified Sampling
• Groups or classes inside a population that share a common characteristic (“strata”)
• Random samples are drawn from each stratum
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Systematic Sampling
• Members of the population are sequentially numbered.
• Select a random starting point.• Select every “kth” item.
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Cluster Sampling
• Population is divided into pre-existing clusters
• Some clusters are randomly selected
• Every member in selected sections is included in the sample
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Convenience Sampling
• Use whatever data is readily available.
• Risk of being severe bias.
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Which sampling technique is described?
College students are waiting in line for registration. Every eighth person in
line is surveyed.
Systematic sampling
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Which sampling technique is described?
College students are waiting in line for registration. Students are asked to volunteer to respond to a survey.
Convenience sampling
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Which sampling technique is described?
In a large high school, students from every homeroom are randomly
selected to participate in a survey
Stratified sampling
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Which sampling technique is described?
An accountant uses a random number generator to select ten accounts for
audit.
Simple random sampling
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Which sampling technique is described?
To determine students’ opinions of a new registration method, a college randomly selects five majors. All students in the selected majors are
surveyed.
Cluster sampling
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Experimental Design
Statistical studies are used to obtain reliable information.
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Planning a Statistical Study
• Identify individuals or object of interest• Specify variables and protocols for
observations• Decide whether to use a census or a sample and
determine viable sampling method• Collect data• Make decisions• List concerns and recommendations
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Census
Measurements or observations from entire populations are used.
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Sample
Measurements or observations from a representative part of the
population are used.
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Simulation
A numerical facsimile of real-world phenomena
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Experiments and Observation
• Observational Study: no change is made in the responses or variable being studied
• Experiment: a treatment is imposed in order to observe a possible change in the response or variable being measured
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Randomized two-treatment experiment
• Subjects are randomly assigned to one of two groups
• One group receives treatment under study• Control group receives placebo• Results are compared• Randomization prevents bias• Replication on many subjects assures changes
not caused by random chance
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Surveys
Data is gathered by asking people questions.
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Problems with data collection• Some individuals do not respond.• People with strong opinions may be over-
represented in voluntary response samples.• There may be a hidden bias in the data
collection process.• There may be hidden effects of other variables.• There is no guarantee that results can be
generalized.
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