point biserial correlation
TRANSCRIPT
Point Biserial Correlation
Welcome to the Point Biserial Correlation Conceptual Explanation
• Point biserial correlation is an estimate of the coherence between two variables, one of which is dichotomous and one of which is continuous.
• Point biserial correlation is an estimate of the coherence between two variables, one of which is dichotomous and one of which is continuous.
Coherence means how much the two variables covary.
• Let’s look at an example of two variables cohering
• The data set below represents the average decibel levels at which different age groups listen to music.
• The data set below represents the average decibel levels at which different age groups listen to music.
Age Group Decibels
80s 30
70s 35
60s 37
50s 39
40s 45
30s 50
20s 75
Teens 95
• The data set below represents the average decibel levels at which different age groups listen to music.
The reason these two variables (age group and decibel level) cohere is because as one increases
the other either increases or decreases commensurately.
Age Group Decibels
80s 30
70s 35
60s 37
50s 39
40s 45
30s 50
20s 75
Teens 95
• The data set below represents the average decibel levels at which different age groups listen to music.
In this case
Age Group Decibels
80s 30
70s 35
60s 37
50s 39
40s 45
30s 50
20s 75
Teens 95
• The data set below represents the average decibel levels at which different age groups listen to music.
Age Group Decibels
80s 30
70s 35
60s 37
50s 39
40s 45
30s 50
20s 75
Teens 95
In this case as age goes up
• The data set below represents the average decibel levels at which different age groups listen to music.
Age Group Decibels
80s 30
70s 35
60s 37
50s 39
40s 45
30s 50
20s 75
Teens 95
In this case as age goes up
• The data set below represents the average decibel levels at which different age groups listen to music.
Age Group Decibels
80s 30
70s 35
60s 37
50s 39
40s 45
30s 50
20s 75
Teens 95
In this case as age goes up, decibels go down
• The data set below represents the average decibel levels at which different age groups listen to music.
Age Group Decibels
80s 30
70s 35
60s 37
50s 39
40s 45
30s 50
20s 75
Teens 95
In this case as age goes up, decibels go down
• The data set below represents the average decibel levels at which different age groups listen to music.
• This is called a negative relationship.
Age Group Decibels
80s 30
70s 35
60s 37
50s 39
40s 45
30s 50
20s 75
Teens 95
In this case as age goes up, decibels go down
• It is called a negative correlation or coherence, because when one variable increases, the other decreases (or vice-a-versa)
• A positive correlation would occur when as one variable increases, the other increases or when one decreases the other decreases.
• A positive correlation would occur when as one variable increases, the other increases or when one decreases the other decreases.
• A positive correlation would occur when as one variable increases, the other increases or when one decreases the other decreases.
• Example
• A positive correlation would occur when as one variable increases, the other increases or when one decreases the other decreases.
• Example
• As the temperature rises the average daily purchase of popsicles increases.
• A positive correlation would occur when as one variable increases, the other increases or when one decreases the other decreases.
• Example
• As the temperature rises the average daily purchase of popsicles increases.
Average Daily Temp
Average Daily
Popsicle Purchases
Per Person
100 2.30
95 1.20
90 1.00
85 .80
80 .70
75 .10
70 .03
65 .01
• A positive correlation would occur when as one variable increases, the other increases or when one decreases the other decreases.
• Example
• As the temperature rises the average daily purchase of popsicles increases.
Average Daily Temp
Average Daily
Popsicle Purchases
Per Person
100 2.30
95 1.20
90 1.00
85 .80
80 .70
75 .10
70 .03
65 .01
• A positive correlation would occur when as one variable increases, the other increases or when one decreases the other decreases.
• Example
• As the temperature rises the average daily purchase of popsicles increases.
• These variables are positively correlated because as one variable (Daily Temp) increases another variable (average daily popsicle purchase) increases.
Average Daily Temp
Average Daily
Popsicle Purchases
Per Person
100 2.30
95 1.20
90 1.00
85 .80
80 .70
75 .10
70 .03
65 .01
• It can be stated another way:
• It can be stated another way:
• As the average daily temperature decreases the average daily popsicle purchases decrease as well.
