Stats -CH1
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Ch 1: Intro to Stats
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
What is Statistics?
Motivating Question: What do you think of when you hear
“statistics”?
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Possible Answers/Examples
Sports — play an important role in recruitment, drafting, and
making predictions
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Possible Answers/Examples
Sports — play an important role in recruitment, drafting, and
making predictions
Medicine — comment on the prevalence of disease/illness,
determine the effectiveness of medications/treatments, etc.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Possible Answers/Examples
Sports — play an important role in recruitment, drafting, and
making predictions
Medicine — comment on the prevalence of disease/illness,
determine the effectiveness of medications/treatments, etc.
News — raise awareness (or chaos), report fads, political
results, etc.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Possible Answers/Examples
Sports — play an important role in recruitment, drafting, and
making predictions
Medicine — comment on the prevalence of disease/illness,
determine the effectiveness of medications/treatments, etc.
News — raise awareness (or chaos), report fads, political
results, etc.
Take-Away
Statistics is actually a useful area of mathematical study for a
variety of careers. You will end up using statistics in professional
fields such as, psychiatry, medicine, sports, politics, business, etc.
and it is also important to understand statistical reports for
everyday life.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
So, what is statistics?
Roughly, statistics is a way of using mathematical analysis to make
decisions on the basis of gathered data.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
So, what is statistics?
Roughly, statistics is a way of using mathematical analysis to make
decisions on the basis of gathered data. More precisely,
Data (1.1) Information gathered from observations, counts,
measurements, or responses.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
So, what is statistics?
Roughly, statistics is a way of using mathematical analysis to make
decisions on the basis of gathered data. More precisely,
Data (1.1) Information gathered from observations, counts,
measurements, or responses.
Statistics (1.1) The science of collecting, organizing, analyzing,
and interpreting data in order to make decisions.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Statistics: this course
Since the study of statistics is based on the analysis of gathered
data, it is important to consider the way that data is gathered,
both in method and in source. In this course, we will:
go into detail about different methods for collecting data,
consider how the method of collection can affect the reliability
of the data and the conclusions we can draw from it,
consider different methods for analyzing data,
discover different statistical methods for drawing conclusions
from data,
and learn how to use statistics can be applied to a variety of
real-world scenarios.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Why study statistics?
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Why study statistics?
Statistics provides useful
tools for making
informed decisions.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Why study statistics?
Statistics provides useful
tools for making
informed decisions.
Statistics is often
misused—so it is
important to be able to
understand what counts
as a good statistical
inference.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Section 1.1: Overview of Statistics
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Data sets
Data is of fundamental importance for statistics. You simply
cannot do statistics without data.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Data sets
Data is of fundamental importance for statistics. You simply
cannot do statistics without data.
Data set
When we collect data, we gather it into what is called a data set.
The data set is just the collection of observations, counts,
measurements, or responses (what ever we were gathering).
Example
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Two Kinds of Data Sets
Population
A population is the collection of all outcomes, responses,
measurements, or counts that are of interest.
Sample
A sample is a subset of a population. In other words, a sample is
only part of the population.
Example: A study is being conducted about the quality of life of
chickens living on Blue Ridge Farm.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Two Kinds of Data Sets
Population
A population is the collection of all outcomes, responses,
measurements, or counts that are of interest.
Sample
A sample is a subset of a population. In other words, a sample is
only part of the population.
Example: A study is being conducted about the quality of life of
chickens living on Blue Ridge Farm.
Population All of the chickens on living Blue Ridge Farm.
Sample The first 50 chickens caught that live on Blue Ridge
Farm.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Examples: Population or Sample?
Determine if the following data sets are populations or samples.
Example 1
The household income of every third household in the United
States.
Example 2
The salary of each member of the New York Mets.
Example 3
The temperature in 65 out of the 100 counties of North Carolina.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Examples 1: Population or Sample?
Example 1
The household income of every third household in the United
States.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Examples 1: Population or Sample?
Example 1
The household income of every third household in the United
States.
Sample. The population would be the household income of every
household in the US.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Examples 2: Population or Sample?
Example 2
The salary of each member of the New York Mets.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Examples 2: Population or Sample?
Example 2
The salary of each member of the New York Mets.
Population–assuming the study is about the salaries of the Mets.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Examples 3: Population or Sample?
Example 3
The temperature in 65 out of the 100 counties of North Carolina.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Examples 3: Population or Sample?
Example 3
The temperature in 65 out of the 100 counties of North Carolina.
Sample–Is this a good sample for studying the overall temperature
of North Carolina?
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Populations vs Samples
Motivating Question
Why is it important to distinguish between populations and
samples?
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Populations vs Samples
Motivating Question
Why is it important to distinguish between populations and
samples?
Some Answers:
Can affect the reliability of the data.
May be relevant in determining what kind of conclusions can
be drawn from the data gathered.
Important if the study wants to be recreated. A good study
will always be able to be recreated.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Example:
Example
The NC department of health is conducting a survey to determine
how many NC adults stay home from work when they have a cold.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Example:
Example
The NC department of health is conducting a survey to determine
how many NC adults stay home from work when they have a cold.
