Math227_Chapter 1_Final_ClassNotes

Chapter 1
Data Collection
Copyright of the definitions and examples is reserved to Pearson Education,
Inc.. In order to use this PowerPoint presentation, the required textbook for
the class is the Fundamentals of Statistics, Informed Decisions Using Data,
Michael Sullivan, III, fourth edition.
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Ch 1.1 & 1.2 Basic Definitions for Statistics
Objective A : Basic Definition
Objective B : Level of measurement of a Variable
Objective C : Observational Study versus Designed
Experiment
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Ch 1.1 & 1.2 Basic Definitions for Statistics
Objective A : Basic Definition
A1. Definition
What is Statistics?
• Statistics is the science of collecting, organizing, summarizing,
and analyzing data to draw conclusions.
Statistics
Descriptive Statistics
Inferential Statistics
• Descriptive statistics consist of collecting, organizing,
summarizing, and presenting data.
• Inferential statistics consists of generalizing from samples to
populations, performing estimations and hypothesis tests, and
making predictions.
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Population versus Sample
• A population consists of all individuals (person or object) that
are being studied.
• A sample is a subset of the population.
Parameter versus Statistic
• A parameter is a numerical summary of a population.
• A statistic is a numerical summary of a sample.
Example 1:
A farmer wanted to learn about the weight of his soybean crop. He
randomly sampled 100 plants and weighed the soybeans on each
plant.
Identify the population and sample in the study.
Population – All soybean plants planted by the farmer.
Sample – 100 randomly selected soybean plants.
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Example 2:
Determine whether the underlined value is a parameter or a statistic.
(a) Only 12 men have walked on the moon. The average age of these
men at the time of their moonwalks was 39 years, 11 months, 15
days.
Parameter.
(b) In a national survey on substance abuse, 66.4% of respondents
who were full-time college students aged 18 to 22 reported
using alcohol within the past month.
Statistic.
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A2. Variables and Type of Data
Variable
• A variable is a characteristic that can assume different values
called data.
Qualitative versus Quantitative Variable
• Qualitative (categorical) variables are variables that can be
placed into distinct categories.
• Quantitative (numerical) variables are variables that can
perform numerical and arithmetic operations.
Discrete variable
Quantitative variable
Continuous variable
• A discrete variable can assume a countable number of values.
• A continuous variable can assume an infinite number of values
between any two specific values. They often include fractions
and decimals.
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Example 1:
Classify each variable as qualitative or quantitative. If the variable
is quantitative, further classify the data as discrete or continuous.
(a) Number of students attending a university for Fall 2012.
Quantitative
Discrete
(b) Colors of football caps in a store.
Qualitative
(c) Social security number.
Qualitative
(d) Water temperature of a swimming pool.
Quantitative
Continuous
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Ch 1.1 & 1.2 Basic Definitions for Statistics
Objective A : Basic Definition
Objective B : Level of measurement of a Variable
Objective C : Observational Study versus Designed
Experiment
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Ch 1.1 & 1.2 Basic Definitions for Statistics
Objective B: Level of measurement of a Variable
In addition to being classified as qualitative or quantitative,
variables can be classified by how they are categorized, counted,
or measured.
Four common types of measurement scales are used: nominal,
ordinal, interval, and ratio.
• The nominal level of measurement classifies data into
categories in which no order or ranking can be imposed on the
data.
For example: Eye color
• The ordinal level of measurement classifies data into categories
that can be ranked.
For example: Course grade
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• The interval level of measurement has the properties of the ordinal
level of measurement and the differences in the values of the
variable have meaning. There is no true zero. A value of zero does
not mean the absence of the quantity.
For example: Sea level; Temperature
• The ratio level of measurement has the properties of the interval
level of measurement and the ratios of the values of the variable
have meaning. There exists a true zero.
For example: Length
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Ch 1.1 & 1.2 Basic Definitions for Statistics
Objective A : Basic Definition
Objective B : Level of measurement of a Variable
Objective C : Observational Study versus Designed
Experiment
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Ch 1.1 & 1.2 Basic Definitions for Statistics
Objective C: Observational Study versus Designed Experiment
Definition
• In an observational study, the researcher observes the behavior
of the individuals without trying to influence the outcome of
the study.
• In a designed experiment, the researcher controls one of the
variables and tries to determine how the manipulation
influences other variables.
• The independent variable which is also called the explanatory
variable in a designed experiment is the one that is being
controlled by the researcher. The dependent variable which is
also called the response variable is the resultant variable.
