Midterm Review Session. Things to Review Concepts Basic formulae Statistical tests.
Basic Concepts of Statistical Studies
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Transcript of Basic Concepts of Statistical Studies
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Introduction
Decision makers make better decisions when they
use all available information in an effective and
meaningful way. The primary role of statistics is
to to provide decision makers with methods for
obtaining and analyzing information to help make
these decisions. Statistics is used to answer long-
range planning questions, such as when and where
to locate facilities to handle future sales.
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Definition
Statistics is defined as the science of
collecting, organizing, presenting,
analyzing and interpreting numerical
data for the purpose of assisting in
making a more effective decision.
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Types of Statistics
There are two types of statistics
1. Descriptive Statistics is concerned with summary
calculations, graphs, charts and tables.
2. Inferential Statistics is a method used to generalize
from a sample to a population. For example, the average
income of all families (the population) in India can be
estimated from figures obtained from a few hundred (the
sample) families.
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Statistical Population
A Population is a collection of all distinct
individuals or objects or items under study.
The number of entities in a population,
Called the Population Size, is denoted by N
A descriptive measure of a population is
called a Parameter
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Sample
A Sample is a part of a population and
the sample size is denoted by n. A
sample should be a representative of the
population.
A descriptive measure of a sample is called a
Statistic
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Data and Data Sets
Data are the facts and figures collected, summarized,
analyzed, and interpreted.
The data collected in a particular study are referred to as the data set.
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The elements are the entities on which data are collected.
A variable is a characteristic of interest for the elements.
The set of measurements collected for a particular element is called an observation.
Elements, Variables, and Observations
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Scales of Measurement
The scale indicates the data summarization and statistical analyses that are most appropriate.
The scale determines the amount of information contained in the data.
Scales of measurement include:
Nominal
Ordinal
Interval
Ratio
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Scales of Measurement Nominal
A nonnumeric label or numeric code may be used.
Data are labels or names used to identify an attribute of the element.
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Scales of Measurement Ordinal
A nonnumeric label or numeric code may be used.
The data have the properties of nominal data and the order or rank of the data is meaningful.
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Scales of Measurement Interval
Interval data are always numeric.
The data have the properties of ordinal data, and the interval between observations is expressed in terms of a fixed unit of measure.
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Scales of Measurement Ratio
The data have all the properties of interval data and the ratio of two values is meaningful.
Variables such as distance, height, weight, and time use the ratio scale.
This scale must contain a zero value that indicates that nothing exists for the variable at the zero point.
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Data can be further classified as being qualitative or quantitative.
The statistical analysis that is appropriate depends on whether the data for the variable are qualitative or quantitative.
In general, there are more alternatives for statistical analysis when the data are quantitative.
Qualitative and Quantitative Data
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Qualitative Data Labels or names used to identify an attribute of each element
Often referred to as categorical data
Use either the nominal or ordinal scale of measurement
Can be either numeric or nonnumeric
Appropriate statistical analyses are rather limited
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Quantitative Data
Quantitative data indicate how many or how much:
discrete, if measuring how many
continuous, if measuring how much
Quantitative data are always numeric.
Ordinary arithmetic operations are meaningful for quantitative data.
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Scales of Measurement
Qualitative Quantitative
Numerical Numerical Non-numerical
Data
Nominal Ordinal Nominal Ordinal Interval Ratio
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Descriptive Statistics
Descriptive statistics are the tabular, graphical, and
numerical methods used to summarize and present data.
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Statistical Inference
Population
Sample
Statistical inference
Census
Sample survey
- the set of all elements of interest in a particular study
- a subset of the population
- the process of using data obtained from a sample to make estimates and test hypotheses about the characteristics of a population
- collecting data for a population
- collecting data for a sample
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Process of Statistical Inference
1. Population consists of all tune-
ups. Average cost of parts is unknown.
2. A sample of 50 engine tune-ups
is examined.
3. The sample data provide a sample average parts cost of $79 per tune-up.
4. The sample average is used to estimate the population average.