• It can be stated another way:
• As the average daily temperature decreases the average daily popsicle purchases decrease as well.
Average Daily Temp
Average Daily
Popsicle Purchases
Per Person
100 2.30
95 1.20
90 1.00
85 .80
80 .70
75 .10
70 .03
65 .01
• It can be stated another way:
• As the average daily temperature decreases the average daily popsicle purchases decrease as well.
Average Daily Temp
Average Daily
Popsicle Purchases
Per Person
100 2.30
95 1.20
90 1.00
85 .80
80 .70
75 .10
70 .03
65 .01
• It can be stated another way:
• As the average daily temperature decreases the average daily popsicle purchases decrease as well.
• These variables are also positively correlated because as one variable (Daily Temp) decreases another variable (average daily popsicle purchase) decreases.
Average Daily Temp
Average Daily
Popsicle Purchases
Per Person
100 2.30
95 1.20
90 1.00
85 .80
80 .70
75 .10
70 .03
65 .01
• Let’s return to our Point Biserial Correlation definition:
• Let’s return to our Point Biserial Correlation definition:
• “Point biserial correlation is an estimate of the coherence between two variables, one of which is dichotomous and one of which is continuous.”
• Let’s return to our Point Biserial Correlation definition:
• “Point biserial correlation is an estimate of the coherence between two variables, one of which is dichotomous and one of which is continuous.”
We discussed coherence
• Let’s return to our Point Biserial Correlation definition:
• “Point biserial correlation is an estimate of the coherence between two variables, one of which is dichotomous and one of which is continuous.”
But, what is a dichotomous variable?
• A dichotomous variable is a variable that can only be one thing or another.
• A dichotomous variable is a variable that can only be one thing or another.
• Here are some examples:
• A dichotomous variable is a variable that can only be one thing or another.
• Here are some examples:– When you can only answer “Yes” or “No”
• A dichotomous variable is a variable that can only be one thing or another.
• Here are some examples:– When you can only answer “Yes” or “No”
– When your statement can only be categorized as “Fact” or “Opinion”
• A dichotomous variable is a variable that can only be one thing or another.
• Here are some examples:– When you can only answer “Yes” or “No”
– When your statement can only be categorized as “Fact” or “Opinion”
– When you are either are something or you are not “Catholic” or “Not Catholic”
• The dichotomous variable may be naturally occurring as in gender
• The dichotomous variable may be naturally occurring as in gender
• The dichotomous variable may be naturally occurring as in gender
• or may be arbitrarily dichotomized as in depressed/not depressed.
• The dichotomous variable may be naturally occurring as in gender
• or may be arbitrarily dichotomized as in depressed/not depressed.
• The range of a point biserial correlation in from -1 to +1.
• The range of a point biserial correlation in from -1 to +1.
-1 0 +1
• Let’s return again to our Point Biserial Correlation definition:
• Let’s return again to our Point Biserial Correlation definition:
• “Point biserial correlation is an estimate of the coherence between two variables, one of which is dichotomous and one of which is continuous.”
• Let’s return again to our Point Biserial Correlation definition:
• “Point biserial correlation is an estimate of the coherence between two variables, one of which is dichotomous and one of which is continuous.”
• Let’s return again to our Point Biserial Correlation definition:
• “Point biserial correlation is an estimate of the coherence between two variables, one of which is dichotomous and one of which is continuous.”
So, we now know what a dichotomous variable is
(either / or)
• Let’s return again to our Point Biserial Correlation definition:
• “Point biserial correlation is an estimate of the coherence between two variables, one of which is dichotomous and one of which is continuous.”
• Let’s return again to our Point Biserial Correlation definition:
• “Point biserial correlation is an estimate of the coherence between two variables, one of which is dichotomous and one of which is continuous.”
What is a continuous variable?
• Definition of Continuous Variable:
• Definition of Continuous Variable:
• If a variable can take on any value between its minimum value and its maximum value, it is called a continuous variable.
• Definition of Continuous Variable:
• If a variable can take on any value between its minimum value and its maximum value, it is called a continuous variable.
