How many dependent variables?

The purpose of this presentation is to assist you in determining the number of dependent variables in the problem you are working on.

Here are your options:

Here are your options:

1 Dependent Variable

2+ Dependent Variables

In statistics we are generally attempting to determine what causes what?

In statistics we are generally attempting to determine what causes what?

Cause

In statistics we are generally attempting to determine what causes what?

Cause

In statistics we are generally attempting to determine what causes what?

Cause Effect

Or what influences what?

Or what influences what?

Influencer Influenced

Or what influences what?

Influencer Influenced

Or what influences what?

Influencer Influenced

Simply put, in the cause and effect model, the effect side of the equation is known as the dependent variable.

Effect

Simply put, in the cause and effect model, the effect side of the equation is known as the dependent variable.

Cause

Effect

Simply put, in the cause and effect model, the effect side of the equation is known as the dependent variable.

Cause

Effect

Simply put, in the cause and effect model, the effect side of the equation is known as the dependent variable.

Cause

Dependent Variable

Or in the influencer / influenced model, the influenced side of the equation is also known as the dependent variable.

Or in the influencer / influenced model, the influenced side of the equation is also known as the dependent variable.

InfluencedInfluencer

Or in the influencer / influenced model, the influenced side of the equation is also known as the dependent variable.

InfluencedInfluencer

Or in the influencer / influenced model, the influenced side of the equation is also known as the dependent variable.

InfluencedInfluencer

Dependent Variable

Let’s look at an example:

A researcher wishes to determine the degree to which test scores are influenced by amount of study time.

A researcher wishes to determine the degree to which test scores are influenced by amount of study time.

What is being influenced here?

A researcher wishes to determine the degree to which test scores are influenced by amount of study time.

What is being influenced here?

A researcher wishes to determine the degree to which test scores are influenced by amount of study time.

This is the Dependent Variable

A researcher wishes to determine the degree to which test scores are influenced by amount of study time.

What is the influencer?

A researcher wishes to determine the degree to which test scores are influenced by amount of study time.

What is the influencer?

A researcher wishes to determine the degree to which test scores are influenced by amount of study time.

A researcher wishes to determine the degree to which test scores are influenced by amount of study time.

InfluencedInfluencer

A researcher wishes to determine the degree to which test scores are influenced by amount of study time.

Dependent Variable

Influencer

Let’s look at another example almost identical to the last one.

A researcher wishes to determine the degree to which test scores are influenced by amount of sleep.

A researcher wishes to determine the degree to which test scores are influenced by amount of sleep.

What is being influenced here?

A researcher wishes to determine the degree to which test scores are influenced by amount of sleep.

What is being influenced here?

A researcher wishes to determine the degree to which test scores are influenced by amount of sleep.

This is the Dependent Variable

A researcher wishes to determine the degree to which test scores are influenced by amount of sleep.

What is the influencer?

A researcher wishes to determine the degree to which test scores are influenced by amount of sleep.

What is the influencer?

A researcher wishes to determine the degree to which test scores are influenced by amount of sleep.

A researcher wishes to determine the degree to which test scores are influenced by amount of sleep.

InfluencedInfluencer

A researcher wishes to determine the degree to which test scores are influenced by amount of sleep.

InfluencedInfluencer

A researcher wishes to determine the degree to which test scores are influenced by amount of sleep.

Test ScoresInfluencer

A researcher wishes to determine the degree to which test scores are influenced by amount of sleep.

Test ScoresInfluencer

The Dependent Variable

A researcher wishes to determine the degree to which test scores are influenced by amount of sleep.

Test ScoresInfluencer

A researcher wishes to determine the degree to which test scores are influenced by amount of sleep.

Test ScoresAmount of

Sleep

Let’s see how this question could be worded as an actual study.

Researchers wish to determine if the amount of sleep can have an effect on test scores.

Researchers wish to determine if the amount of sleep can have an effect on test scores. So, they randomly select two similar groups.

Researchers wish to determine if the amount of sleep can have an effect on test scores. So, they randomly select two similar groups. They ensure that one group gets 6-8 hours of sleep and a second group gets only 3-4 hours of sleep.

Researchers wish to determine if the amount of sleep can have an effect on test scores. So, they randomly select two similar groups. They ensure that one group gets 6-8 hours of sleep and a second group gets only 3-4 hours of sleep. That morning both groups are administered an academic test. The results are examined for differences.

