After determining that the question is inferential in nature, we then must classify it as one of the following:

After determining that the question is inferential in nature, we then must classify it as one of the following:

These four classifications encompass the majority of inferential statistical methods that exist.

So, let’s begin with . . .

So, let’s begin with . . .

Drum-roll please?

Questions of difference

Questions of difference

Questions of difference

As a general rule, a question of difference asks if one group is different, similar, or comparable to another group in terms of some outcome.

Let’s see this visually:

Let’s see this visually:

Group 1

Let’s see this visually:

Group 1is different, similar, or

comparable to

Let’s see this visually:

Group 1 Group 2is different, similar, or

comparable to

Let’s see this visually:

Group 1 based onGroup 2is different, similar, or

comparable to

Let’s see this visually:

Group 1 based on Some Outcome

Group 2is different, similar, or

comparable to

Let’s look at an example:

Researchers want to determine who drives faster women or men.

Researchers want to determine who drives faster women or men.

Researchers want to determine who drives faster women or men.

Group 1 based on Some Outcome

Group 2

is different, similar, or

comparable to

Researchers want to determine who drives faster women or men.

Group 1 based on Some Outcome

Group 2

is different, similar, or

comparable to

Researchers want to determine who drives faster women or men.

WOMEN based on Some Outcome

Group 2

are different, similar, or

comparable to

Researchers want to determine who drives faster women or men.

WOMEN based on Some Outcome

Group 2

are different, similar, or

comparable to

Researchers want to determine who drives faster women or men.

WOMEN based on Some Outcome

Group 2

are different, similar, or

comparable to

Researchers want to determine who drives faster women or men.

WOMEN based on Some Outcome

Group 2

are different, similar, or

comparable to

Researchers want to determine who drives faster women or men.

WOMEN based on Some Outcome

MEN

are different, similar, or

comparable to

Researchers want to determine who drives faster women or men.

WOMEN based on Some Outcome

MEN

are different, similar, or

comparable to

Researchers want to determine who drives faster women or men.

WOMEN based on DRIVING SPEED

MEN

are different, similar, or

comparable to

Researchers want to determine who drives faster women or men.

WOMEN based on DRIVING SPEED

MEN

Therefore, this is a question of Difference

are different, similar, or

comparable to

Here is another example,

A study seeks to understand if teenagers are more likely to text while driving than adults.

A study seeks to understand if teenagers are more likely to text while driving than adults.

A study seeks to understand if teenagers are more likely to text while driving than adults.

Group 1 based on Some Outcome

Group 2

are different, similar, or

comparable to

A study seeks to understand if teenagers are more likely to text while driving than adults.

Group 1 based on Some Outcome

Group 2

are different, similar, or

comparable to

are different, similar, or

comparable to

Group 1 based on Some Outcome

Group 2

Investigators seeks to understand if teenagersare more likely to text while driving than adults. They administer an anonymous survey to each group and compare the results.

are different, similar, or

comparable to

TEENAGERS based on Some Outcome

Group 2

Investigators seeks to understand if teenagersare more likely to text while driving than adults. They administer an anonymous survey to each group and compare the results.

TEENAGERS based on Some Outcome

Group 2

are different, similar, or

comparable to

Investigators seeks to understand if teenagers are more likely to text while driving than adults. They administer an anonymous survey to each group and compare the results.

TEENAGERS based on Some Outcome

Group 2

are different, similar, or

comparable to

Investigators seeks to understand if teenagers are more likely to text while driving than adults. They administer an anonymous survey to each group and compare the results.

Investigators seeks to understand if teenagers are more likely to text while driving than adults. They administer an anonymous survey to each group and compare the results.

TEENAGERS based on Some Outcome

Group 2

are different, similar, or

comparable to

TEENAGERS based on Some Outcome

ADULTS

are different, similar, or

comparable to

Investigators seeks to understand if teenagers are more likely to text while driving than adults. They administer an anonymous survey to each group and compare the results.

TEENAGERS based on Some Outcome

ADULTS

are different, similar, or

comparable to

Investigators seeks to understand if teenagers are more likely to text while driving than adults. They administer an anonymous survey to each group and compare the results.

