How many independent variables?

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

Here are your options:

Here are your options:

1 Independent Variable

2+ Independent Variables

0 Independent Variables

As you may remember from previous instruction, in statistics we are generally attempting to determine what causes what?

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


Cause


Cause Effect

Or what influences what?

Or what influences what?

Influencer Influenced

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

Effect


Cause

Effect


Cause

Independent Variable

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


InfluencedInfluencer

Let’s look at an example

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


What is being influenced here?


This is the Dependent Variable


What is the influencer?


This is the Independent Variable


Dependent Variable

Influencer


Dependent Variable


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.


This is the Dependent Variable


What is the influencer?


Test ScoresInfluencer



The Dependent Variable


Test ScoresAmount of

Sleep


Test ScoresAmount of

Sleep

The Independent Variable

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.


This is the DEPENDENT VARIABLE


What is doing the influencing?

See if you can identify the independent variable and 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.






This is the INDEPENDENT VARIABLE




- exercise effects heart health.


Now, see if you can identify the independent and 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:


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 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



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


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:


Levels of Volume

Low Volume

ModerateVolume

High Volume

Number of errors

2 4 6

1 3 5

4 2 7

1 3 5

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

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

Here are some examples:

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



1st




2nd


Next problem:

You have been asked to determine the degree to which the amount of sleep and study time both effect student test scores.



1st




2nd


Next example:

You have been asked to determine how the processes known as fracking and hydraulic propulsion impact the subterranean as well as the above ground environments.


1st

Dependent Variable



2nd

Dependent Variable




1st




2nd


Quick note -

Quick note – there will be some research questions that only have a dependent variable and no independent variable.

You will find that there are 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.


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.


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 independent variable 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 independent variable

(e.g., study habits, instructional software) are then conducted.

In this course, only a few problems will be like this.

Here is another issue to consider:

There can be some confusion as to what an independent variable is when you read some word problems.

Here is an example of this possible confusion:

A pizza café owner wishes to know who to market her pizza to: Football, Basketball, or Soccer players. So, she conducts a study to determine which group eats more pizza slices in one sitting.


As you know the Dependent Variable

is pizza slices

A pizza café owner wishes to know who to market her pizza to: Football, Basketball, or Soccer players. So, she conducts a study to determine which group eats more pizza slices in one sitting.At this point, some might think that there

are three independent variables: Football, Basketball, and Soccer Players


However, there is really only one Independent Variable: Type of Athlete


What you will learn at the next decision point is that

independent variables have at least two levels


So, here is a way to visualize this:


Football Players


Football Players

Basketball Players


Football Players

Basketball Players

Soccer Players


Football Players

Basketball Players

Soccer Players

Independent Variable: Type of Athlete


Football Players

Basketball Players

Soccer Players


A Group


Football Players

Basketball Players

Soccer Players

Group A Group B



Football Players

Basketball Players

Soccer Players


Group CGroup A Group B

Here is another example:

Educational researchers wish to investigate if there is a difference in test scores between a group that received instruction using an innovative software and another group that did not.


The Dependent Variable is test

scores


The Levels are


The Levels areGroup using

Software


The Levels areGroup using

Software

Group NOT using Software


The Independent Variable is

Group using

Software




Group using

Software


INSTRUCTION TYPE



Group using

Software


INSTRUCTION TYPE

Group 1



Group using

Software


INSTRUCTION TYPE

Group 1 Group 2


INSTRUCTION TYPE

Notice that the expression instruction type does not show up any where in the problem. So, what you do is look at the levels and come up with a descriptive word or words that describe the independent variable.

Other examples

Problem #1

Problem #1

Dependent Variable: Degree of Anxiety

Problem #1


Levels:

Problem #1


Levels:

• Group 1 – takes anxiety medication

Problem #1


Levels:


• Group 2 – does not take anxiety medication

Problem #1


Levels:



What shall we call the Independent Variable?

Problem #1


Levels:



Independent Variable: Medication Status

Problem #2

Problem #2

Dependent Variable:

Problem #2

Dependent Variable: Bowling performance

Problem #2


Levels:

Problem #2


Levels:

• Group 1 – use a specialty glove

Problem #2


Levels:


• Group 2 – does not use a specialty glove

Problem #2


Levels:



What shall we call the Independent Variable?

Problem #2


Levels:



Independent Variable: Glove Type

Sometimes the independent variable is time.

Here is an example:

A class of 30 students are given a pre-class test to determine their level of statistical knowledge.

A class of 30 students are given a pre-class test to determine their level of statistical knowledge. At the end of the term they are given an end of the term test.

A class of 30 students are given a pre-class test to determine their level of statistical knowledge. At the end of the term they are given an end of the term test. And then, three months after the course is over, they take post-term test.

