Is the problem you are working on a question of Independence?

Is the problem you are working on a question of Independence?

Questions of Independence are actually the flip side of questions of relationship.

If a variable is independent of another variable,

If a variable is independent of another variable, then an increase or decrease in one WILL NOT be accompanied

If a variable is independent of another variable, then an increase or decrease in one WILL NOT be accompanied by an increase or decrease in the other.

A question of independence generally can be detected by an equation like this one:

A question of independence generally can be detected by an equation like this one:

Variable 1An Increase or decrease in

IS NOT accompanied by an increaseor decrease in

Variable 2

Questions of Independence are often posed as questions of bias.

Here is an example:

In the 1970s tobacco companies spent resources on research that showed there was no link between the amount of cigarette smoking (packs per day) and cognitive impairment. Cognitive impairment was measured in terms of the amount of time it took someone to respond to certain questions.

In the 1970s tobacco companies spent resources on research that showed there was no link between the amount of cigarette smoking (packs per day) and cognitive impairment. Cognitive impairment was measured in terms of the amount of time it took someone to respond to certain questions.

In the 1970s tobacco companies spent resources on research that showed there was no link between the amount of cigarette smoking (packs per day) and cognitive impairment. Cognitive impairment was measured in terms of the amount of time it took someone to respond to certain questions.

Variable 1An Increase or decrease in

IS NOT accompanied by an increaseor decrease in

Variable 2

In the 1970s tobacco companies spent resources on research that showed there was no link between the amount of cigarette smoking (packs per day) and cognitive impairment. Cognitive impairment was measured in terms of the amount of time it took someone to respond to certain questions.

Variable 1An Increase or decrease in

IS NOT accompanied by an increaseor decrease in

Variable 2

In the 1970s tobacco companies spent resources on research that showed there was no link between the amount of cigarette smoking (packs per day) and cognitive impairment. Cognitive impairment was measured in terms of the amount of time it took someone to respond to certain questions.

Variable 1An Increase or decrease in

IS NOT accompanied by an increaseor decrease in

Variable 2

In the 1970s tobacco companies spent resources on research that showed there was no link between the amount of cigarette smoking (packs per day) and cognitive impairment. Cognitive impairment was measured in terms of the amount of time it took someone to respond to certain questions.

Packs smoked per

day

An Increase or decrease in

IS NOT accompanied by an increaseor decrease in

Variable 2

In the 1970s tobacco companies spent resources on research that showed there was no link between the amount of cigarette smoking (packs per day) and cognitive impairment. Cognitive impairment was measured in terms of the amount of time it took someone to respond to certain questions.

Packs smoked per

day

An Increase or decrease in

IS NOT accompanied by an increaseor decrease in

Variable 2

In the 1970s tobacco companies spent resources on research that showed there was no link between the amount of cigarette smoking (packs per day) and cognitive impairment. Cognitive impairment was measured in terms of the amount of time it took someone to respond to certain questions.

Packs smoked per

day

An Increase or decrease in

IS NOT accompanied by an increaseor decrease in

Variable 2

In the 1970s tobacco companies spent resources on research that showed there was no link between the amount of cigarette smoking (packs per day) and cognitive impairment. Cognitive impairment was measured in terms of the amount of time it took someone to respond to certain questions.

Packs smoked per

day

An Increase or decrease in

IS NOT accompanied by an increaseor decrease in

Response Time

In the 1970s tobacco companies spent resources on research that showed there was no link between the amount of cigarette smoking (packs per day) and cognitive impairment. Cognitive impairment was measured in terms of the amount of time it took someone to respond to certain questions.