TEENAGERS based on Some Outcome

ADULTS

are different, similar, or

comparable to

Investigators seeks to understand if teenagers are more likely to text while driving than adults. They administer an anonymous survey to each group and compare the results.

TEENAGERS based onTEXTING WHILE

DRIVINGADULTS

Therefore, this is a question of Difference

are different, similar, or

comparable to

Investigators seeks to understand if teenagers are more likely to text while driving than adults. They administer an anonymous survey to each group and compare the results.

Now let’s see an example examining the difference between three groups.

Investigators wish to determine who spends more time on electronics: tweens, teenagers or college freshmen.

Investigators wish to determine who spends more time on electronics: tweens, teenagers or college freshmen.

Investigators wish to determine who spends more time on electronics: tweens, teenagers or college freshmen.

Group 1

are different, similar or

comparable to one another

based on

Some Outcome

Group 2 & Group 3

Investigators wish to determine who spends more time on electronics: tweens, teenagers or college freshmen.

Group 1Some

OutcomeGroup 2 & Group 3

are different, similar or

comparable to one another

based on

Investigators wish to determine who spends more time on electronics: tweens, teenagers or college freshmen.

TWEENSSome

OutcomeGroup 2 & Group 3

are different, similar or

comparable to one another

based on

Investigators wish to determine who spends more time on electronics: tweens, teenagers or college freshmen.

TWEENSSome

OutcomeGroup 2 & Group 3

are different, similar or

comparable to one another

based on

Investigators wish to determine who spends more time on electronics: tweens, teenagers or college freshmen.

TWEENSSome

OutcomeTEENAGERS & Group 3

are different, similar or

comparable to one another

based on

Investigators wish to determine who spends more time on electronics: tweens, teenagers or college freshmen.

TWEENSSome

OutcomeTEENAGERS & Group 3

are different, similar or

comparable to one another

based on

Investigators wish to determine who spends more time on electronics: tweens, teenagers or college freshmen.

TWEENSSome

OutcomeTEENAGERS &

COLLEGE FRESHMEN

are different, similar or

comparable to one another

based on

Investigators wish to determine who spends more time on electronics: tweens, teenagers or college freshmen.

TWEENSSome

OutcomeTEENAGERS &

COLLEGE FRESHMEN

are different, similar or

comparable to one another

based on

Investigators wish to determine who spends more time on electronics: tweens, teenagers or college freshmen.

TWEENSSome

OutcomeTEENAGERS &

COLLEGE FRESHMEN

are different, similar or

comparable to one another

based on

Investigators wish to determine who spends more time on electronics: tweens, teenagers or college freshmen.

TWEENS TEENAGERS &COLLEGE

FRESHMENSome

Outcome

are different, similar or

comparable to one another

based on

Investigators wish to determine who spends more time on electronics: tweens, teenagers or college freshmen.

TWEENS

TIME SPENT ON

ELECTRONICSTEENAGERS &

COLLEGE FRESHMEN

are different, similar or

comparable to one another

based on

Investigators wish to determine who spends more time on electronics: tweens, teenagers or college freshmen.

TWEENS

TIME SPENT ON

ELECTRONICSTEENAGERS &

COLLEGE FRESHMEN

are different, similar or

comparable to one another

based onTherefore, this is a question of Difference between more than two

groups

This time, let’s see an example where we are looking at similarities between two groups instead of differences:

The average score nationwide on the verbal section of the GRE is 610.

The average score nationwide on the verbal section of the GRE is 610.

The average score nationwide on the verbal section of the GRE is 610. A researcher wants to do an experiment on a group (or sample) of graduate students that represent those with typical GRE verbal scores.

The average score nationwide on the verbal section of the GRE is 610. A researcher wants to do an experiment on a group (or sample) of graduate students that represent those with typical GRE verbal scores. So, she takes a sample of 50 grad students to see if they have statistically similar GRE verbal scores to the population.