What is the population relevant for this study?
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Example:
Example
The NC department of health is conducting a survey to determine
how many NC adults stay home from work when they have a cold.
What is the population relevant for this study? All NC adults.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Example:
Example
The NC department of health is conducting a survey to determine
how many NC adults stay home from work when they have a cold.
What is the population relevant for this study? All NC adults.
Name an example of sample that might be used for this
study?
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Example:
Example
The NC department of health is conducting a survey to determine
how many NC adults stay home from work when they have a cold.
What is the population relevant for this study? All NC adults.
Name an example of sample that might be used for this
study? 10,000 NC adults selected at random.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Example:
Example
The NC department of health is conducting a survey to determine
how many NC adults stay home from work when they have a cold.
What is the population relevant for this study? All NC adults.
Name an example of sample that might be used for this
study? 10,000 NC adults selected at random.
Bad sample choice:
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Example:
Example
The NC department of health is conducting a survey to determine
how many NC adults stay home from work when they have a cold.
What is the population relevant for this study? All NC adults.
Name an example of sample that might be used for this
study? 10,000 NC adults selected at random.
Bad sample choice: All male adults over 50 yrs old in
Watauga County.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Example:
Example
The NC department of health is conducting a survey to determine
how many NC adults stay home from work when they have a cold.
What is the population relevant for this study? All NC adults.
Name an example of sample that might be used for this
study? 10,000 NC adults selected at random.
Bad sample choice: All male adults over 50 yrs old in
Watauga County.
Note: Whether some data set is a population or sample depends
on the context determined by the study in which the data set is
being used.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Parameter vs Statistic
In order to help us distinguish between populations and sample, we
introduce some vocab to use in each case.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Parameter vs Statistic
In order to help us distinguish between populations and sample, we
introduce some vocab to use in each case.
Parameter
A parameter is a numerical description of a population
characteristics, i.e., a general statement that describes the
population as a whole.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Parameter vs Statistic
In order to help us distinguish between populations and sample, we
introduce some vocab to use in each case.
Parameter
A parameter is a numerical description of a population
characteristics, i.e., a general statement that describes the
population as a whole.
Example: LMC is conducting a survey to determine how many
credits of math graduating seniors have taken. Out of the 218
graduating seniors, 81 have taken more than 6 credits of math
classes.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Parameter vs Statistic
In order to help us distinguish between populations and sample, we
introduce some vocab to use in each case.
Statistic
A statistic is a numerical description of a sample characteristic,
i.e., a statement that describes the outcomes/responses of a
particular sample.
Example: 100 Walmarts were selected across the country reported
that in June 2022 they sold an average of 81.4 gallons of ice cream
each day.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Parameter vs Statistic
In order to help us distinguish between populations and sample, we
introduce some vocab to use in each case.
Statistic
A statistic is a numerical description of a sample characteristic,
i.e., a statement that describes the outcomes/responses of a
particular sample.
Example: 100 Walmarts were selected across the country reported
that in June 2022 they sold an average of 81.4 gallons of ice cream
each day.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Examples: Parameter or Statistic?
Determine whether each of the following is a parameter or a
statistic.
Example 1
The freshman class at a university has an average math SAT score
of 514.
Example 2
In a random check of several hundred grocery stores, the FDA
found that 34% of the store were not storing fish at the proper
temperature.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Results: Parameter or Statistic?
Example 1
The freshman class at a university has an average math SAT score
of 514.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Results: Parameter or Statistic?
Example 1
The freshman class at a university has an average math SAT score
of 514.
Parameter—the population is the freshman class at the university.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Results: Parameter or Statistic?
Example 1
The freshman class at a university has an average math SAT score
of 514.
Parameter—the population is the freshman class at the university.
Example 2
In a random check of several hundred grocery stores, the FDA
found that 34% of the store were not storing fish at the proper
temperature.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Results: Parameter or Statistic?
Example 1
The freshman class at a university has an average math SAT score
of 514.
Parameter—the population is the freshman class at the university.
Example 2
In a random check of several hundred grocery stores, the FDA
found that 34% of the store were not storing fish at the proper
temperature.
Statistic—the randomly checked grocery stores are a sample.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
2 Kinds of Statistics
Now that we have a better understanding of data sets, we can talk
about the kinds of statistics we can do with these data sets. There
are two main branches of statistics:
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
2 Kinds of Statistics
Now that we have a better understanding of data sets, we can talk
about the kinds of statistics we can do with these data sets. There
are two main branches of statistics:
1 Descriptive Statistics
2 Inferential Statistics
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Descriptive vs Inferential Statistics
Descriptive statistics is the branch that involves The
organization, summarization, and display of data. (Note, no
inferences are made nor conclusions drawn).
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Descriptive vs Inferential Statistics
Descriptive statistics is the branch that involves The
organization, summarization, and display of data. (Note, no
inferences are made nor conclusions drawn).
Inferential Statistics is the branch that involves the use of a
sample to draw conclusions and inferences about an overall
population. Note that probability is an important tool in drawing
these conclusions and inferences.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Example: Descriptive or Inferential?
Example 1
A company creates a bar graph to represent profits earned in each
month of 2021.
