Calculate SP (the sum of products of deviations) for the

following scores. Note: Both means are decimal values,
so the computational formula works well.

X Y
0 2
0 1
1 0
2 1
1 2
0 3

Assume a two-tailed test with � � .05.
(Note: The table does not list all the possible df values. Use the sample size corresponding to the appropriate df value that is listed in the table.)
a. A correlation of r � 0.30.
b. A correlation of r � 0.25.
c. A correlation of r � 0.20.

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To calculate the SP (sum of products of deviations), we need to follow these steps:

1. Determine the mean for each set of scores, X and Y.
- To find the mean, add up all the scores and divide by the total number of scores.

2. Calculate the deviation for each score in both X and Y.
- To find the deviation, subtract the mean from each score.

3. Multiply the deviations of X and Y for each score.
- Multiply the deviation of X for a specific score with the deviation of Y for the same score.

4. Add up all the products of deviations calculated in the previous step.
- Sum all the values obtained from multiplying the deviations.

Let's now calculate the SP for each correlation value:

a. Correlation (r) = 0.30:
- Calculate the mean for X: (0 + 0 + 1 + 2 + 1 + 0) / 6 = 0.667 (approximately)
- Calculate the mean for Y: (2 + 1 + 0 + 1 + 2 + 3) / 6 = 1.5
- Calculate the deviation for each score in X and Y:
- For X: Deviation = X - Mean(X)
- Deviations for X: (-0.667, -0.667, 0.333, 1.333, 0.333, -0.667)
- For Y: Deviation = Y - Mean(Y)
- Deviations for Y: (0.5, -0.5, -1.5, -0.5, 0.5, 1.5)
- Multiply the deviations of X and Y for each score:
- Products of deviations: (-0.667 * 0.5, -0.667 * -0.5, 0.333 * -1.5, 1.333 * -0.5, 0.333 * 0.5, -0.667 * 1.5)
- Products of deviations: (-0.334, 0.334, -0.5, -0.667, 0.167, -1.001)
- Add up the products of deviations:
- SP = -0.334 + 0.334 + -0.5 + -0.667 + 0.167 + -1.001 = -2 (approximately)

b. Correlation (r) = 0.25:
- Follow the same steps as above with the new correlation value to calculate the SP.

c. Correlation (r) = 0.20:
- Follow the same steps as above with the new correlation value to calculate the SP.

Remember to check your calculations to ensure accuracy.