Researchers wish to determine if the amount of sleep can have an effect on test scores. So, they randomly select two similar groups. They ensure that one group gets 6-8 hours of sleep and a second group gets only 3-4 hours of sleep. That morning both groups are administered an academic test. The results are examined for differences.

What is being influenced here?

Researchers wish to determine if the amount of sleep can have an effect on test scores. So, they randomly select two similar groups. They ensure that one group gets 6-8 hours of sleep and a second group gets only 3-4 hours of sleep. That morning both groups are administered an academic test. The results are examined for differences.

What is being influenced here?

Researchers wish to determine if the amount of sleep can have an effect on test scores. So, they randomly select two similar groups. They ensure that one group gets 6-8 hours of sleep and a second group gets only 3-4 hours of sleep. That morning both groups are administered an academic test. The results are examined for differences.

This is the DEPENDENT VARIABLE

Researchers wish to determine if the amount of sleep can have an effect on test scores. So, they randomly select two similar groups. They ensure that one group gets 6-8 hours of sleep and a second group gets only 3-4 hours of sleep. That morning both groups are administered an academic test. The results are examined for differences.

What is doing the influencing?

Researchers wish to determine if the amount of sleep can have an effect on test scores. So, they randomly select two similar groups. They ensure that one group gets 6-8 hours of sleep and a second group gets only 3-4 hours of sleep. That morning both groups are administered an academic test. The results are examined for differences.

What is doing the influencing?

See if you can identify the dependent variable in the following research studies.

Scientist wish to determine if -

- good nutrition results in increased longevity.

- time on social media impacts verbal skills.

- exercise effects heart health

- an instructional software helps students overcome conceptual gaps.

Scientist wish to determine if -

- good nutrition results in increased longevity.

- time on social media impacts verbal skills.

- exercise effects heart health

- an instructional software helps students overcome conceptual gaps.

Scientist wish to determine if -

- good nutrition results in increased longevity.

- time on social media impacts verbal skills.

- exercise effects heart health

- an instructional software helps students overcome conceptual gaps.

This is the DEPENDENT VARIABLE

Scientist wish to determine if -

- good nutrition results in increased longevity.

- time on social media impacts verbal skills.

- exercise effects heart health

- an instructional software helps students overcome conceptual gaps.

Scientist wish to determine if -

- good nutrition results in increased longevity.

- time on social media impacts verbal skills.

- exercise effects heart health

- an instructional software helps students overcome conceptual gaps.

This is the DEPENDENT VARIABLE

Scientist wish to determine if -

- good nutrition results in increased longevity.

- time on social media impacts verbal skills.

- exercise effects heart health.

- an instructional software helps students overcome conceptual gaps.

Scientist wish to determine if -

- good nutrition results in increased longevity.

- time on social media impacts verbal skills.

- exercise effects heart health

- an instructional software helps students overcome conceptual gaps.

This is the DEPENDENT VARIABLE

Scientist wish to determine if -

- good nutrition results in increased longevity.

- time on social media impacts verbal skills.

- exercise effects heart health.

- an instructional software helps students overcome conceptual gaps.

Scientist wish to determine if -

- good nutrition results in increased longevity.

- time on social media impacts verbal skills.

- exercise effects heart health

- an instructional software helps students overcome conceptual gaps.

This is the DEPENDENT VARIABLE

Now, see if you can identify the dependent variables in the following word problems:

A researcher investigated the number of viral infections people contract as function of the amount of stress they experienced during a six-month period.

A researcher investigated the number of viral infections people contract as function of the amount of stress they experienced during a six-month period. She obtained the following data set:

A researcher investigated the number of viral infections people contract as function of the amount of stress they experienced during a six-month period. She obtained the following data set:

Amount of Stress

Negligible stress

Minimal stress

Moderate stress

Sever stress

Number of viral

infections

2 4 6 5

1 3 5 7

4 2 7 8

1 3 5 4

A researcher investigated the number of viral infections people contract as function of the amount of stress they experienced during a six-month period. She obtained the following data set:

Amount of Stress

Negligible stress

Minimal stress

Moderate stress

Sever stress

Number of viral

infections

2 4 6 5

1 3 5 7

4 2 7 8

1 3 5 4

What is being influenced here?

A researcher investigated the number of viral infections people contract as a function of the amount of stress they experienced during a six-month period. She obtained the following data set:

Amount of Stress

Negligible stress

Minimal stress

Moderate stress

Sever stress

Number of viral

infections

2 4 6 5

1 3 5 7

4 2 7 8

1 3 5 4

What is being influenced here?

