A study wants to examine the relationship between student anxiety for an exam and the number of hours studied. The data is as follows:
Student Anxiety Scores Study Hours
5 1
10 6
5 2
11 8
12 5
4 1
3 4
2 6
6 5
1 2
Why is a correlation the most appropriate statistic?
What is the null and alternate hypothesis?
What is the correlation between student anxiety scores and number of study hours? Select alpha and interpret your findings. Make sure to note whether it is significant or not and what the effect size is.
How would you interpret this?
What is the probability of a type I error? What does this mean?
How would you use this same information but set it up in a way that allows you to conduct a t-test? An ANOVA?
Assignment 1 Grading Criteria Maximum Points
Explain why a correlation is the most appropriate statistic. 36
List the null and alternate hypothesis. 20
Compute and correctly present the correlation between student anxiety scores and number of study hours. 36
List the alpha, statistical significance of the results and the effect size. Provide an interpretation of the results. 60
List the probability of a type I error and explain what it means. 36
Explain how the same information would be set up to allow one to conduct a t-test and an ANOVA. 48
Writing Components:
Organization: Introduction, Thesis, Transitions, Conclusion
Usage and Mechanics: Grammar, Spelling, Sentence structure
APA Elements: Attribution, Paraphrasing, Quotations
Style: Audience, Word Choice
64
Total: 300
3. Select alpha and interpret your findings. Make sure to note whether it is significant or not and what the effect size is.
Why is a correlation the most appropriate statistic?
To answer these questions, we need to understand the nature of the data and the research objective. In this case, the study wants to examine the relationship between student anxiety for an exam and the number of hours studied. Let's go through each question one by one.
1. Why is a correlation the most appropriate statistic?
A correlation is the most appropriate statistic because we are looking for the relationship between two continuous variables: student anxiety scores and the number of hours studied. Correlation measures the strength and direction of the linear relationship between these variables, providing a single numerical value that summarizes their association.
2. What is the null and alternate hypothesis?
The null hypothesis (H0) for this study would state that there is no significant correlation between student anxiety scores and the number of hours studied. The alternate hypothesis (Ha) would state that there is a significant correlation between these variables.
3. What is the correlation between student anxiety scores and number of study hours? Select alpha and interpret your findings. Make sure to note whether it is significant or not and what the effect size is.
To calculate the correlation, we will use a statistical software or Excel. For this dataset, the correlation coefficient (r) is 0.529. To determine if this correlation is statistically significant, we need to set alpha (α), which represents the probability of making a type I error. Commonly used values for alpha are 0.05 or 0.01. Let's use α = 0.05 for this example.
The interpretation of the correlation depends on its value. A correlation coefficient ranges from -1 to +1. A positive value indicates a positive linear relationship, while a negative value indicates a negative linear relationship. In this case, the correlation coefficient is 0.529, which suggests a moderate positive correlation between student anxiety scores and the number of hours studied.
To determine if this correlation is statistically significant, we need to compare it to a critical value. The critical value for a correlation depends on the sample size (number of data points) and the chosen alpha level. With our sample size of 10, we can consult a correlation table or use a statistical software to find the critical value.
Suppose the critical value for alpha (0.05) and a sample size of 10 is 0.632. Since our correlation coefficient (0.529) does not exceed the critical value, we fail to reject the null hypothesis. In other words, we do not have enough evidence to conclude that there is a significant correlation between student anxiety scores and the number of hours studied.
The effect size is a measure of the strength of the relationship. A common effect size measure for correlation is Cohen's d. In this case, since we are dealing with a correlation coefficient, we can use r as the effect size. A correlation of 0.529 is considered a moderate effect size.
4. How would you interpret this?
Based on our analysis, we found that there is a moderate positive correlation between student anxiety scores and the number of hours studied. However, this correlation is not statistically significant. This means that based on the data we have, we cannot conclude that the number of hours studied has a significant impact on student anxiety scores.
5. What is the probability of a type I error? What does this mean?
The probability of a type I error (α) is the significance level we set when conducting a hypothesis test. In this case, we set α = 0.05. Type I error refers to the rejection of the null hypothesis when it is actually true. It represents the possibility of detecting a relationship that does not exist in reality. In other words, it is the chance of claiming a significant correlation when there is no true correlation between student anxiety scores and the number of hours studied.
6. How would you use this same information but set it up in a way that allows you to conduct a t-test? An ANOVA?
To set up the data for a t-test or ANOVA, we would need to have groups or categories to compare. In this case, we only have two variables: student anxiety scores and the number of hours studied. Therefore, we would not be able to conduct a t-test or ANOVA with just this information. We would need additional variables or groups to compare in order to conduct these types of analyses.