The average score nationwide on the verbal section of the GRE is 610. A researcher wants to do an experiment on a group (or sample) of graduate students that represent those with typical GRE verbal scores. So, she takes a sample of 50 grad students to see if they have statistically similar GRE verbal scores to the population.

is similar to based on Some Outcome

A population

A sample

The average score nationwide on the verbal section of the GRE is 610. A researcher wants to do an experiment on a group (or sample) of graduate students that represent those with typical GRE verbal scores. So, she takes a sample of 50 grad students to see if they have statistically similar GRE verbal scores to the population.

is similar to based on Some Outcome

Group 1A

population

The average score nationwide on the verbal section of the GRE is 610. A researcher wants to do an experiment on a group (or sample) of graduate students that represent those with typical GRE verbal scores. So, she takes a sample of 50 grad students to see if they have statistically similar GRE verbal scores to the population.

is similar to based on Some Outcome

Sample of 50 Grad Students

A population

The average score nationwide on the verbal section of the GRE is 610. A researcher wants to do an experiment on a group (or sample) of graduate students that represent those with typical GRE verbal scores. So, she takes a sample of 50 grad students to see if they have statistically similar GRE verbal scores to the population.

is similar to based on Some Outcome

Sample of 50 Grad Students

A population

The average score nationwide on the verbal section of the GRE is 610. A researcher wants to do an experiment on a group (or sample) of graduate students that represent those with typical GRE verbal scores. So, she takes a sample of 50 grad students to see if they have statistically similar GRE verbal scores to the population.

is similar to based on Some Outcome

Sample of 50 Grad Students

A population

The average score nationwide on the verbal section of the GRE is 610. A researcher wants to do an experiment on a group (or sample) of graduate students that represent those with typical GRE verbal scores. So, she takes asample of 50 grad students to see if they have statistically similar GRE verbal scores to the population.

is similar to based on Some Outcome

Sample of 50 Grad Students

A population

The average score nationwide on the verbal section of the GRE is 610. A researcher wants to do an experiment on a group (or sample) of graduate students that represent those with typical GRE verbal scores. So, she takes asample of 50 grad students to see if they have statistically similar GRE verbal scores to the population.

is similar to based on Some Outcome

Sample of 50 Grad Students

Populationof Grad

Students

The average score nationwide on the verbal section of the GRE is 610. A researcher wants to do an experiment on a group (or sample) of graduate students that represent those with typical GRE verbal scores. So, she takes a sample of 50 grad students to see if they have statistically similar GRE verbal scores to the population.

is similar to based on Some Outcome

Sample of 50 Grad Students

Populationof Grad

Students

The average score nationwide on the verbal section of the GRE is 610. A researcher wants to do an experiment on a group (or sample) of graduate students that represent those with typical GRE verbal scores. So, she takes a sample of 50 grad students to see if they have statistically similar GRE verbal scores to the population.

is similar to based on Some Outcome

Sample of 50 Grad Students

Populationof Grad

Students

The average score nationwide on the verbal section of the GRE is 610. A researcher wants to do an experiment on a group (or sample) of graduate students that represent those with typical GRE verbal scores. So, she takes a sample of 50 grad students to see if they have statistically similar GRE verbal scores to the population.

is similar to based on

GRE Verbal Scores

Populationof Grad

Students

Sample of 50 Grad Students

The average score nationwide on the verbal section of the GRE is 610. A researcher wants to do an experiment on a group (or sample) of graduate students that represent those with typical GRE verbal scores. So, she takes a sample of 50 grad students to see if they have statistically similar GRE verbal scores to the population.

is similar to based on

GRE Verbal Scores

The Population

of Grad Students

A Sample of 50 Grad

Students

Therefore, this is a question of Similarity between a sample and a

population, but classified as difference

In many studies the only difference is that one group experiences something and the other group does not experience it.

In many studies the only difference is that one group experiences something and the other group does not experience it.

The group that experiences or is given something is generally known as the “experimental” or “treatment” group.

In many studies the only difference is that one group experiences something and the other group does not experience it.

The group that experiences or is given something is generally known as the “experimental” or “treatment” group.

In many studies the only difference is that one group experiences something and the other group does not experience it.

The group that does not experience nor is given something is generally known as the “control” group.

Here is how a problem like this is generally written:

Scientist wish to determine the effect of an innovative instructional software on high school student AP stats exam scores.