A researcher investigated the number of viral infections people contract as function of the amount of stress they experienced during a six-month period. She obtained the following data set:

Amount of Stress

Negligible stress

Minimal stress

Moderate stress

Sever stress

Number of viral

infections

2 4 6 5

1 3 5 7

4 2 7 8

1 3 5 4

What is being influenced here?

A researcher investigated the number of viral infections people contract as function of the amount of stress they experienced during a six-month period. She obtained the following data set:

Amount of Stress

Negligible stress

Minimal stress

Moderate stress

Sever stress

Number of viral

infections

2 4 6 5

1 3 5 7

4 2 7 8

1 3 5 4

This is the DEPENDENT VARIABLE

Next example:

A researcher investigated the effect of volume background noise on participant’s error rates while performing a boring task.

A researcher investigated the effect of volume background noise on participant’s error rates while performing a boring task. She tested three groups of randomly selected students and obtained the following error data:

A researcher investigated the effect of volume background noise on participant’s error rates while performing a boring task. She tested three groups of randomly selected students and obtained the following error data:

Levels of Volume

Low Volume

ModerateVolume

High Volume

Number of errors

2 4 6

1 3 5

4 2 7

1 3 5

A researcher investigated the effect of volume background noise on participant’s error rates while performing a boring task. She tested three groups of randomly selected students and obtained the following error data:

Levels of Volume

Low Volume

ModerateVolume

High Volume

Number of errors

2 4 6

1 3 5

4 2 7

1 3 5

What is being influenced here?

A researcher investigated the effect of volume background noise on participant’s error rates while performing a boring task. She tested three groups of randomly selected students and obtained the following error data:

Levels of Volume

Low Volume

ModerateVolume

High Volume

Number of errors

2 4 6

1 3 5

4 2 7

1 3 5

What is being influenced here?

A researcher investigated the effect of volume background noise on participant’s error rates while performing a boring task. She tested three groups of randomly selected students and obtained the following error data:

Levels of Volume

Low Volume

ModerateVolume

High Volume

Number of errors

2 4 6

1 3 5

4 2 7

1 3 5

What is being influenced here?

A researcher investigated the effect of volume background noise on participant’s error rates while performing a boring task. She tested three groups of randomly selected students and obtained the following error data:

Levels of Volume

Low Volume

ModerateVolume

High Volume

Number of errors

2 4 6

1 3 5

4 2 7

1 3 5

This is the DEPENDENT VARIABLE

Next example:

A researcher investigated the effects of (1) whether participants meditate, and (2) the degree of introversion they exhibit on hypnotic suggestibility.

A researcher investigated the effects of (1) whether participants meditate, and (2) the degree of introversion they exhibit on hypnotic suggestibility.

What is being influenced here?

A researcher investigated the effects of (1) whether participants meditate, and (2) the degree of introversion they exhibit on hypnotic suggestibility.

What is being influenced here?

A researcher investigated the effects of (1) whether participants meditate, and (2) the degree of introversion they exhibit on hypnotic suggestibility.

This is the DEPENDENT VARIABLE

A researcher investigated the effects of (1) whether participants meditate, and (2) the degree of introversion they exhibit on hypnotic suggestibility.

In this case there are two influencers

A researcher investigated the effects of (1) whether participants meditate, and (2) the degree of introversion they exhibit on hypnotic suggestibility.

In this case there are two influencers

A researcher investigated the effects of (1) whether participants meditate, and (2) the degree of introversion they exhibit on hypnotic suggestibility.

In this case there are two influencers

All of the examples shown so far are examples of problems with only one dependent variable.

What does a word problem look like with more than one dependent variable?

Here are some examples:

You have been asked to determine the degree to which the amount of sleep effects students both academically and socially.

You have been asked to determine the degree to which the amount of sleep effects students both academically and socially.

What is being influenced here?

You have been asked to determine the degree to which the amount of sleep effects students both academically and socially.

What is being influenced here?

1st

Dependent Variable

You have been asked to determine the degree to which the amount of sleep effects students both academically and socially.

What is being influenced here?

2nd

Dependent Variable

You have been asked to determine the degree to which the amount of sleep effects students both academically and socially.

What is doing the influencing?

You have been asked to determine the degree to which the amount of sleep effects students both academically and socially.