Packs per day smoked

An Increase or decrease in

IS NOT accompanied by an increaseor decrease in

Response TimeThis is a question of independence

Here is a data set for this problem:

Here is a data set for this problem:

Research Subjects

A

B

C

D

E

F

G

Here is a data set for this problem:

Research Subjects

Amount of Packs Smoked each Day

A 3

B 2

C 3

D 1

E 0

F 0

G 4

Here is a data set for this problem:

Research Subjects

Amount of Packs Smoked each Day

Minutes to respond to a cognitive question

A 3 10

B 2 4

C 3 1

D 1 2

E 0 3

F 0 14

G 4 3

Here is a data set for this problem:

Research Subjects

Amount of Packs Smoked each Day

Minutes to respond to a cognitive question

A 3 10

B 2 4

C 3 1

D 1 2

E 0 3

F 0 14

G 4 3

Researchers are hoping NO LINK between these two variables will be found.

Here is a data set for this problem:

Research Subjects

Amount of Packs Smoked each Day

Minutes to respond to a cognitive question

A 3 10

B 2 4

C 3 1

D 1 2

E 0 3

F 0 14

G 4 3

Researchers are hoping NO LINK between these two variables will be found.

Here is a data set for this problem:

Research Subjects

Amount of Packs Smoked each Day

Minutes to respond to a cognitive question

A 3 10

B 2 4

C 3 1

D 1 2

E 0 3

F 0 14

G 4 3

Researchers are hoping NO LINK between these two variables will be found.

Here is a data set for this problem:

Research Subjects

Amount of Packs Smoked each Day

Minutes to respond to a cognitive question

A 3 10

B 2 4

C 3 1

D 1 2

E 0 3

F 0 14

G 4 3

Researchers are hoping NO LINK between these two variables will be found.

NO LINK

You will be shown in future presentations how to analyze the data to determine if the variables are independent of one another or not.

As with relationship questions there will be some situations where you are determining independence between a variable with unlimited values (e.g., speed, height, age) and a variable with limited values (e.g., gender, year in school).

As with relationship questions there will be some situations where you are determining independence between a variable with unlimited values (e.g., speed, height, age) and a variable with limited values (e.g., gender, year in school).

Variable 1Higher and

lower scores in

tend to be UNRELATED to

certain groups in Variable 2

For example:

Complaints have arisen that a local raceway has more accidents because of more “hot headed” (angry) drivers.

Complaints have arisen that a local raceway has more accidents because of more “hot headed” (angry) drivers.

Complaints have arisen that a local raceway has more accidents because of more “hot headed” (angry) drivers. You have been asked to investigate.

Complaints have arisen that a local raceway has more accidents because of more “hot headed” (angry) drivers. You have been asked to investigate.

Complaints have arisen that a local raceway has more accidents because of more “hot headed” (angry) drivers. You have been asked to investigate. You administer a “easily provoked to anger” survey with a score range of 0 to 30 to approximately forty drivers.

Complaints have arisen that a local raceway has more accidents because of more “hot headed” (angry) drivers. You have been asked to investigate. You administer a “easily provoked to anger” survey with a score range of 0 to 30 to approximately forty drivers. You then add up the number of accidents they are in during the period of a month.

Complaints have arisen that a local raceway has more accidents because of more “hot headed” (angry) drivers. You have been asked to investigate. You administer a “easily provoked to anger” survey with a score range of 0 to 30 to approximately forty drivers. You then add up the number of accidents they are in during the period of a month. You wish to determine if anger scores are independent of accidents.

Complaints have arisen that a local raceway has more accidents because of more “hot headed” (angry) drivers. You have been asked to investigate. You administer a “easily provoked to anger” survey with a score range of 0 to 30 to approximately forty drivers. You then add up the number of accidents they are in during the period of a month. You wish to determine if anger scores are independent of accidents.

Variable 1Higher and

lower scores in

tend to be UNRELATED to

certain groups in Variable 2

Complaints have arisen that a local raceway has more accidents because of more “hot headed” (angry) drivers. You have been asked to investigate. You administer a “easily provoked to anger” survey with a score range of 0 to 30 to approximately forty drivers. You then add up the number of accidents they are in during the period of a month. You wish to determine if anger scores are independent of accidents.