Scientist wish to determine the effect of an innovative instructional software on high school student AP stats exam scores.

Scientist wish to determine the effect of an innovative instructional software on high school student AP stats exam scores.

Two groups are selected.

Scientist wish to determine the effect of an innovative instructional software on high school student AP stats exam scores.

Two groups are selected. One group uses the innovative software and the other group does not.

Scientist wish to determine the effect of an innovative instructional software on high school student AP stats exam scores.

Two groups are selected. One group uses the innovative software and the other group does not. Their exam scores are then compared.

Scientist wish to determine the effect of an innovative instructional software on high school student AP stats exam scores.

Two groups are selected. One group uses the innovative software and the other group does not. Their exam scores are then compared.

based on Some Outcome

Group 2Group 1 is different than

Scientist wish to determine the effect of an innovative instructional software on high school student AP stats exam scores.

Two groups are selected. One group uses the innovative software and the other group does not. Their exam scores are then compared.

based on Some Outcome

Group 2Group 1 is different than

Scientist wish to determine the effect of an innovative instructional software on high school student AP stats exam scores.

Two groups are selected. One group uses the innovative software and the other group does not. Their exam scores are then compared.

based on Some Outcome

Group 2Group using

software

is different than

Scientist wish to determine the effect of an innovative instructional software on high school student AP stats exam scores.

Two groups are selected. One group uses the innovative software and the other group does not. Their exam scores are then compared.

based on Some Outcome

Group 2Group using

software

is different than

Scientist wish to determine the effect of an innovative instructional software on high school student AP stats exam scores.

Two groups are selected. One group uses the innovative software and the other group does not. Their exam scores are then compared.

based on Some Outcome

Group NOT using software

Group using

software

is different than

Scientist wish to determine the effect of an innovative instructional software on high school student AP stats exam scores.

Two groups are selected. One group uses the innovative software and the other group does not. Their exam scores are then compared.

based on Some Outcome

Group using

software

is different than

Group NOT using software

Scientist wish to determine the effect of an innovative instructional software on high school student AP stats exam scores.

Two groups are selected. One group uses the innovative software and the other group does not. Their exam scores are then compared.

based onAP Stats

Exam Scores

Group using

software

is different than

Group NOT using software

In some situation the difference will not be between two groups,

In some situation the difference will not be between two groups, but between the same group on two or more different occasions or times.

Let’s see a visual of that:

Let’s see a visual of that:

Group 1 (Time 1)

Let’s see a visual of that:

Group 1 (Time 1)

is different than

Let’s see a visual of that:

Group 1 (Time 2)

Group 1 (Time 1)

is different than

Let’s see a visual of that:

Group 1 (Time 2)

Group 1 (Time 1)

is different than

The time is different but the

group is the same

Let’s see a visual of that:

based onGroup 1 (Time 2)

Group 1 (Time 1)

is different than

Let’s see a visual of that:

based on Some Outcome

Group 1 (Time 2)

Group 1 (Time 1)

is different than

Here is an example of this:

An anti-boredom medication has been developed by scientists to combat boredom.

An anti-boredom medication has been developed by scientists to combat boredom.

An anti-boredom medication has been developed by scientists to combat boredom. A group of students who report being bored with school are administered a boredom survey and then administered the anti-boredom medication for three weeks.

An anti-boredom medication has been developed by scientists to combat boredom. A group of students who report being bored with school are administered a boredom survey and then administered the anti-boredom medication for three weeks. At the beginning of the fourth week the boredom survey is administered again and the results are compared.

An anti-boredom medication has been developed by scientists to combat boredom. A group of students who report being bored with school are administered a boredom survey and then administered the anti-boredom medication for three weeks. At the beginning of the fourth week the boredom survey is administered again and the results are compared.

based on Some Outcome

Group 1 (Time 2)

Group 1 (Time 1)

is different than

An anti-boredom medication has been developed by scientists to combat boredom. A group of students who report being bored with school are administered a boredom survey and then administered the anti-boredom medication for three weeks. At the beginning of the fourth week the boredom survey is administered again and the results are compared.

based on Some Outcome

Group 1 (Time 2)

is different than

Group 1 (Time 1)