What is doing the influencing?

This next example has more complicated wording, but you should be able to identify the dependent variable:

You have been asked to determine how the process known as fracking impacts the subterranean as well as the above ground environments.

You have been asked to determine how the process known as fracking impacts the subterranean as well as the above ground environments.

What is being influenced here?

You have been asked to determine how the process known as fracking impacts thesubterranean as well as the above ground environments.

What is being influenced here?

1st

Dependent Variable

You have been asked to determine how the process known as fracking impacts the subterranean as well as the above ground environments.

What is being influenced here?

2nd

Dependent Variable

You have been asked to determine how the process known as fracking impacts the subterranean as well as the above ground environments.

What is doing the influencing?

You have been asked to determine how the process known as fracking impacts the subterranean as well as the above ground environments.

What is doing the influencing?

Quick note -

Quick note – there will be some research questions that only have a dependent variable (the thing being influenced) without an influencer.

These usually take the form of questions that focus on the degree to which a sample is similar to a population. Their similarity will be based on the dependent variable, but no influencer will be present.

Quick note – there will be some research questions that only have a dependent variable (the thing being influenced) without an influencer.

These usually take the form of questions that focus on the degree to which a sample is similar to a population. Their similarity will be based on the dependent variable, but no influencer will be present.

Quick note – there will be some research questions that only have a dependent variable (the thing being influenced) without an influencer.

These usually take the form of questions that focus on the degree to which a sample is similar to a population. Their similarity will be based on the dependent variable, but no influencer will be present.

Here is an example:

A random sample of 22 fifth grade pupils have a grade point average of 3.6.

A random sample of 22 fifth grade pupils have a grade point average of 3.6. The grade point average (GPA) of all fifth grade pupils of the last five years is 3.4.

A random sample of 22 fifth grade pupils have a grade point average of 3.6. The grade point average (GPA) of all fifth grade pupils of the last five years is 3.4. Is the GPA of the 22 pupils significantly different from the populations’ GPA?

A random sample of 22 fifth grade pupils have a grade point average of 3.6. The grade point average (GPA) of all fifth grade pupils of the last five years is 3.4. Is the GPA of the 22 pupils significantly different from the populations’ GPA?

In this case, the dependent variable is GPA. This type of analysis is generally a preliminary step. If the sample GPA is

shown to be representative of the population GPA, then studies showing the impact of some influencer (e.g., study

habits, instructional software) are then conducted.

A random sample of 22 fifth grade pupils have a grade point average of 3.6. The grade point average (GPA) of all fifth grade pupils of the last five years is 3.4. Is the GPA of the 22 pupils significantly different from the populations’ GPA?

In this case, the dependent variable is GPA. This type of analysis is generally a preliminary step. If the sample GPA is

shown to be representative of the population GPA, then studies showing the impact of some influencer (e.g., study

habits, instructional software) are then conducted.

A random sample of 22 fifth grade pupils have a grade point average of 3.6. The grade point average (GPA) of all fifth grade pupils of the last five years is 3.4. Is the GPA of the 22 pupils significantly different from the populations’ GPA?

In this case, the dependent variable is GPA. This type of analysis is generally a preliminary step. If the sample GPA is shown to be representative of the population GPA, then studies showing the impact of some influencer (e.g., study

habits, instructional software) are then conducted.

A random sample of 22 fifth grade pupils have a grade point average of 3.6. The grade point average (GPA) of all fifth grade pupils of the last five years is 3.4. Is the GPA of the 22 pupils significantly different from the populations’ GPA?

In this case, the dependent variable is GPA. This type of analysis is generally a preliminary step. If the sample GPA is

shown to be representative of the population GPA, then studies showing the impact of some influencer (e.g., study

habits, instructional software) are then conducted.

A random sample of 22 fifth grade pupils have a grade point average of 3.6. The grade point average (GPA) of all fifth grade pupils of the last five years is 3.4. Is the GPA of the 22 pupils significantly different from the populations’ GPA?

In this case, the dependent variable is GPA. This type of analysis is generally a preliminary step. If the sample GPA is

shown to be representative of the population GPA, then studies showing the impact of some influencer (e.g., study

habits, instructional software) are then conducted.

Note – the majority of the problems in this course will not be like this, but in case you run into the few that are, hopefully this last bit of instruction will be helpful to you.

Now, determine the number of dependent variables in the problem you are working on.

1 Dependent Variable

2+ Dependent Variables