Example 2
A school system decides to alter their curriculum to better prepare
students for the SAT based on test scores from previous years.
Example 3
A pharmacy decides to stop carrying a brand of gum after
analyzing its sales from the past year.
Example 4
A political campaign team creates a pie chart to present reasons
that voters support and oppose their campaign.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Results: Descriptive or Inferential?
Example 1
A company creates a bar graph to represent profits earned in each
month of 2021.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Results: Descriptive or Inferential?
Example 1
A company creates a bar graph to represent profits earned in each
month of 2021.–Descriptive
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Results: Descriptive or Inferential?
Example 1
A company creates a bar graph to represent profits earned in each
month of 2021.–Descriptive
Example 2
A school system decides to alter their curriculum to better prepare
students for the SAT based on test scores from previous
years.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Results: Descriptive or Inferential?
Example 1
A company creates a bar graph to represent profits earned in each
month of 2021.–Descriptive
Example 2
A school system decides to alter their curriculum to better prepare
students for the SAT based on test scores from previous
years.—Inferential
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Results: Descriptive or Inferential?
Example 3
A pharmacy decides to stop carrying a brand of gum after
analyzing its sales from the past year.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Results: Descriptive or Inferential?
Example 3
A pharmacy decides to stop carrying a brand of gum after
analyzing its sales from the past year.–Inferential
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Results: Descriptive or Inferential?
Example 3
A pharmacy decides to stop carrying a brand of gum after
analyzing its sales from the past year.–Inferential
Example 4
A political campaign team creates a pie chart to present reasons
that voters support and oppose their campaign.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Results: Descriptive or Inferential?
Example 3
A pharmacy decides to stop carrying a brand of gum after
analyzing its sales from the past year.–Inferential
Example 4
A political campaign team creates a pie chart to present reasons
that voters support and oppose their campaign.–Descriptive
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Why Distinguish between Descriptive and
Inferential?
The divide between descriptive and inferential statistics is an
important one because both contribute different things to our
statistical study.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Why Distinguish between Descriptive and
Inferential?
The divide between descriptive and inferential statistics is an
important one because both contribute different things to our
statistical study.
Within descriptive statistics, we ask important questions about
how to best organize and represent data. An important
precursor to making inferences and drawing conclusions.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Why Distinguish between Descriptive and
Inferential?
The divide between descriptive and inferential statistics is an
important one because both contribute different things to our
statistical study.
Within descriptive statistics, we ask important questions about
how to best organize and represent data. An important
precursor to making inferences and drawing conclusions.
Within inferential statistics, we ask important questions about
what we can do with the data and representations we’ve come up
with. Here we are focused on making the reliable conclusions
from our data.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Section 1.2: Data Classification
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
2 Kinds of Data
Qualitative Data Data entries consisting of attributes, labels, or
nonnumerical entries.
Examples: car models, cities, eye color,
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
2 Kinds of Data
Qualitative Data Data entries consisting of attributes, labels, or
nonnumerical entries.
Examples: car models, cities, eye color,
Quantitative Data Data entries consisting of numerical
measurements or counts.
Examples: population size, height, distance, salaries,
frequencies.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Levels of Measurement
Within these two categories of data (qualitative and quantitative),
we can also identify different levels of measurement. These levels
are determined by the amount of calculation we can do with the
given data.
1 Nominal level
2 Ordinal level
3 Interval level
4 Ratio level
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Levels of Measurement: Nominal Level
Nominal
Data that can be put into qualitative categories without any kind
of mathematical sorting (i.e., without ordering)
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Levels of Measurement: Nominal Level
Nominal
Data that can be put into qualitative categories without any kind
of mathematical sorting (i.e., without ordering)
“Nominal” means “naming” so this is the level where the only
thing you can do with data is categorize it using labels.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Levels of Measurement: Nominal Level
Nominal
Data that can be put into qualitative categories without any kind
of mathematical sorting (i.e., without ordering)
“Nominal” means “naming” so this is the level where the only
thing you can do with data is categorize it using labels.
Example: A data set consisting of the hometowns of LMC
students is at the nominal level. You could organize this data by
categorizing students by their hometown.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Levels of Measurement: Ordinal Level
Ordinal
Data that can be put into an order of some sort (qualitative of
quantitative). In other words the data can be understood on some
kind of scale and placed in order on that scale.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Levels of Measurement: Ordinal Level
Ordinal
Data that can be put into an order of some sort (qualitative of
quantitative). In other words the data can be understood on some
kind of scale and placed in order on that scale.
“Ordinal” means ordering so this is the level where the you are
able to put the data into an ordering. Note that both qualitative
and quantitative data can be ordered.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Levels of Measurement: Ordinal Level
Ordinal
Data that can be put into an order of some sort (qualitative of
quantitative). In other words the data can be understood on some
kind of scale and placed in order on that scale.
“Ordinal” means ordering so this is the level where the you are
able to put the data into an ordering. Note that both qualitative
and quantitative data can be ordered.