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• Confounding in a study occurs when the effects of two or more
explanatory variables are not separated.
• A lurking variable is an explanatory variable that was not
considered in a study, but that effects the value of the response
variable in the study.
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Example 1:
Determine whether the study depicts an observational study or
an experiment.
(a) Rats with cancer are divided into two groups. One group receives 5
mg of a medication that is thought to fight cancer, and the other
receives 10 mg. After 2 years, the spread of the cancer is measured.
An experiment
(b) Conservation agents netted 320 large-trout in a lake and determined
how many were carrying parasites.
An observational study
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Example 2:
Identify the explanatory variable and the response variable for
the following studies.
(a) Rats with cancer are divided into two groups. One group receives 5
mg of a medication that is thought to fight cancer, and the other
receives 10 mg. After 2 years, the spread of the cancer is measured.
Explanatory variable – the amount of medication dosage
Response variable – measure of the spread of the cancer
(b) A researcher wants to determine whether young couples who marry
are more likely to gain weight than those who stay single.
Explanatory variable – marital status
Response variable – weight gained
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Ch 1.3 to 1.5 Sampling
Objective A : Ch 1.3 Simple Random Sampling
Objective B : Ch 1.4 More Sampling Methods
Objective C : Ch 1.5 Bias in Sampling
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Ch 1.3 to 1.5 Sampling
Objective A : Ch 1.3 Simple Random Sampling
Simple Random Sampling
The goal of sampling is to obtain as much information as possible about
the population at the least cost.
• A random sample is obtained by using chance methods or random
numbers.
Example : Selecting a card from a well shuffled deck of cards.
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Steps for Obtaining a Simple Random Sample
1. Number all the individuals in the population of interest.
2. Use a random number table, graphing calculator, or statistical
software to randomly generate n numbers where n is the
desired sample size.
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Ch 1.3 to 1.6 Sampling
Objective A : Ch 1.3 Simple Random Sampling
Objective B : Ch 1.4 More Sampling Methods
Objective C : Ch 1.5 Bias in Sampling
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Objective B : Ch 1.4 More Sampling Methods
• A systematic sample is obtained by selecting every k th individual
from the population.
• A stratified sample is obtained by dividing the population into nonoverlapping groups (called strata) according to some similar
characteristic, then sampling from each stratum.
• A cluster is obtained by dividing the population into groups called the
clusters such as geographic area or schools in a large district. Then all
the individuals within a randomly selected clusters are selected.
• A convenience sample is a sample in which the individuals are easily
obtained and not based on randomness.
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Example 1:
Identify the type of sampling method.
(Random, systematic, stratified, cluster, convenience)
(a) Every tenth customer entering a grocery store is asked to select her
or his favor color.
Systematic
(b) A farmer divides his orchard into 30 subsections, randomly selects 4,
and sample all the trees within the 4 subsections to approximate the
yield of his orchard.
Cluster
(c) A survey regarding download time on a certain website is
administered on the Internet by a market research firm to anyone
who would like to take it.
Convenience
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(d) In an effort to identify is an advertising campaign has been effective,
a marketing firm conducts a nationwide poll by randomly selecting
individuals from a list of known users of the product.
Random
(e) A school official divides the student population into five classes:
freshman, sophomore, junior, senior, and graduate student. The
official takes a simple random sample from each class and asks the
members’ opinions regarding student services.
Stratified
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Ch 1.3 to 1.5 Sampling
Objective A : Ch 1.3 Simple Random Sampling
Objective B : Ch 1.4 More Sampling Methods
Objective C : Ch 1.5 Bias in Sampling
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Ch 1.3 to 1.5 Sampling
Objective C : Ch1.5 Bias in Sampling
• Sampling bias means that the technique used to obtain the individuals
to be in the sample tends to favor one part of the population over
another.
• Non-response bias exists when individuals selected to be in the sample
do not wish to respond.
• Response bias exists when the answers on the survey do not reflect
the true feelings of the respondent.
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Example 1:
The survey has bias. Determine the type of bias.
(Sampling , non-response, response)
(a) To determine the public’s opinion of the police department, the
police chief obtains a cluster sample of 15 census tracts within his
jurisdiction and samples all households in the randomly selected
tracts. Uniformed police officers go door to door to conduct the
survey.
Response bias
(b) The village of Oak Lawn wishes to conduct a study regarding the
income level of households within the village. The village manager
selects 10 homes in the southwest corner of the village and sends
an interviewer to the homes to determine household income.
Sampling bias
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