A class of 30 students are given a pre-class testto determine their level of statistical knowledge. At the end of the term they are given an end of the term test. And then, three months after the course is over, they take post-term test.

The dependent variable is the test

scores


The independent variable is the times the test was given



Pre-class test



Pre-class testFirst Test



Pre-class test1st Test



Pre-class test

End-term test2nd Test

1st Test



Pre-class test

End-term test

Post-term test3rd Level

2nd Test

1st Test



Pre-class test

End-term test

Post-term test

Once again, time is the independent variable with three levels.

3rd Level

2nd Test

1st Test

Finally,

Finally, some problems will have what are called covariates.

You will learn more about covariates later.

Here is what a problem looks like with a covariate:

A pizza café owner wishes to know who to market her pizza to: Football, Basketball, or Soccer players. So, she conducts a study to determine which group eats more pizza slices in one sitting. She also wants to control for gender in order to see the unique effect of player type minus the gender factor.

A pizza café owner wishes to know who to market her pizza to: Football, Basketball, or Soccer players. So, she conducts a study to determine which group eats more pizza slices in one sitting. She also wants to control for genderin order to see the unique effect of player type minus the gender factor.

Gender is what we call the covariate in this problem


You will be able to recognize it because it will use words like, control for, eliminate the effect, etc.

A pizza café owner wishes to know who to market her pizza to: Football, Basketball, or Soccer players. So, she conducts a study to determine which group eats more pizza slices in one sitting. She also wants to eliminate the effect of gender in order to see the unique effect of player type minus the gender factor.

You will be able to recognize it because it will use words like, control for, eliminate the effect of, hold

constant.etc.

A pizza café owner wishes to know who to market her pizza to: Football, Basketball, or Soccer players. So, she conducts a study to determine which group eats more pizza slices in one sitting. She also wants to hold gender constant in order to see the unique effect of player type minus the gender factor.

You will be able to recognize it because it will use words like, control for, eliminate the effect of, or

hold constant.


In either case, you may think that you are working with two independent variables:

Player type and Gender.


In this case, you may think that you are working with two independent variables:



However, there is really only one independent variable that is of concern to us: Player type.

Gender is just an additional analysis.

As with the previous scenario you will not run into a problem like this very often.

In Summary

Main Points:

Main Points:

– The independent variable does the influencing or the causing in a word problem.

– The independent variable may not be stated in the word problem, but you can determine it by coming up with an expression that ties to the two or more levels together.

Main Points:


– The independent variable may not be stated in the word problem, but you can determine it by coming up with an expression that ties to the two or more levels together.

For example, if the study asks if study habits have an effect on test scores, then Study habits will be in the

influencer and thus the independent variable.

Main Points:


– The independent variable may not be stated in the word problem, but you can determine it by coming up with an expression that ties the two or more levels together.

Main Points:



For example, if the study examines who eats more pizza slices, football, basketball, or soccer players. The

dependent variable will be pizza slices and the independent variable will be something that ties these

three levels together, like Player Type

Main Points:



Or, if one group receives a treatment (like a medication) and the other does not, then the two

levels would be (1) receiving treatment and the other (2) not receiving treatment. The independent variable

could be: Treatment Status

Main Points:



Or, if one group receives a treatment (like a medication) and the other group does not, then the

two levels would be (1) group receiving treatment and the other (2) group not receiving treatment. The independent variable could be: Treatment Status

Main Points:



Or, if one group receives a treatment (like a medication) and the other group does not, then the two levels would be: (1) group receiving treatment

and the other (2) group not receiving treatment. The independent variable could be: Treatment Status

Additional Points-

Additional Points-

– There can be more than one independent variable.

Additional Points-


For example, test scores being influenced by a combination of (1) hours of sleep and (2) study time

Additional Points-


– In a few cases, when dealing with difference questions,

Additional Points-



• one problem type does not have an independent variable.

Additional Points-



• one problem type does not have an independent variable.

For example, when you simply want to see if the sample you are about to study is statistically similar to the population based on some dependent variablelike test scores, level of anxiety, or amount of pizza eaten. In this case we do not have an independent variable yet to test to see what influence it has on the dependent variable.

Additional Points-



• one problem type does not have a independent variable.

• another problem type has a covariate which is not counted as an independent variable.

Additional Points-



• one problem type does not have a independent variable.

• another problem type has a covariate which is not counted as an independent variable.

For example, if you are comparing football players and soccer players in terms of the amount of pizza they eat. And then run an additional analysis eliminating the effect of gender to determine if gender plays a role in the amount of pizza eaten as well.

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

1 Independent Variable

2+ Independent Variables

0 Independent Variables

How many independent variables?

Education

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