Variable 1Higher and

lower scores in

tend to be UNRELATED to

certain groups in Variable 2

Complaints have arisen that a local raceway has more accidents because of more “hot headed” (angry) drivers. You have been asked to investigate. You administer a “easily provoked to anger” survey with a score range of 0 to 30 to approximately forty drivers. You then add up the number of accidents they are in during the period of a month. You wish to determine if anger scores are independent of accidents.

Anger Survey Scores

Higher and lower scores

in

tend to be UNRELATED to

certain groups in Variable 2

Complaints have arisen that a local raceway has more accidents because of more “hot headed” (angry) drivers. You have been asked to investigate. You administer a “easily provoked to anger” survey with a score range of 0 to 30 to approximately forty drivers. You then add up the number of accidents they are in during the period of a month. You wish to determine if anger scores are independent of accidents.

Anger Survey Scores

Higher and lower scores

in

tend to be UNRELATED to

certain groups in Variable 2

Complaints have arisen that a local raceway has more accidents because of more “hot headed” (angry) drivers. You have been asked to investigate. You administer a “easily provoked to anger” survey with a score range of 0 to 30 to approximately forty drivers. You then add up the number of accidents they are in during the period of a month. You wish to determine if anger scores are independent of accidents.

Anger Survey Scores

Higher and lower scores

in

tend to be UNRELATED to

certain groups in Variable 2

Complaints have arisen that a local raceway has more accidents because of more “hot headed” (angry) drivers. You have been asked to investigate. You administer a “easily provoked to anger” survey with a score range of 0 to 30 to approximately forty drivers. You then add up the number of accidents they are in during the period of a month. You wish to determine if anger scores are independent of accidents.

Anger Survey Scores

Higher and lower scores

in

tend to be UNRELATED to

certain groups in

Number of Accidents

Here is what a data set might look like for this problem:

Here is what a data set might look like for this problem:

Drivers

A

B

C

D

E

F

G

Here is what a data set might look like for this problem:

Drivers Anger Survey Scores

A 28

B 5

C 21

D 14

E 25

F 18

G 1

Here is what a data set might look like for this problem:

Drivers Anger Survey Scores

Number of Accidentsin a Month

A 28 4

B 5 5

C 21 12

D 14 7

E 25 4

F 18 7

G 1 6

Here is what a data set might look like for this problem:

Drivers Anger Survey Scores

Number of Accidentsin a Month

A 28 4

B 5 5

C 21 12

D 14 7

E 25 4

F 18 7

G 1 6

Owners of the speedway hope that NO LINK between these two variables will be found.

Here is what a data set might look like for this problem:

Drivers Anger Survey Scores

Number of Accidentsin a Month

A 28 4

B 5 5

C 21 12

D 14 7

E 25 4

F 18 7

G 1 6

Owners of the speedway hope that NO LINK between these two variables will be found.

No link

You will be shown in future presentations how to analyze the data to determine if the variables are independent from one another or not.

Finally, there will be some situations where you will determine independence between two variables with limited values (e.g., gender, year in school).

For example:

A claim has been made that admission decisions are biased toward minority groups.

A claim has been made that admission decisions are biased toward minority groups. You have been asked by an outside evaluation agency to look into this allegation.

A claim has been made that admission decisions are biased toward minority groups. You have been asked by an outside evaluation agency to look into this allegation. You have decided to state your research question as follows: “To what degree are admission decisions independent of minority group status?”

A claim has been made that admission decisions are biased toward minority groups. You have been asked by an outside evaluation agency to look into this allegation. You have decided to state your research question as follows: “To what degree are admission decisions independent of minority group status?”

Variable 1Is independent of Variable 2

A claim has been made that admission decisions are biased toward minority groups. You have been asked by an outside evaluation agency to look into this allegation. You have decided to state your research question as follows: “To what degree are admission decisions independent of minority group status?”

