Four researcher participants take a test of manual dexerity(high scores mean better dexerity) and an anxiety test(high scores mean more anxiety). The scores are as followed.
PersonDexerityAnxiety
1 1 10
2 1 8
3 2 4
4 4 -2
There is no question
Even with no question, the data suggest a small, inverse relationship between anxiety and dexterity. However, there is not enough data to indicate that this is a significant result. The n is too small, and you do not indicate the possible range of scores on the scales. For example, if both scales range from 0-100, there is definitely no significant variation.
I hope this helps a little. Thanks for asking.
To analyze the data, we can calculate the correlation coefficient between manual dexterity and anxiety scores for the four research participants. The correlation coefficient measures the strength and direction of the linear relationship between two variables.
To calculate the correlation coefficient, we will use the formula:
r = (nΣxy - ΣxΣy) / sqrt((nΣx^2 - (Σx)^2)(nΣy^2 - (Σy)^2))
Where:
- r is the correlation coefficient
- n is the number of data points (in this case, 4)
- Σxy is the sum of the product of each participant's manual dexterity and anxiety score
- Σx is the sum of all manual dexterity scores
- Σy is the sum of all anxiety scores
- Σx^2 is the sum of the squares of manual dexterity scores
- Σy^2 is the sum of the squares of anxiety scores
Let's calculate the correlation coefficient step by step:
1. Calculate the values needed for the formula:
Σxy = (1*10) + (1*8) + (2*4) + (4*-2) = 10 + 8 + 8 - 8 = 18
Σx = 1 + 1 + 2 + 4 = 8
Σy = 10 + 8 + 4 - 2 = 20
Σx^2 = (1^2) + (1^2) + (2^2) + (4^2) = 1 + 1 + 4 + 16 = 22
Σy^2 = (10^2) + (8^2) + (4^2) + (-2^2) = 100 + 64 + 16 + 4 = 184
2. Calculate the correlation coefficient using the formula:
r = (4 * 18 - 8 * 20) / sqrt((4 * 22 - 8^2)(4 * 184 - 20^2))
r = (72 - 160) / sqrt((88 - 64)(736 - 400))
r = -88 / sqrt(24 * 336)
r = -88 / sqrt(8064)
r ≈ -88 / 89.89
r ≈ -0.978
The correlation coefficient between manual dexterity and anxiety scores for the four research participants is approximately -0.978. This negative value indicates a strong negative (inverse) relationship between the two variables. In other words, as manual dexterity scores increase, anxiety scores tend to decrease.