Example: A data set consisting of the shade of blue of a closet of
t-shirts is at the ordinal level because it can be ordered from light
to dark.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Levels of Measurement: Interval Level
Interval
At this level data can be meaningfully subtracted. In other words
you can subtract data entries and that calculation will be provide
information about the collected data.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Levels of Measurement: Interval Level
Interval
At this level data can be meaningfully subtracted. In other words
you can subtract data entries and that calculation will be provide
information about the collected data.
Example: A data set consisting of the birth years of family
members is at the interval level. We can subtract birth years to
gain information about relative age.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Levels of Measurement: Ratio Level
Ratio
Data entries at the ratio level can be understood as multiples of
one another.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Levels of Measurement: Ratio Level
Ratio
Data entries at the ratio level can be understood as multiples of
one another.
Example: A data set consisting of the heights of trees on campus
falls at the ratio level of measurement. We are able to say that one
tree is twice as tall as another—hence, we are able to determine
whether data entries are multiples of another.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Differentiating Interval vs Ratio
Use the following methods to differentiate between the interval and
ratio levels:
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Differentiating Interval vs Ratio
Use the following methods to differentiate between the interval and
ratio levels:
Ask if it makes sense to say that one entry is twice as much as
another.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Differentiating Interval vs Ratio
Use the following methods to differentiate between the interval and
ratio levels:
Ask if it makes sense to say that one entry is twice as much as
another.
Example: It makes to say that something is twice as tall as
something else, but it doesn’t make sense to say that one
birth year is twice as much as another.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Differentiating Interval vs Ratio
Use the following methods to differentiate between the interval and
ratio levels:
Ask if it makes sense to say that one entry is twice as much as
another.
Example: It makes to say that something is twice as tall as
something else, but it doesn’t make sense to say that one
birth year is twice as much as another.
Check for an “inherent zero”. An inherent zero is when a data
entry of zero means “none” or “no value”. Only data sets at
the ratio level have inherent zeros.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Differentiating Interval vs Ratio
Use the following methods to differentiate between the interval and
ratio levels:
Ask if it makes sense to say that one entry is twice as much as
another.
Example: It makes to say that something is twice as tall as
something else, but it doesn’t make sense to say that one
birth year is twice as much as another.
Check for an “inherent zero”. An inherent zero is when a data
entry of zero means “none” or “no value”. Only data sets at
the ratio level have inherent zeros.
Example: A data set consisting amount in people’s savings
account is at the ratio because $0 on a bank statement means
there are no savings. However, temperature is not on the ratio
level because 0◦ does not mean no temperature.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Hierarchy: Levels of Measurement
It’s important to remember that the levels of measurement form a
hierarchy so that the possible calculations increase as we move up
the hierarchy.
Nominal–name
Ordinal–order
Interval–subtract
Ratio–multiply
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Hierarchy: Levels of Measurement
It’s important to remember that the levels of measurement form a
hierarchy so that the possible calculations increase as we move up
the hierarchy.
Nominal–name
Ordinal–order
Interval–subtract
Ratio–multiply
Data entries that fall at the ratio level can be multiplies of one
another and they can be subtracted, ordered, and categorized.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Examples
Determine which level of measurement each of the following stats
falls under.
Note: we always categorize data at the highest level of
measurement that it falls under.
Example 1
The distance employees of LMC commute to campus.
Example 2
The top ten fiction books on the New York Times Best Sellers List.
Example 3
The times a person wakes up each day in July 2022.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Examples
Example 1
The distance employees of LMC commute to campus.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Examples
Example 1
The distance employees of LMC commute to campus.
Ratio level: we can say that one employee has a commute twice as
long as another.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Examples
Example 1
The distance employees of LMC commute to campus.
Ratio level: we can say that one employee has a commute twice as
long as another.
Example 2
The top ten fiction books on the New York Times Best Sellers List.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Examples
Example 1
The distance employees of LMC commute to campus.
Ratio level: we can say that one employee has a commute twice as
long as another.
Example 2
The top ten fiction books on the New York Times Best Sellers List.
Ordinal level: The top ten list is ordered.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Examples
Example 3
The times a person wakes up each day in July 2022.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Examples
Example 3
The times a person wakes up each day in July 2022.
Interval Level: Wake-up times can be subtracted to say things like
“the subject woke up 5 minutes later the next day”. But it does
not make sense to say that one wake-up time is twice as much as
another.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Examples
Example 3
The times a person wakes up each day in July 2022.
Interval Level: Wake-up times can be subtracted to say things like
“the subject woke up 5 minutes later the next day”. But it does
not make sense to say that one wake-up time is twice as much as
another.
Take-Away
The main take-away here is that when we’re conducting a
statistical study it is important to be aware of the kind of data we
have so that we know what tools we are able to use to analyze it.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Section 1.3: Data Collection and
Experimental Design
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Motivation
It’s important to know how to design a statistical study for a
couple reasons:
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Motivation
It’s important to know how to design a statistical study for a
couple reasons:
1 If you want to conduct a statistical study of your own, then
you’ll have to design it from the ground up.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Motivation
It’s important to know how to design a statistical study for a
couple reasons:
1 If you want to conduct a statistical study of your own, then
you’ll have to design it from the ground up.