An anti-boredom medication has been developed by scientists to combat boredom. A group of students who report being bored with school are administered a boredom survey and then administered the anti-boredom medication for three weeks. At the beginning of the fourth week the boredom survey is administered again and the results are compared.

based on Some Outcome

Group 1 (Time 2)

The Group BEFORE taking

medication

is different than

An anti-boredom medication has been developed by scientists to combat boredom. A group of students who report being bored with school are administered a boredom survey and then administered the anti-boredom medication for three weeks. At the beginning of the fourth week the boredom survey is administered again and the results are compared.

based on Some Outcome

Group 1 (Time 2)

The Group BEFOREtaking

medication

is different than

An anti-boredom medication has been developed by scientists to combat boredom. A group of students who report being bored with school are administered a boredom survey and then administered the anti-boredom medication for three weeks. At the beginning of the fourth week the boredom survey is administered again and the results are compared.

based on Some Outcome

The Group BEFOREtaking

medication

is different than or

comparableto

Group 1 (Time 2)

An anti-boredom medication has been developed by scientists to combat boredom. A group of students who report being bored with school are administered a boredom survey and then administered the anti-boredom medication for three weeks. At the beginning of the fourth week the boredom survey is administered again and the results are compared.

based on Some Outcome

Group 1 (Time 2)

The Group BEFOREtaking

medication

is different than or

comparableto

An anti-boredom medication has been developed by scientists to combat boredom. A group of students who report being bored with school are administered a boredom survey and then administered the anti-boredom medication for three weeks. At the beginning of the fourth week the boredom survey is administered again and the results are compared.

based on Some Outcome

The Group AFTER taking

medicaion

The Group BEFORE taking

medication

is different than or

comparableto

An anti-boredom medication has been developed by scientists to combat boredom. A group of students who report being bored with school are administered a boredom survey and then administered the anti-boredom medication for three weeks. At the beginning of the fourth week the boredom survey is administered again and the results are compared.

based on Some Outcome

The Group AFTER taking

medicaion

The Group BEFORE taking

medication

is different than or

comparableto

An anti-boredom medication has been developed by scientists to combat boredom. A group of students who report being bored with school are administered a boredom survey and then administered the anti-boredom medication for three weeks. At the beginning of the fourth week the boredom survey is administered again and the results are compared.

based on Some Outcome

The Group AFTER taking

medicaion

The Group BEFORE taking

medication

is different than or

comparableto

An anti-boredom medication has been developed by scientists to combat boredom. A group of students who report being bored with school are administered a boredom survey and then administered the anti-boredom medication for three weeks. At the beginning of the fourth week the boredom survey is administered again and the results are compared.

based on Degree of Boredom

The Group AFTER taking

medicaion

The Group BEFORE taking

medication

is different than or

comparableto

Finally, let’s look at a “difference” problem that has a lot of other elements in it, that may make it difficult to classify as difference.

Scientist wish to determine the effect of an innovative instructional software on high school student AP stats exam scores across gender.

Scientist wish to determine the effect of an innovative instructional software on high school student AP stats exam scores across gender.

Two groups are selected.

Scientist wish to determine the effect of an innovative instructional software on high school student AP stats exam scores across gender.

Two groups are selected. One group uses the innovative software and the other group does not. Their exam scores are then compared.

Scientist wish to determine the effect of an innovative instructional software on high school student AP stats exam scores across gender.

Two groups are selected. One group uses the innovative software and the other group does not. Their exam scores are then compared.

After running this comparison the scientist control for year in school as well as IQ scores.

Scientist wish to determine the effect of an innovative instructional software on high school student AP stats exam scores across gender.

Two groups are selected. One group uses the innovative software and the other group does not. Their exam scores are then compared. After running this comparison the scientist control for year in school as well as IQ scores.

Wow, there is a lot going on here!

Scientist wish to determine the effect of an innovative instructional software on high school student AP stats exam scores across gender.

Two groups are selected. One group uses the innovative software and the other group does not. Their exam scores are then compared. After running this comparison control for year in school as well as IQ scores.

The first thing we need to do is determine if there is a difference

here.

