2 For a sample of n = 20 individuals, how large a Pearson correlation is necessary to be statistically significant for a two-tailed test with = .05?
3 The Pearson correlation is calculated for a sample of n = 25 individuals. What value of df should be used to determine whether or not the correlation is significant?
4 What is the value of SP for the following set of data?
X Y
1 5
3 3
8 1
5 A set of n = 5 pairs of X and Y values has SSX = 4, SSY = 16 and SP = 8. For these data, what is the Pearson correlation?
Which of the following sets of correlations correctly shows the highest to lowest degree of relationship?
6 The Pearson correlation is calculated for a sample of n = 25 individuals. What value of df should be used to determine whether or not the correlation is significant?
0.41
2. To determine the minimum Pearson correlation necessary to be statistically significant for a two-tailed test with α = 0.05 and a sample size of n = 20 individuals, you would need to consult a statistical table or use a statistical software to find the critical value for the given α level and degrees of freedom (df). In this case, the df would be n - 2 = 20 - 2 = 18. Once you have the critical value, you can convert it to a correlation coefficient value using the inverse correlation formula.
3. To determine the appropriate value of df for the Pearson correlation calculated on a sample of n = 25 individuals, you would use the formula df = n - 2, where n is the sample size. Therefore, for n = 25 individuals, the value of df would be 25 - 2 = 23.
4. To find the value of SP for the given set of data, which includes X and Y values, you need to calculate the sum of the products of X and Y. In this case:
X: 1, 3, 8
Y: 5, 3, 1
The sum of the products of X and Y (SP) can be calculated as:
SP = (1 * 5) + (3 * 3) + (8 * 1) = 5 + 9 + 8 = 22
Therefore, the value of SP for this data set is 22.
5. Given a set of data with n = 5 pairs of X and Y values, SSX = 4, SSY = 16, and SP = 8, we can use the formula for Pearson correlation (r) to calculate the correlation coefficient. The formula is:
r = SP / sqrt(SSX * SSY)
Plugging the given values into the formula:
r = 8 / sqrt(4 * 16) = 8 / sqrt(64) = 8 / 8 = 1
Therefore, the Pearson correlation for these data is 1.
6. To determine the appropriate value of df for the Pearson correlation calculated on a sample of n = 25 individuals, you can use the formula df = n - 2. In this case, the value of df would be 25 - 2 = 23.
2. The required Pearson correlation coefficient for statistical significance can be determined using a significance level of α = 0.05 and the sample size, n = 20.
For a two-tailed test, the significance level is divided equally between the two tails. Therefore, each tail has an α/2 = 0.05/2 = 0.025 significance level.
To find the critical value for the correlation coefficient, we can use a table or a statistical software. For a sample size of 20, the critical value for a two-tailed test at a 0.025 significance level is approximately 0.444.
Therefore, the Pearson correlation coefficient should be at least 0.444 for it to be statistically significant at α = 0.05 for a two-tailed test.
3. For calculating the degrees of freedom (df) to determine the significance of a Pearson correlation, we need the sample size (n). In this case, n = 25.
To calculate df for the Pearson correlation, we use the formula:
df = n - 2
Therefore, for a sample size of 25 individuals, the value of df to determine the significance of the correlation would be 25 - 2 = 23.
4. To calculate the value of SP (sum of products) for the given set of data:
X Y
1 5
3 3
8 1
The formula to calculate SP is:
SP = Σ(XY) - (ΣX)(ΣY)/n
First, calculate Σ(XY) (sum of the products of X and Y values):
Σ(XY) = 1 * 5 + 3 * 3 + 8 * 1 = 5 + 9 + 8 = 22
Then, calculate ΣX (sum of X values):
ΣX = 1 + 3 + 8 = 12
Next, calculate ΣY (sum of Y values):
ΣY = 5 + 3 + 1 = 9
Finally, calculate SP:
SP = Σ(XY) - (ΣX)(ΣY)/n = 22 - (12 * 9)/3 = 22 - 108/3 = 22 - 36 = -14
Therefore, the value of SP for the given set of data is -14.
5. To calculate the Pearson correlation coefficient from the given information:
SSX = 4
SSY = 16
SP = 8
The formulas to calculate the Pearson correlation coefficient are:
r = SP / sqrt(SSX * SSY)
First, calculate the square root of SSX and SSY:
sqrt(SSX) = sqrt(4) = 2
sqrt(SSY) = sqrt(16) = 4
Next, calculate the Pearson correlation coefficient:
r = SP / sqrt(SSX * SSY) = 8 / (2 * 4) = 8 / 8 = 1
Therefore, the Pearson correlation coefficient for these data is 1.
6. To determine the value of df for the Pearson correlation coefficient with a sample size of n = 25, the formula to calculate df is:
df = n - 2
Therefore, for a sample size of 25 individuals, the value of df to determine the significance of the correlation would be 25 - 2 = 23.