2 If you’re trying to determine whether the conclusions of a
statistical study are reliable, then you’ll need to be able to
determine whether the study was well-designed.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Designing a Statistical Study
A statistical study should (at least roughly) follow this outline:
Outline for Statistical Study
Step 1: Identify the variable(s) and the population.
Step 2: Develop a plan for collecting data.
Step 3: Collect the data.
Step 4: Describe the data (using descriptive statistics).
Step 5: Interpret the data and make decisions about the
population (using inferential statistics).
Step 6: Identify any possible errors.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Designing a Statistical Study
A statistical study should (at least roughly) follow this outline:
Outline for Statistical Study
Step 1: Identify the variable(s) and the population.
Step 2: Develop a plan for collecting data.
Step 3: Collect the data.
Step 4: Describe the data (using descriptive statistics).
Step 5: Interpret the data and make decisions about the
population (using inferential statistics).
Step 6: Identify any possible errors.
For now, we’ll focus on steps 1-3 and discuss how to carry out
these steps reliably in order to set up a statistical study for success.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Step 1: Identify Variables and Population
Population
The first step of any statistical study is to determine what
population is relevant to your study is. Note that this doesn’t
mean that you will collect data from the entire population—you
may still choose to use a sample.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Step 1: Identify Variables and Population
Population
The first step of any statistical study is to determine what
population is relevant to your study is. Note that this doesn’t
mean that you will collect data from the entire population—you
may still choose to use a sample.
Variable(s)
The variables of a study are the focus or subject of the study. A
good indicator of a variable is that changes in the study.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Step 1: Identify Variables and Population
Example
An electrical company in North Carolina is interested in studying
changes in average household electric bill costs throughout the
year.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Step 1: Identify Variables and Population
Example
An electrical company in North Carolina is interested in studying
changes in average household electric bill costs throughout the
year.
What’s the relevant population?
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Step 1: Identify Variables and Population
Example
An electrical company in North Carolina is interested in studying
changes in average household electric bill costs throughout the
year.
What’s the relevant population?
All NC households with electric bills.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Step 1: Identify Variables and Population
Example
An electrical company in North Carolina is interested in studying
changes in average household electric bill costs throughout the
year.
What’s the relevant population?
All NC households with electric bills.
What are the variables?
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Step 1: Identify Variables and Population
Example
An electrical company in North Carolina is interested in studying
changes in average household electric bill costs throughout the
year.
What’s the relevant population?
All NC households with electric bills.
What are the variables?
Electric bill amounts
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Examples: Populations and variables
Example 1
The provost wants to study the average number of hours LMC
students spend studying each day of the week.
Example 2
A town’s animal control office wants to determine how many pets
in the town are spayed or neutered.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Examples: Populations and variables
Example 1
The provost wants to study the average number of hours LMC
students spend studying each day of the week.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Examples: Populations and variables
Example 1
The provost wants to study the average number of hours LMC
students spend studying each day of the week.
Population: All LMC students.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Examples: Populations and variables
Example 1
The provost wants to study the average number of hours LMC
students spend studying each day of the week.
Population: All LMC students.
Variable: Day of the week.
Variable: Hours spent studying in a day.
Example 2
A town’s animal control office wants to determine how many pets
in the town are spayed or neutered.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Examples: Populations and variables
Example 1
The provost wants to study the average number of hours LMC
students spend studying each day of the week.
Population: All LMC students.
Variable: Day of the week.
Variable: Hours spent studying in a day.
Example 2
A town’s animal control office wants to determine how many pets
in the town are spayed or neutered.
Population: All pets in the town.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Examples: Populations and variables
Example 1
The provost wants to study the average number of hours LMC
students spend studying each day of the week.
Population: All LMC students.
Variable: Day of the week.
Variable: Hours spent studying in a day.
Example 2
A town’s animal control office wants to determine how many pets
in the town are spayed or neutered.
Population: All pets in the town.
Variable: Pet status as spayed/neutered or not.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Step 2: Plan for Collecting Data
Two Methods of Data Collection
1 Simulation: The use of a mathematical or physical model to
reproduce the conditions of a situation or process.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Step 2: Plan for Collecting Data
Two Methods of Data Collection
1 Simulation: The use of a mathematical or physical model to
reproduce the conditions of a situation or process.
2 Survey: An investigation of one or more characteristics of a
population, which is most often carried out by asking people
for their responses to established questions.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Simulations
Examples
Using a computer program to simulate population sizes of
predator-prey relations.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Simulations
Examples
Using a computer program to simulate population sizes of
predator-prey relations.
Automobile manufacturers using test dummies to assess the
effects of car crashes.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Simulations
Examples
Using a computer program to simulate population sizes of
predator-prey relations.
Automobile manufacturers using test dummies to assess the
effects of car crashes.
Features of Simulations
They are often more practical and safer.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Simulations
Examples
Using a computer program to simulate population sizes of
predator-prey relations.
Automobile manufacturers using test dummies to assess the
effects of car crashes.
Features of Simulations
They are often more practical and safer.
