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Chapter 1. Section 1-1,1-2,1-3,1-4. Triola, Essentials of Statistics, Second Edition. Copyright 2004. Pearson/Addison-Wesley^1
Elementary Probability
and Statistics
MATH 1530
Cheryl B. Slayden Associate Professor of Mathematics
Some Graphics by Bob Maschak Media Specialist
Chapter 1. Section 1-1,1-2,1-3,1-4. Triola, Essentials of Statistics, Second Edition. Copyright 2004. Pearson/Addison-Wesley^2
Permission has been granted by
Pearson/Addison-Wesley
Publishing Company for use of
the graphics and text problems
from Elementary Statistics and
Essentials of Statistics by
Mario F. Triola
1-1 Overview
1-2 Types of Data
1-3 Critical Thinking
1-4 Design of Experiments
Chapter 1
Introduction to Statistics
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Chapter 1. Section 1-1,1-2,1-3,1-4. Triola, Essentials of Statistics, Second Edition. Copyright 2004. Pearson/Addison-Wesley^4
Statistics
Two Meanings
Method of analysis
Specific numbers
1-1 Overview
Chapter 1. Section 1-1,1-2,1-3,1-4. Triola, Essentials of Statistics, Second Edition. Copyright 2004. Pearson/Addison-Wesley^5
Method of analysis
a collection of methods for planning experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data
Statistics
Specific number
numerical measurement describing
some characteristic of a sample
Statistic
Example: Twenty-three percent of people
polled believed that there are
too many polls.
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Chapter 1. Section 1-1,1-2,1-3,1-4. Triola, Essentials of Statistics, Second Edition. Copyright 2004. Pearson/Addison-Wesley^10
1-2 Types of Data
Chapter 1. Section 1-1,1-2,1-3,1-4. Triola, Essentials of Statistics, Second Edition. Copyright 2004. Pearson/Addison-Wesley^11
Parameter
a numerical measurement describing
some characteristic of a population
population
parameter
Definitions
Definitions
Statistic
a numerical measurement describing
some characteristic of a sample
sample
statistic
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Chapter 1. Section 1-1,1-2,1-3,1-4. Triola, Essentials of Statistics, Second Edition. Copyright 2004. Pearson/Addison-Wesley^13
Definitions
Quantitative Data
numbers representing counts or measurements
Qualitative (or categorical or attribute) Data
can be separated into different categories that are distinguished by some nonnumerical characteristic.
Chapter 1. Section 1-1,1-2,1-3,1-4. Triola, Essentials of Statistics, Second Edition. Copyright 2004. Pearson/Addison-Wesley^14
Definitions
Quantitative Data
the incomes of college graduates
Qualitative (or categorical or attribute) Data
the genders (male/female) of college graduates
Discrete
data result when the number of possible values is either a finite number or a ‘countable’ number of possible values
Continuous
(numerical) data result from infinitely many possible values that correspond to some continuous scale that covers a range of values without gaps, interruptions, or jumps
Definitions
(^2 )
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Chapter 1. Section 1-1,1-2,1-3,1-4. Triola, Essentials of Statistics, Second Edition. Copyright 2004. Pearson/Addison-Wesley^19
ordinal level of measurement
involves data that can be arranged in some order, but differences between data values either cannot be determined or are meaningless
Example: Course grades A, B, C, D, or F
Definitions
Chapter 1. Section 1-1,1-2,1-3,1-4. Triola, Essentials of Statistics, Second Edition. Copyright 2004. Pearson/Addison-Wesley^20
interval level of measurement
like the ordinal level, with the additional property that the difference between any two data values is meaningful. However, there is
no natural zero starting point (where none of
the quantity is present)
Example: Years 1000, 2000, 1776, and 1492
Definitions
ratio level of measurement
the interval level modified to include the natural zero starting point (where zero
indicates that none of the quantity is
present). For values at this level, differences and ratios are meaningful.
