Hypothesis Testing With Pearsons r Flashcards
What is the null hypothesis in a correlational analysis?
The null hypothesis states that a relationship between two observed variables does not exist.
What is the alternative hypothesis in a correlational analysis?
The alternative hypothesis states that a relationship does exist and can be directional or non-directional.
How is the null hypothesis represented mathematically?
H0: ρ=0 (No relationship between the variables)
How is the alternative hypothesis represented mathematically?
Ha: ρ≠0 (Non-directional relationship), Ha: ρ>0 (Predicted positive relationship), Ha: ρ<0 (Predicted negative relationship)
What is the first step in hypothesis testing with Pearson’s r?
State the hypotheses.
What is the second step in hypothesis testing with Pearson’s r?
Establish the decision criteria.
How are degrees of freedom (df) calculated for Pearson’s r?
df is calculated as two less than the number of ordered pairs (n) in the dataset: df=n−2.
What is the critical value (rcrit) used for?
The critical value is used to determine whether to reject the null hypothesis.
What is the third step in hypothesis testing with Pearson’s r?
Collect data and compute sample statistics.
What does an r value of -1 indicate?
It indicates a very strong negative correlation.
What does an r value of 0 indicate?
It indicates no correlation.
What does an r value of +1 indicate?
It indicates a very strong positive correlation.
What is the fourth step in hypothesis testing with Pearson’s r?
Make a decision based on the comparison of the calculated r-value and the critical r-value.
What does it mean if the obtained r-value exceeds the critical r-value?
The null hypothesis is rejected, suggesting that the predicted relationship exists.
What are the hypotheses for the example problem?
H0: ρ=0 (No relationship); Ha: ρ≠0 (There is a relationship).
How are the results reported in APA format for the example problem?
r(3)=−0.959,p<0.05.
What does a correlation coefficient of r=−0.959 indicate?
It indicates a very strong negative relationship between the two variables.
What is a limitation of correlational analysis mentioned in the text?
A strong correlation does not imply a causal relationship.