They allow us to study impossible scenarios.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Survey
Examples
Surveys usually take the form of a questionnaire carried out
through interview, the internet, phone, or mail.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Survey
Examples
Surveys usually take the form of a questionnaire carried out
through interview, the internet, phone, or mail.
The US census.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Survey
Examples
Surveys usually take the form of a questionnaire carried out
through interview, the internet, phone, or mail.
The US census.
Student evaluations of instructors.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Survey
Examples
Surveys usually take the form of a questionnaire carried out
through interview, the internet, phone, or mail.
The US census.
Student evaluations of instructors.
Features of Surveys
Surveys are practical and can be far-reaching (allowing for
larger sample sizes).
Surveys need to be carefully designed so that the survey
questions do not lead to biased results.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Kinds of Statistical Studies
There are two different kinds of statistical studies:
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Kinds of Statistical Studies
There are two different kinds of statistical studies:
Observational Study
An observational study is when the researcher collects and
analyzes the data without intervening.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Kinds of Statistical Studies
There are two different kinds of statistical studies:
Observational Study
An observational study is when the researcher collects and
analyzes the data without intervening.
Examples:
Cholera Outbreak of 1854
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Kinds of Statistical Studies
There are two different kinds of statistical studies:
Observational Study
An observational study is when the researcher collects and
analyzes the data without intervening.
Examples:
Cholera Outbreak of 1854
your semester projects
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Kinds of Statistical Studies
There are two different kinds of statistical studies:
Observational Study
An observational study is when the researcher collects and
analyzes the data without intervening.
Examples:
Cholera Outbreak of 1854
your semester projects
Experiment
An experiment is when the researcher introduces specifics changes
in order to observe the effects of these changes.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Kinds of Statistical Studies
There are two different kinds of statistical studies:
Observational Study
An observational study is when the researcher collects and
analyzes the data without intervening.
Examples:
Cholera Outbreak of 1854
your semester projects
Experiment
An experiment is when the researcher introduces specifics changes
in order to observe the effects of these changes.
Example: Pavlov’s experiment on classical conditioning
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Observational Study vs Experiment
The key difference between observational studies and experiments
are the role that the research plays in the study.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Observational Study vs Experiment
The key difference between observational studies and experiments
are the role that the research plays in the study.
In observational studies, the researcher only plays a passive,
observational role. They do not play any kind of interactive role
with what they are studying.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Observational Study vs Experiment
The key difference between observational studies and experiments
are the role that the research plays in the study.
In observational studies, the researcher only plays a passive,
observational role. They do not play any kind of interactive role
with what they are studying.
In experiments, the researcher manipulates one variable to see
how it affects another variable, which requires active interaction
with what they are studying.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Variables
Variables in Observational Studies
1 Response Variables A variable that is the primary focus of
observation in the study.
2 Explanatory Variable A variable that may explain changes in
the response variable. Note an observational study may not
have explanatory variables.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Variables
Variables in Observational Studies
1 Response Variables A variable that is the primary focus of
observation in the study.
2 Explanatory Variable A variable that may explain changes in
the response variable. Note an observational study may not
have explanatory variables.
Variables in Experiments
1 Independent Variable: A variable that is stand alone. That
is, they do not change as a result of other variables in the
study.
2 Dependent Variables: these are variables that do depend on
another variable. In other words, these variables change in
response to a change in another variable.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Experimental Design
3 key elements of a well designed experiment:
1 control
2 randomization
3 replication
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Control
It is important for the researcher to have sufficient control over an
experiment. If there isn’t sufficient control, then the results of the
experiments may be biased.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Control
It is important for the researcher to have sufficient control over an
experiment. If there isn’t sufficient control, then the results of the
experiments may be biased.
Confounding variables
A confounding variable occurs when the researcher cannot tell
the difference between the effects of different factors on the
variable.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Control
It is important for the researcher to have sufficient control over an
experiment. If there isn’t sufficient control, then the results of the
experiments may be biased.
Confounding variables
A confounding variable occurs when the researcher cannot tell
the difference between the effects of different factors on the
variable.
Example: A coffee shop is experimenting about how offering
different kinds of food increases business. But if a local attraction
opens down the road at the same time as this experiment, then it
will not be clear what the cause of the increase in business is. In
this case, the opening of the local attraction is the confounding
variable.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Control
Blinding
The technique of blinding is when subjects of the experiment do
not know whether they are receiving treatment or the placebo.
That is, the do not know whether they are a part of the test group
or the control group.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Control
Blinding
The technique of blinding is when subjects of the experiment do
not know whether they are receiving treatment or the placebo.
That is, the do not know whether they are a part of the test group
or the control group.
Example: Scientists who are testing the side-effects of a new
pharmaceutical may use the technique of blinding so that the
subjects are more likely to give genuine reactions and responses to
the treatment.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Control
Blinding
The technique of blinding is when subjects of the experiment do
not know whether they are receiving treatment or the placebo.
That is, the do not know whether they are a part of the test group
or the control group.
Example: Scientists who are testing the side-effects of a new
pharmaceutical may use the technique of blinding so that the
subjects are more likely to give genuine reactions and responses to
the treatment.
