Two Variable Two Variable StatisticsStatistics

Correlation CoefficientCorrelation Coefficient

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Pearson’s Correlation Pearson’s Correlation CoefficientCoefficient

CorrelationCorrelation

Finding the relationship between two quantitative variables without being able to infer causal relationships

Correlation is a statistical technique used to determine the degree to which two variables are related

Correlation CoefficientCorrelation Coefficient

Statistic showing the degree of relation between two variables

Simple Correlation coefficient (r)Simple Correlation coefficient (r)

It is also called Pearson's correlation It is also called Pearson's correlation or product moment correlation or product moment correlationcoefficient. coefficient.

It measures the It measures the naturenature and and strengthstrength between two variables ofbetween two variables ofthe the quantitativequantitative type. type.

The The signsign of of rr denotes the nature of denotes the nature of association association

while the while the valuevalue of of rr denotes the denotes the strength of association.strength of association.

If the sign is If the sign is +ve+ve this means the relation this means the relation is is direct direct (an increase in one variable is (an increase in one variable is associated with an increase in theassociated with an increase in theother variable and a decrease in one other variable and a decrease in one variable is associated with avariable is associated with adecrease in the other variable).decrease in the other variable).

While if the sign is While if the sign is -ve-ve this means an this means an inverse or indirectinverse or indirect relationship (which relationship (which means an increase in one variable is means an increase in one variable is associated with a decrease in the other).associated with a decrease in the other).

The value of r ranges between ( -1) and ( +1)The value of r ranges between ( -1) and ( +1) The value of r denotes the strength of the The value of r denotes the strength of the

association as illustratedassociation as illustratedby the following diagram.by the following diagram.

-1 10-0.87-0.95

strong strongmoderate moderateweak weak

no relation

perfect correlation

perfect correlation

Directindirect

-0.50 0.870.50 0.95

verystrong

verystrong

If If rr = Zero = Zero this means no association or this means no association or correlation between the two variables.correlation between the two variables.

If If 0.1 ≤ 0.1 ≤ rr < 0.50 < 0.50 = weak correlation. = weak correlation.

If If 0.50 ≤ 0.50 ≤ rr < 0.87 < 0.87 = moderate correlation. = moderate correlation.

If If 0.87 ≤ 0.87 ≤ rr < 0.95 < 0.95 = strong correlation. = strong correlation.

If If 0.95 ≤ 0.95 ≤ rr < 1 < 1 = very strong correlation. = very strong correlation.

If If r r = l= l = perfect correlation. = perfect correlation.

How to compute the simple correlation coefficient (r)

YOU DO NOT NEED TO MEMORIZE THIS !!!!

Find the Correlation Coefficient on Your Calculator (TI83 TI84)

In Case Link Does Not Work:https://www.youtube.com/watch?v=HK-gyKwNR6M

Using TI-Nspire to Find Correlation Coefficient

In Case Link Does Not Work:https://www.youtube.com/watch?v=YncLnRpdMOM

WATCH ONE OF THE FOLLOWING VIDEOS

ExampleExample::

A sample of 6 children was selected, data about their A sample of 6 children was selected, data about their age in years and weight in kilograms was recorded as age in years and weight in kilograms was recorded as shown in the following table . It is required to find the shown in the following table . It is required to find the correlation between age and weight.correlation between age and weight.

serial No

Age (years)

Weight (Kg)

1712

268

3812

4510

5611

6913

These 2 variables are of the quantitative type, one These 2 variables are of the quantitative type, one variable (Age) is called the independent and variable (Age) is called the independent and denoted as (X) variable and the other (weight)denoted as (X) variable and the other (weight)is called the dependent and denoted as (Y) is called the dependent and denoted as (Y) variables to find the relation between age and variables to find the relation between age and weight compute the simple correlation coefficient weight compute the simple correlation coefficient using the following formula:using the following formula:

WE WILL USE THE CALCULATOR.

STEP 1: On your STEP 1: On your calculator choose calculator choose the STAT button.the STAT button.

STEP 2: Choose the STEP 2: Choose the EDIT menu and then EDIT menu and then the first option Edit...the first option Edit...

STEP 3: Enter the STEP 3: Enter the data into the table. data into the table. Enter the Age into Enter the Age into L1 and the Weight L1 and the Weight into L2 as follows.into L2 as follows.

STEP 4: On your STEP 4: On your calculator choose calculator choose the STAT button the STAT button again.again.

STEP 5: Choose the STEP 5: Choose the CALC menu and CALC menu and then the fourth then the fourth option LinReg(ax+b)option LinReg(ax+b)

STEP 6: You will see STEP 6: You will see the LinReg(ax+b) the LinReg(ax+b) option pop up on option pop up on your screen.your screen.

STEP 7: Press the STEP 7: Press the ENTER button and ENTER button and then it will show all then it will show all the calculations the calculations including including rr, the , the correlation correlation coefficient.coefficient.

Based on the data collected we were able to Based on the data collected we were able to calculate a correlation coefficient of r = 0.760.calculate a correlation coefficient of r = 0.760.

This value means that there is a This value means that there is a moderately moderately direct direct or or moderately positive moderately positive correlation correlation between the age and weight of these children in between the age and weight of these children in the example.the example.

ExampleExample::

A sample of 6 students was selected, data about the A sample of 6 students was selected, data about the number of hours studied and percentage grades number of hours studied and percentage grades earned on an assessment were recorded as shown in earned on an assessment were recorded as shown in the following table . It is required to find the correlation the following table . It is required to find the correlation between the hours studies and the percentage grade.between the hours studies and the percentage grade.

StudentHours studied% Grade

A682

B263

C157

D588

E368

F275

These 2 variables are of the quantitative type, one These 2 variables are of the quantitative type, one variable (Hours Studied) is called the independent variable (Hours Studied) is called the independent and denoted as (X) variable and the other and denoted as (X) variable and the other (Percentage Grade) is called the dependent and (Percentage Grade) is called the dependent and denoted as (Y) variables to find the relation denoted as (Y) variables to find the relation between hours studies and percentage grade between hours studies and percentage grade compute the simple correlation coefficient using compute the simple correlation coefficient using your calculatoryour calculator

Perform the steps as in the previous example.

Based on the data collected we were able to Based on the data collected we were able to calculate a correlation coefficient of r = 0.860.calculate a correlation coefficient of r = 0.860.

This value means that there is a This value means that there is a moderately moderately direct direct or or moderately positive moderately positive correlation correlation between the hours studied and percentage between the hours studied and percentage grade on an assessment of these students in grade on an assessment of these students in this example.this example.