Example: Prices of college textbooks
Definitions
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Chapter 1. Section 1-1,1-2,1-3,1-4. Triola, Essentials of Statistics, Second Edition. Copyright 2004. Pearson/Addison-Wesley^22
Levels of Measurement
Nominal - categories only
Ordinal - categories with some order
Interval - differences but no natural
starting point
Ratio - differences and a natural
starting point
Chapter 1. Section 1-1,1-2,1-3,1-4. Triola, Essentials of Statistics, Second Edition. Copyright 2004. Pearson/Addison-Wesley^23
Section 1-
Critical Thinking
Almost all fields of study benefit
from the application of
statistical methods
Critical Thinking
Bad Samples
self-selected survey
(or voluntary response sample)
one in which the respondents themselves decide whether to be included
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Chapter 1. Section 1-1,1-2,1-3,1-4. Triola, Essentials of Statistics, Second Edition. Copyright 2004. Pearson/Addison-Wesley^28
Bachelor High School Degree Diploma
Salaries of People with Bachelor’s Degrees and with High School Diplomas
$40,
30,
25,
20,
35,
$40,
20,
10,
0
30,
Bachelor High School Degree Diploma (a) (b)
$40,500 $40,
$24,
$24,
Chapter 1. Section 1-1,1-2,1-3,1-4. Triola, Essentials of Statistics, Second Edition. Copyright 2004. Pearson/Addison-Wesley^29
Critical Thinking
Graphs
Voluntary Response Samples
Small Samples
Pictographs
Double the length, width, and height of a cube, and the volume increases by a factor of eight
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Chapter 1. Section 1-1,1-2,1-3,1-4. Triola, Essentials of Statistics, Second Edition. Copyright 2004. Pearson/Addison-Wesley^31
Critical Thinking
Percentages Loaded Questions Order of Questions Refusals Etc.
Voluntary Response Samples Small Samples Graphs Pictographs
Chapter 1. Section 1-1,1-2,1-3,1-4. Triola, Essentials of Statistics, Second Edition. Copyright 2004. Pearson/Addison-Wesley^32
Design of Experiments
Section 1-
If sample data are not collected in an appropriate way, the data may be completely useless.
Randomness typically plays a crucial role in determining which data to collect.
Two Major Points
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Chapter 1. Section 1-1,1-2,1-3,1-4. Triola, Essentials of Statistics, Second Edition. Copyright 2004. Pearson/Addison-Wesley^37
Confounding occurs in an experiment when the effects from two or more variables cannot be distinguished from each other
Definitions
Chapter 1. Section 1-1,1-2,1-3,1-4. Triola, Essentials of Statistics, Second Edition. Copyright 2004. Pearson/Addison-Wesley^38
Replication used when an experiment is repeated on a sample of subjects that is large enough so that we can see the true nature of any effects (instead of being misled by erratic behavior of samples that are too small)
Definitions
Random Sample
when members from the population are selected in such a way that each individual member has an equal chance of being selected.
Randomization and
Other Sampling Strategies
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Chapter 1. Section 1-1,1-2,1-3,1-4. Triola, Essentials of Statistics, Second Edition. Copyright 2004. Pearson/Addison-Wesley^40
Simple Random Sample
when size n subjects is selected in such a way that every possible sample of the same size n has the same chance of being chosen.
Randomization and
Other Sampling Strategies
Chapter 1. Section 1-1,1-2,1-3,1-4. Triola, Essentials of Statistics, Second Edition. Copyright 2004. Pearson/Addison-Wesley^41
Random Sampling - selection so that
each has an equal chance of being selected
Systematic Sampling - Select some starting point and then select every K th element in the population.
Example: Every third person
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Chapter 1. Section 1-1,1-2,1-3,1-4. Triola, Essentials of Statistics, Second Edition. Copyright 2004. Pearson/Addison-Wesley^46
Random
Systematic
Convenience
Stratified
Cluster
Methods of Sampling
Chapter 1. Section 1-1,1-2,1-3,1-4. Triola, Essentials of Statistics, Second Edition. Copyright 2004. Pearson/Addison-Wesley^47
Sampling Error
the difference between a sample result and the true population result; such an error results from chance sample fluctuations.
Non-sampling Error
sample data that are incorrectly collected, recorded, or analyzed (such as by selecting a biased sample, using a defective instrument, or copying the data incorrectly).
Definitions