This technique counteracts the placebo effect which is when
subjects reacts favorably to a placebo even though they have not
been given the actual treatment.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Randomization
During the set-up of an experiment, researchers will often have to
assign subjects to different groups—test groups and control
groups. It is important that groups are not set-up in a way that
introduces bias.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Randomization
During the set-up of an experiment, researchers will often have to
assign subjects to different groups—test groups and control
groups. It is important that groups are not set-up in a way that
introduces bias.
Randomization
Randomization is the method of randomly assigning subjects to
groups.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Randomization
Methods of Randomization
Completely Randomized Design: Here subjects are
assigned to treatment groups completely at random.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Randomization
Methods of Randomization
Completely Randomized Design: Here subjects are
assigned to treatment groups completely at random.
Randomized Block Design: This method is used if there is
some property or characteristic that researchers want to make
sure is distributed throughout the experiment. For instance,
subjects may be first broken into age group and then randomly
assigned to a treatment group from within their age group.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Replication
Replication
A good experiment or study should always be able to be
replicated. Replication is a test of the validity and reliability of
the experiment’s results.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Replication
Replication
A good experiment or study should always be able to be
replicated. Replication is a test of the validity and reliability of
the experiment’s results.
Why is replication important?
When an experiment or study is replicated and the same
conclusions are drawn from the replication, then we get a
better confirmation of those conclusions. We have more
reason to accept them.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Replication
Replication
A good experiment or study should always be able to be
replicated. Replication is a test of the validity and reliability of
the experiment’s results.
Why is replication important?
When an experiment or study is replicated and the same
conclusions are drawn from the replication, then we get a
better confirmation of those conclusions. We have more
reason to accept them.
If an experiment cannot be replicated, then it suggests that
there was something specific about it’s process that could
have biased the results.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Step 3: Collect the Data
An important component of data collection is using a reliable
sampling method. There are several sampling methods to consider:
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Step 3: Collect the Data
An important component of data collection is using a reliable
sampling method. There are several sampling methods to consider:
Sampling Methods
1 Random sampling
2 Stratified Sample
3 Cluster Sample
4 Systematic Sample
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Sampling Methods
Random Sampling
A random sample is one in which every member of the population
is equally likely to be selected for the sample.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Sampling Methods
Random Sampling
A random sample is one in which every member of the population
is equally likely to be selected for the sample.A simple random
sampling is when every member of the population has an equal
chance of being selected and every possible sample (of the same
size) is equally likely to be the actual sample.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Sampling Methods
Random Sampling
A random sample is one in which every member of the population
is equally likely to be selected for the sample.A simple random
sampling is when every member of the population has an equal
chance of being selected and every possible sample (of the same
size) is equally likely to be the actual sample.
Example: One way to select a random sample is to assign every
member of the population a number and then randomly select
numbers to include in the sample.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Sampling Methods
Random Numbers in Excel
Note that you can generate a random number in excel using the
command =RANDBETWEEN(lower number, higher number).
This can allow you to generate a random sample.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Sampling Methods
Stratified Sample
In a stratified sample, the population is broken into groups or
strata before the sample is selected. This is to ensure that some
members from each group are included in the sample.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Sampling Methods
Stratified Sample
In a stratified sample, the population is broken into groups or
strata before the sample is selected. This is to ensure that some
members from each group are included in the sample.
Example: If a new drug is being tested, then a stratified sample
may be used to ensure that people all of ages are being tested. To
do this, the population would be broken into groups by age before
the sample is selected.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Sampling Methods
Stratified Sample
In a stratified sample, the population is broken into groups or
strata before the sample is selected. This is to ensure that some
members from each group are included in the sample.
Example: If a new drug is being tested, then a stratified sample
may be used to ensure that people all of ages are being tested. To
do this, the population would be broken into groups by age before
the sample is selected.
30 − 39 40 − 49 50 − 59
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Sampling Methods
Cluster Sample
A cluster sample is used when the population is naturally divided
into groups and it is appropriate to use one or more (but not all of
them) of these groups as the sample.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Sampling Methods
Cluster Sample
A cluster sample is used when the population is naturally divided
into groups and it is appropriate to use one or more (but not all of
them) of these groups as the sample.
Example: A study about what LMC students think about the new
food service in the cafeteria could be conducted using a cluster
sample. LMC students are naturally divided into groups based on
the dorms where they live. For this study the sample could be
chosen as the students in one or more specific dorms.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Sampling Methods
Systematic Sample
A systematic sample involves assigning each member of the
population, then ordering the members of the population, and
systematically selecting them. That is, a random number is
selected as a starting place and then you select every nth member
of the list.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Sampling Methods
Systematic Sample
A systematic sample involves assigning each member of the
population, then ordering the members of the population, and
systematically selecting them. That is, a random number is
selected as a starting place and then you select every nth member
of the list.
Example:
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Sampling
All of these sampling methods can be useful, but it is important to
consider the details of the study and data collection to ensure that
a sampling method does not introduce bias.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Sampling
All of these sampling methods can be useful, but it is important to
consider the details of the study and data collection to ensure that
a sampling method does not introduce bias.