Variable 1Is independent of Variable 2

A claim has been made that admission decisions are biased toward minority groups. You have been asked by an outside evaluation agency to look into this allegation. You have decided to state your research question as follows: “To what degree are admission decisions independent of minority group status?”

admissions status

Is independent of Variable 2

A claim has been made that admission decisions are biased toward minority groups. You have been asked by an outside evaluation agency to look into this allegation. You have decided to state your research question as follows: “To what degree are admission decisions independent of minority group status?”

admissions status

Is independent of Variable 2

A claim has been made that admission decisions are biased toward minority groups. You have been asked by an outside evaluation agency to look into this allegation. You have decided to state your research question as follows: “To what degree are admission decisions independent of minority group status?”

admissions status

Is independent of Variable 2

A claim has been made that admission decisions are biased toward minority groups. You have been asked by an outside evaluation agency to look into this allegation. You have decided to state your research question as follows: “To what degree are admission decisions independent of minority group status?”

admissions status

Is independent of Variable 2

A claim has been made that admission decisions are biased toward minority groups. You have been asked by an outside evaluation agency to look into this allegation. You have decided to state your research question as follows: “To what degree are admission decisions independent of minority group status?”

admissions status

Is independent ofminority

group status

Here is a data set for this problem:

Here is a data set for this problem:

Research Subjects

A

B

C

D

E

F

G

Here is a data set for this problem:

Research Subjects

Admitted1 = yes, 2 = no

A 1

B 1

C 2

D 1

E 2

F 1

G 1

Here is a data set for this problem:

Research Subjects

Admitted1 = yes, 2 = no

Minority Group Status 1 = yes, 2 = no

A 1 1

B 1 1

C 2 2

D 1 2

E 2 2

F 1 1

G 1 1

Here is a data set for this problem:

Research Subjects

Admitted1 = yes, 2 = no

Minority Group Status 1 = yes, 2 = no

A 1 1

B 1 1

C 2 2

D 1 2

E 2 2

F 1 1

G 1 1

The admissions office hopes that NO LINK between these two variables will be found.

Here is a data set for this problem:

Research Subjects

Admitted1 = yes, 2 = no

Minority Group Status 1 = yes, 2 = no

A 1 1

B 1 1

C 2 2

D 1 2

E 2 2

F 1 1

G 1 1

The admissions office hopes that NO LINK between these two variables will be found.

No link

Here are more examples of independence-oriented questions:

To what degree is -

To what degree is -

• math proficiency independent of gender?

To what degree is -

• math proficiency independent of gender?

To what degree is -

• math proficiency independent of gender?

• news reporting void of political bias?

To what degree is -

• math proficiency independent of gender?

• news reporting void of political bias?

To what degree is -

• math proficiency independent of gender?

• news reporting void of political bias?

• the risk of lung cancer independent of cigarette smoking?

To what degree is -

• math proficiency independent of gender?

• news reporting void of political bias?

• the risk of lung cancer independent of cigarette smoking?

To what degree is -

• math proficiency independent of gender?

• news reporting void of political bias?

• the risk of lung cancer independent of cigarette smoking?

• incarceration independent of race?

To what degree is -

• math proficiency independent of gender?

• news reporting void of political bias?

• the risk of lung cancer independent of cigarette smoking?

• incarceration independent of race?

Note – that any independence question can be worded as a relationship question.

For example,

Is math proficiency independent of gender?

Is math proficiency independent of gender?

can be worded as –

Is math proficiency independent of gender?

can be worded as –

Is there a relationship between math proficiency and gender?

The key takeaway – relationship questions can be worded as independence questions and independence questions can be worded as relationship questions.

The key takeaway – relationship questions can be worded as independence questions and independence questions can be worded as relationship questions.

It all depends on the nature of the research question!

Examine the question or problem you are working on.

Is it a question of independence?

If so, select INDEPENDENCE