I have ti figure out the correlation coefficient of a statistical factor o 4 personin a dextrity and anxiety test.
1 1 10, 2 1 8, 3 2 4, 4 4 2 .
So I have to figure out the correlation coeficient? this is may part of the task.
To calculate the correlation coefficient, you will need to follow these steps:
Step 1: Organize the data
Write down the given data in a table or spreadsheet. In this case, you have three variables: person, dexterity, and anxiety. The data you provided can be organized as follows:
person dexterity anxiety
1 1 10
2 1 8
3 2 4
4 4 2
Step 2: Calculate the means
Find the mean (average) for each variable. To do this, add up all the values in each column and divide by the total number of values. In this case:
mean(dexterity) = (1+1+2+4)/4 = 2
mean(anxiety) = (10+8+4+2)/4 = 6
Step 3: Calculate the sum of products
For each person, calculate the product of the difference between their dexterity and the mean dexterity, and the difference between their anxiety and the mean anxiety. Then add up all these products. In this case:
sum of products = (1-2)*(10-6) + (1-2)*(8-6) + (2-2)*(4-6) + (4-2)*(2-6)
= (-1)*4 + (-1)*2 + 0*(-2) + 2*(-4)
= -4 + (-2) + 0 + (-8)
= -14
Step 4: Calculate the sum of squares
For each variable, calculate the sum of the squares of the differences between each value and the mean value. Then add up all these squared differences. In this case:
sum of squares(dexterity) = (1-2)^2 + (1-2)^2 + (2-2)^2 + (4-2)^2
= 1 + 1 + 0 + 4
= 6
sum of squares(anxiety) = (10-6)^2 + (8-6)^2 + (4-6)^2 + (2-6)^2
= 16 + 4 + 4 + 16
= 40
Step 5: Calculate the correlation coefficient
Now, use the calculated values to find the correlation coefficient using the formula:
correlation coefficient = sum of products / sqrt(sum of squares(dexterity) * sum of squares(anxiety))
correlation coefficient = -14 / sqrt(6 * 40)
Calculating the square root and dividing, you should get:
correlation coefficient = -14 / sqrt(240)
≈ -14 / 15.4919333848
≈ -0.903
Therefore, the correlation coefficient for the given dataset is approximately -0.903.