Two Variable Statistics

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Presentation transcript:

Two Variable Statistics Correlation Coefficient & Pearson’s Correlation Coefficient

Correlation 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 Coefficient Statistic showing the degree of relation between two variables

Simple Correlation coefficient (r) It is also called Pearson's correlation or product moment correlation coefficient. It measures the nature and strength between two variables of the quantitative type.

The sign of r denotes the nature of association while the value of r denotes the strength of association.

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

The value of r ranges between ( -1) and ( +1) The value of r denotes the strength of the association as illustrated by the following diagram. very strong very strong strong moderate weak weak moderate strong -1 -0.95 -0.87 -0.50 0.50 0.87 0.95 1 indirect Direct perfect correlation perfect correlation no relation

If r = Zero this means no association or correlation between the two variables. If 0.1 ≤ r < 0.50 = weak correlation. If 0.50 ≤ r < 0.87 = moderate correlation. If 0.87 ≤ r < 0.95 = strong correlation. If 0.95 ≤ r < 1 = very strong correlation. If r = l = perfect correlation.

YOU DO NOT NEED TO MEMORIZE THIS !!!! How to compute the simple correlation coefficient (r) YOU DO NOT NEED TO MEMORIZE THIS !!!!

WATCH ONE OF THE FOLLOWING VIDEOS 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

Example: A sample of 6 children was selected, data about their age in years and weight in kilograms was recorded as shown in the following table . It is required to find the correlation between age and weight. Weight (Kg) Age (years) serial No 12 7 1 8 6 2 3 10 5 4 11 13 9

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

STEP 1: On your calculator choose the STAT button. STEP 2: Choose the EDIT menu and then the first option Edit...

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

STEP 4: On your calculator choose the STAT button again. STEP 5: Choose the CALC menu and then the fourth option LinReg(ax+b)

STEP 6: You will see the LinReg(ax+b) option pop up on your screen. STEP 7: Press the ENTER button and then it will show all the calculations including r, the correlation coefficient.

Based on the data collected we were able to calculate a correlation coefficient of r = 0.760. This value means that there is a moderately direct or moderately positive correlation between the age and weight of these children in the example.

Example: A sample of 6 students was selected, data about the number of hours studied and percentage grades earned on an assessment were recorded as shown in the following table . It is required to find the correlation between the hours studies and the percentage grade. Student Hours studied % Grade A 6 82 B 2 63 C 1 57 D 5 88 E 3 68 F 75

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

Based on the data collected we were able to calculate a correlation coefficient of r = 0.860. This value means that there is a moderately direct or moderately positive correlation between the hours studied and percentage grade on an assessment of these students in this example.

Thank You