Convenience Sampling
One method of sampling that should be avoided is called
convenience sampling. This method is when members of the
population are selected for the sample out of convenience.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Bad Statistics
Throughout this chapter, we’ve emphasized the importance of how
a statistical study is designed and the fact that statistical methods
can sometimes be misused. To further illustrate the significance of
this, let’s look at some example of failed statistical studies.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Bad Statistics
Throughout this chapter, we’ve emphasized the importance of how
a statistical study is designed and the fact that statistical methods
can sometimes be misused. To further illustrate the significance of
this, let’s look at some example of failed statistical studies.
Failures of Statistics
The Law of Small Numbers
Francis Galton’s work on heredity and intelligence.
Norwegian testing of the meningococcus vaccine.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
The Law of Small Numbers
The Law of Small Numbers
This the incorrect belief that a small sample will display the same
behavior as the total population.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
The Law of Small Numbers
The Law of Small Numbers
This the incorrect belief that a small sample will display the same
behavior as the total population.
This law is appealed to quite commonly and can lead to
harmful generalizations about a population.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
The Law of Small Numbers
The Law of Small Numbers
This the incorrect belief that a small sample will display the same
behavior as the total population.
This law is appealed to quite commonly and can lead to
harmful generalizations about a population.
Has been appealed to in politics, medicine, for new articles.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
The Law of Small Numbers
The Law of Small Numbers
This the incorrect belief that a small sample will display the same
behavior as the total population.
This law is appealed to quite commonly and can lead to
harmful generalizations about a population.
Has been appealed to in politics, medicine, for new articles.
To be sure that a conclusion from a statistical study is
reliable, it is necessary to determine that the chosen sample is
representative.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Francis Galton
Galton’s work on Intelligence
Francis Galton was a scientist working in the 1800s in a
variety of fields. He hypothesized that human intelligence is
hereditary—i.e., passed on through genetics.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Francis Galton
Galton’s work on Intelligence
Francis Galton was a scientist working in the 1800s in a
variety of fields. He hypothesized that human intelligence is
hereditary—i.e., passed on through genetics.
Galton’s work on intelligence was problematic in several ways:
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Francis Galton
Galton’s work on Intelligence
Francis Galton was a scientist working in the 1800s in a
variety of fields. He hypothesized that human intelligence is
hereditary—i.e., passed on through genetics.
Galton’s work on intelligence was problematic in several ways:
He ignored confounding variables—such as the role that
environmental influences play.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Francis Galton
Galton’s work on Intelligence
Francis Galton was a scientist working in the 1800s in a
variety of fields. He hypothesized that human intelligence is
hereditary—i.e., passed on through genetics.
Galton’s work on intelligence was problematic in several ways:
He ignored confounding variables—such as the role that
environmental influences play.
He did not conduct his study in a systematic and rigorous way.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Francis Galton
Galton’s work on Intelligence
Francis Galton was a scientist working in the 1800s in a
variety of fields. He hypothesized that human intelligence is
hereditary—i.e., passed on through genetics.
Galton’s work on intelligence was problematic in several ways:
He ignored confounding variables—such as the role that
environmental influences play.
He did not conduct his study in a systematic and rigorous way.
There is evidence that he fabricated at least some of the
statistical evidence he relied on.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Francis Galton
Galton’s work on Intelligence
Francis Galton was a scientist working in the 1800s in a
variety of fields. He hypothesized that human intelligence is
hereditary—i.e., passed on through genetics.
Galton’s work on intelligence was problematic in several ways:
He ignored confounding variables—such as the role that
environmental influences play.
He did not conduct his study in a systematic and rigorous way.
There is evidence that he fabricated at least some of the
statistical evidence he relied on.
Consequences
The conclusions of Galton’s research and the theory that
intelligence is purely hereditary was used to justify oppressive social
programs and gave rise to eugenics movements.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Meningococcus vaccine in Norway
Meningococcus vaccine study
In Norway, one-hundred and eighty thousand teenagers were
subjects of a test of a new vaccine for meningococcus. Going
into the study, subjects were told that “it is unlikely to expect
serious complications” as a result of the trial.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Meningococcus vaccine in Norway
Meningococcus vaccine study
In Norway, one-hundred and eighty thousand teenagers were
subjects of a test of a new vaccine for meningococcus. Going
into the study, subjects were told that “it is unlikely to expect
serious complications” as a result of the trial.
Before the study, began the researchers were aware that
serious side-effects of the vaccine could not be ruled out, but
they neglected to honestly report this to the subjects of the
study.
Ch 1: Intro to Stats
Section 1.1: Overview of Statistics
Section 1.2: Data Classification
Section 1.3: Data Collection and Experimental Design
Meningococcus vaccine in Norway
Meningococcus vaccine study
In Norway, one-hundred and eighty thousand teenagers were
subjects of a test of a new vaccine for meningococcus. Going
into the study, subjects were told that “it is unlikely to expect
serious complications” as a result of the trial.
Before the study, began the researchers were aware that
serious side-effects of the vaccine could not be ruled out, but
they neglected to honestly report this to the subjects of the
study.
Several subjects of the trial did experience serious side-effects,
including the development of serious neurological diseases.
Ch 1: Intro to Stats