Question

Lab Questions for Correlation

State the purpose of the procedure and write two research questions for a negative and a positive bivariate correlation. Label and operationally define the Independent(X) and Dependent(Y) Variables.

Write the Null, Alternative, and Working Hypotheses for both research questions.

Answer 1

Correlation is the extent of linear relationship between two variables.

By using correlation we can determine which relationship between dependent and independent variable.

In correlation there are two variables dependent variable and independent variable.

Positive correlation example :

Hypothesis for the test is,

H0 : Rho = 0 Vs H1 : Rho > 0

where Rho is population correlation between dependent and independent variable.

Assume alpha = level of significance = 0.05

sample size (n) = 12

sample correlation coefficient (r) = 0.541

The test statistic is,

t = r*sqrt(n-2) / sqrt(1-r²)

= 0.541*sqrt(12-2) / sqrt(1-0.541²) = 2.03

Now we have to find P-value for taking decision.

P--value we can find in excel.

syntax :

=TDIST(x, deg_freedom, tails)

where x is absolute value of test statistic.

deg_freedom = n-2 = 12-2 = 10

tails = 1

P-value = 0.0349

P-value < alpha

Reject H0 at 5% level of significance.

COnclusion : There is positive relationship between dependent and independent variable.

Similarly we have to find the example for negative correlation.

Hypothesis for the test is,

H0 : Rho = 0 Vs H1 : Rho < 0

where Rho is negative relationship between dependent and independent variable.

r = -0.903

n= 12

t = -0.903*sqrt(12-2) / sqrt(1 - (-0.903)^2)) = 0.43

P-value = 0.3383

P-value > alpha

Accept H0 at 5% level of significance.

Conclusion : There is not significant negative relationship between dependent and independent variable.