Session 2 Notes, Chapter 1
The Nature of Probability and Statistic
The applications of statistics are many and varied. People encounter them in
everyday life, such as in reading newspapers or magazines, listening to the
radio, or watching television. In this chapter you will be introduced to
statistics, the terminology of statistics, and the basic uses and misuses of
statistics as a branch of science.
At the end of this chapter you will be able to:
If you have learned all of these objectives, then close this window to
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- Statistics is the science of conducting studies to collect, organize, summarize,
analyze, and draw conclusions from data.
- Probability is the chance of an event occurring.
- A population consists of all subjects that are being studied.
- A sample is a group of subjects selected from a population.
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- Descriptive statistics consists of the collection, organization, summarization,
and presentation of data.
- Inferential statistics consists of generalizing from
samples to populations,
performing estimations, hypothesis testing, determining relationships among
variables, and making predictions.
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In order to gain knowledge about seemingly haphazard events, statisticians
collect information for variables that describe the events.
- A variable is a characteristic or attribute that can assume
different values.
- Data are the values that variables can assume.
- A data set is a collection of data values.
- Each value in the data set is called a data value or a datum.
- Random variables have values that are determined by chance.
- Insurance companies set their rates based on random variables.
Over a long period of time, the rate of the occurrence of accidents
tends to be constant.
- Qualitative variables can be placed into distinct categories
according to some characteristic or attribute.
- Quantitative variables are numerical in nature and can be
ordered or ranked.
- Discrete variables assume values that can be counted.
- Continuous variables can assume all values between any two
specific values.
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- Nominal—classifies data into mutually exclusive (nonoverlapping),
exhausting categories in which no order or ranking can be imposed on
the data.
- zip code, license number, gender, eye color, blood type
- Ordinal—classifies data into categories that can be ranked;
however, precise differences between the ranks do not exist.
- Interval—ranks data, and precise differences between units
of measure do exist; however, there is no meaningful zero.
- Sat score, IQ, Temperature (C and F)
- Ratio—possesses all the characteristics of interval
measurement, and there exists a true zero.
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- Surveys are the most common method of collecting data. Three methods of
surveying are:
- Telephone surveys
- Mailed questionnaire surveys
- Personal interviews
- Basic sampling techniques:
- Random samples are selected using chance methods or random methods.
- Researchers obtain systematic samples by numbering each subject of the
populations and then selecting every kth number.
- Researchers select stratified samples by dividing the population into groups
according to some characteristic that is important to the study, then sampling
from each group.
- Researchers select cluster samples by using intact groups called clusters.
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- In an observational study, the researcher merely observes what is happening or
what has happened in the past and tries to draw conclusions based on these
observations.
- In an experimental study, the researcher manipulates one of the variables and
tries to determine how the manipulation influences other variables.
- The independent variable (explanatory variable) in an
experimental study is the one that is being manipulated by the
researcher.
- The dependent variable (outcome variable) is the
resultant variable.
- A confounding variable is one that influences the dependent or
outcome variable but cannot be separated from the independent
variable.
- The treatment group is the group for which the
independent variable is manipulated.
- The control group is the group for which nothing is
manipulated.
- A study that uses intact groups it is said to be
quasi-experimental study.
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- Improper selection of samples lead to misused statistics:
- Very small samples
- Bias sample selection
- Volunteer samples
- Ambiguous averages
- When mean, mode, median, and midrange differ, selecting
the statistic that best supports the desired outcome.
- Changing the subject
- Most numbers are relative. Half of the children
became ill after eating Aunt Mary's chocolate has a different
meaning when referring to Aunt Mary's two nephews than when
referring to the Freemont school picnic where the 500 school
children ate Aunt Mary brand chocolate fudge bars. In
the first case we should say Joe became ill and in the second
250 of Freemont's 500 school children became ill.
- Detached statistics
- Our brand has 1/3 fewer calories
- Implied connections
- May, could, in some people, might help.
- Misleading graphs
- ratios wrong or only small portions of the data portrayed
(see chapter 2)
- Faulty survey questions
- bias built into wording, questioner, or place/time of
delivery
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In the past, statistical calculations were done with pencil and paper. However,
with the advent of calculators, numerical computations became easier.
Excel, MINITAB, and the TI-83 graphing calculator can be used to perform
statistical computations.
Students should realize that the computer and calculator merely give numerical
answers and save time and effort of doing calculations by hand
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- The two major areas of statistics are
- descriptive and inferential.
- When the populations to be studied are large,
statisticians use subgroups called
- The four basic methods for obtaining samples are:
- random, systematic, stratified,
and cluster.
- Data can be classified as
- qualitative or quantitative.
- The four basic types of measurement are
- nominal, ordinal, interval, and
ratio.
- The two basic types of statistical studies are
- observational and experimental.
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When you finish these notes, then close this window to return to where
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