• Here is an example:
• Definition of Continuous Variable:
• If a variable can take on any value between its minimum value and its maximum value, it is called a continuous variable.
• Here is an example:
Suppose the fire department mandates that all fire fighters must weigh between 150 and 250 pounds. The weight of a fire fighter would be an example of a continuous variable; since a fire fighter's weight could take on any value between 150 and 250 pounds.
• Definition of Continuous Variable:
• If a variable can take on any value between its minimum value and its maximum value, it is called a continuous variable.
• Here is an example:
Suppose the fire department mandates that all fire fighters must weigh between 150 and 250 pounds. The weight of a fire fighter would be an example of a continuous variable; since a fire fighter's weight could take on any value between 150 and 250 pounds.
• The direction of the correlation depends on how the variables are coded.
• The direction of the correlation depends on how the variables are coded.
• Let’s say we are comparing the shame scores (continuous variable from 1-10) and whether someone is depressed or not (dichotomous variable – not depressed = 1 and depressed = 2). .
• If the dichotomous variable is coded with the higher value representing the presence of an attribute (depressed)
• If the dichotomous variable is coded with the higher value representing the presence of an attribute (depressed)
Person
Depressed
1 = not depressed
2 = depressed
A
B
C
D
E
• If the dichotomous variable is coded with the higher value representing the presence of an attribute (depressed)
Person
Depressed
1 = not depressed
2 = depressed
A Depressed
B Depressed
C Depressed
D Not Depressed
E Not Depressed
• If the dichotomous variable is coded with the higher value representing the presence of an attribute (depressed)
Person
Depressed
1 = not depressed
2 = depressed
A 2
B 2
C 2
D 1
E 1
• . . . and the continuous variable is coded with higher values representing the increasing presence of an attribute (shame),
• . . . and the continuous variable is coded with higher values representing the increasing presence of an attribute (shame),
Person
Depressed
1 = not depressed
2 = depressed
Amount of Shame
A 2 10
B 2 9
C 2 10
D 1 2
E 1 2
• . . . and the continuous variable is coded with higher values representing the increasing presence of an attribute (shame),
• then positive values of the point-biserial would indicate higher shame associated with depressed status. In this case we would compute a phi-coefficient of +.99
Person
Depressed
1 = not depressed
2 = depressed
Amount of Shame
A 2 10
B 2 9
C 2 10
D 1 2
E 1 2
• . . . and the continuous variable is coded with higher values representing the increasing presence of an attribute (shame),
• then positive values of the point-biserial would indicate higher shame associated with depressed status. In this case we would compute a Point Biserial of +.99
Person
Depressed
1 = not depressed
2 = depressed
Amount of Shame
A 2 10
B 2 9
C 2 10
D 1 2
E 1 2
• If we switch the codes where not depressed = 2 and depressed = 1
• If we switch the codes where not depressed = 2 and depressed = 1
Person
Depressed
1 = not depressed
2 = depressed
Amount of Shame
A 1 10
B 1 9
C 1 10
D 2 2
E 2 2
• If we switch the codes where not depressed = 2 and depressed = 1
• We would have a -.99 correlation.
Person
Depressed
1 = not depressed
2 = depressed
Amount of Shame
A 1 10
B 1 9
C 1 10
D 2 2
E 2 2
• If we switch the codes where not depressed = 2 and depressed = 1
• We would have a -.99 correlation.
Person
Depressed
1 = not depressed
2 = depressed
Amount of Shame
A 1 10
B 1 9
C 1 10
D 2 2
E 2 2
• If we switch the codes where not depressed = 2 and depressed = 1
• We would have a -.99 correlation.
• Therefore, instead of looking at the numbers, we think in terms of whether something is present or not in this case (presence of depression or the lack of depression) and how that relates to the amount of shame.
Person
Depressed
1 = not depressed
2 = depressed
Amount of Shame
A 2 10
B 2 9
C 2 10
D 1 2
E 1 2
• The strength of the association can be tested against chance just as the Pearson Product Moment Correlation Coefficient.