Conducting and Analyzing Statistical Test
By: Rachel Richardson
1) We have two variables and both are measured on the ratio scale of measurement. We are interested to see if there is any correlation between the anxiety scores and study hours. In particular, we want to see if more anxiety before an exam results in more hours of study. Therefore correlation is the most appropriate statistic.
2) Null Hypothesis: Anxiety scores and Study hours are not correlated
Alternate Hypothesis: Anxiety scores and Study hours are correlated (Argosy University 2015).
3) Regression analysis results:
Correlation coefficient, r = 0.5654
Let us use a 5% level of significance (α = 0.05)
n = 10
r = 0.5654
From the table of critical values for Pearson correlation, we find critical r = 0.632
Since 0.5654 is less than 0.632, the correlation is not significant.
One measure of effect size is the coefficient of determination r^2 = 0.5654^2 = 0.32. This means
only about 32% of the variation in Study hours is due to the variation in Anxiety scores
4) The above results mean that Anxiety scores and Study hours are not significantly correlated with only about 32% of the observed variation in the response variable (Study hours) accounted for by the predictor variable (Anxiety score) (NCBI 2012).
5) Probability of Type I error = α = 0.05. This means 5% of the time, our decision to reject Ho will be wrong. In other words, 5% of the time, we will find correlation between Anxiety scores and Study hours, where in reality there is none (Texas University 2011).
6) A t- test can be used to test if the two variables are correlated or not by using the t- statistic with n – 2 degrees of freedom. The steps are below:
Null Hypothesis: There is no significant correlation, that is = 0
Alternate Hypothesis: There is significant...