Scientist wish to determine the effect of an innovative instructional software on high school student AP stats exam scores across gender.

Two groups are selected. One group uses the innovative software and the other group does not. Their exam scores are then compared. After running this comparison control for year in school as well as IQ scores.

Are there two or more groups?

Scientist wish to determine the effect of an innovative instructional software on high school student AP stats exam scores across gender.

Two groups are selected. One group uses the innovative software and the other group does not. Their exam scores are then compared. After running this comparison control for year in school as well as IQ scores.

Are there two or more groups?

Scientist wish to determine the effect of an innovative instructional software on high school student AP stats exam scores across gender.

Two groups are selected. One group uses the innovative software and the other group does not. Their exam scores are then compared. After running this comparison control for year in school as well as IQ scores.

Are there two or more groups?

Scientist wish to determine the effect of an innovative instructional software on high school student AP stats exam scores across gender.

Two groups are selected. One group uses the innovative software and the other group does not. Their exam scores are then compared. After running this comparison control for year in school as well as IQ scores.

Yes, there are two groups

Scientist wish to determine the effect of an innovative instructional software on high school student AP stats exam scores across gender.

Two groups are selected. One group uses the innovative software and the other group does not. Their exam scores are then compared. After running this comparison control for year in school as well as IQ scores.

Are we looking for differences, similarities or comparisons?

Scientist wish to determine the effect of an innovative instructional software on high school student AP stats exam scores across gender.

Two groups are selected. One group uses the innovative software and the other group does not. Their exam scores are then compared. After running this comparison control for year in school as well as IQ scores.

Are we looking for differences, similarities or comparisons?

Scientist wish to determine the effect of an innovative instructional software on high school student AP stats exam scores across gender.

Two groups are selected. One group uses the innovative software and the other group does not. Their exam scores are then compared. After running this comparison control for year in school as well as IQ scores.

Even though there are many other things going on in this

problem, like

Scientist wish to determine the effect of an innovative instructional software on high school student AP stats exam scores across gender.

Two groups are selected. One group uses the innovative software and the other group does not. Their exam scores are then compared. After running this comparison control for year in school as well as IQ scores.

Questions about the role of gender on the results

Scientist wish to determine the effect of an innovative instructional software on high school student AP stats exam scores across gender.

Two groups are selected. One group uses the innovative software and the other group does not. Their exam scores are then compared. After running this comparison control for year in school as well as IQ scores.

or year in school

Scientist wish to determine the effect of an innovative instructional software on high school student AP stats exam scores across gender.

Two groups are selected. One group uses the innovative software and the other group does not. Their exam scores are then compared. After running this comparison control for year in school as well as IQ scores.

or IQ scores

Scientist wish to determine the effect of an innovative instructional software on high school student AP stats exam scores across gender.

Two groups are selected. One group uses the innovative software and the other group does not. Their exam scores are then compared. After running this comparison control for year in school as well as IQ scores.

The CENTRAL FOCUS of the question is on the difference between the GROUP who uses the

software and the GROUP who does not.

In summary

Questions of difference essentially examine the difference, similarity or comparison between two or more groups based on some outcome.

Questions of difference essentially examine the difference, similarity or comparison between two or more groups based on some outcome.

Group 1 based on Some Outcome

Group 2is different, similar, or

comparable to

At times, there may be more than two groups in the problem or research question.

At times, there may be more than two groups in the problem or research question.

Group 1

are different, similar or

comparable to one another

based on

Some Outcome

Group 2 & Group 3

Some times those differences are between two groups or the same group at two different times.

Some times those differences are between two groups or the same group at two different times.

based on Some Outcome

Group 1 (Time 2)

Group 1 (Time 1)

is different than

And at times you may be examining how similar or representative a sample is to a population.

And at times you may be examining how similar or representative a sample is to a population.

is similar to based on Some Outcome

A population

A sample

Some of the words to look for in your problem to determine if it is a question of difference are:

Some of the words to look for in your problem to determine if it is a question of difference are:

• More

• Statistically different

• Two groups

• Two samples

• Etc.

Examine the question or problem you are working on.

Is it a question of difference?

If so, select DIFFERENCE

If so, select DIFFERENCE