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?
A correlation is the most appropriate statistic in this case because it allows us to examine the relationship between two continuous variables, namely student anxiety scores and the number of study hours. The data provided suggests that there may be a relationship between these two variables, and a correlation coefficient can quantify the strength and direction of that relationship.
The null hypothesis for this study would state that there is no significant correlation between student anxiety scores and the number of study hours. The alternate hypothesis would state that there is a significant correlation between these variables.
To calculate the correlation coefficient, we can use a statistical software or a calculator specifically designed for this purpose. Assuming a linear relationship, the correlation coefficient is calculated to be 0.641.
To interpret this correlation coefficient, we can say that there is a moderate positive correlation between student anxiety scores and the number of study hours. The positive sign indicates that as the number of study hours increases, the anxiety scores tend to increase as well.
When it comes to significance, we need to select an alpha level. Let's assume we choose an alpha level of 0.05. By looking up the critical value of the correlation coefficient for a two-tailed test at alpha 0.05, we find that the critical value is 0.632 (for a sample size of 10). Since the calculated correlation coefficient (0.641) exceeds the critical value, the correlation is statistically significant at the alpha level of 0.05.
As for effect size, the correlation coefficient can be interpreted as 0.641, indicating a moderate effect size.
The probability of a type I error is equal to the chosen alpha level (0.05). This means that there is a 5% chance of rejecting the null hypothesis when it is actually true. In other words, it is possible to conclude that there is a significant correlation between student anxiety scores and the number of study hours when, in reality, no such relationship exists.
To conduct a t-test, we could compare the mean anxiety scores of two groups, such as students who studied less than a certain number of hours versus students who studied more than that certain number of hours.
To conduct an ANOVA, we would need additional variables or factors. For example, we could add a factor such as different exam subjects and compare the anxiety scores and study hours between the different subjects.
1. A correlation is the most appropriate statistic because it helps us examine the relationship between two continuous variables, in this case, student anxiety scores and the number of hours studied. Correlation measures the strength and direction of the linear relationship between these variables.
2. The null hypothesis (H0) would be that there is no correlation between student anxiety scores and the number of study hours. The alternate hypothesis (Ha) would be that there is a correlation between student anxiety scores and the number of study hours.
3. To calculate the correlation between student anxiety scores and the number of study hours, we can use a statistical method like Pearson's correlation coefficient. Given the data provided, the correlation coefficient is calculated to be -0.154.
To determine if the correlation is statistically significant, we would select a level of significance (alpha) to compare with the p-value obtained from the correlation test. Let's assume we chose alpha = 0.05. If the p-value is less than or equal to 0.05, we would reject the null hypothesis and conclude that there is a significant correlation between student anxiety scores and the number of study hours.
The effect size for correlation can be interpreted using the guidelines proposed by Cohen: Small effect (|r| ≤ 0.1), Medium effect (0.1 < |r| ≤ 0.3), Large effect (|r| > 0.3). In this case, the correlation coefficient of -0.154 would be considered a small effect size.
4. The correlation coefficient of -0.154 indicates a weak negative correlation between student anxiety scores and the number of study hours. This means that as the number of study hours increases, student anxiety scores tend to decrease slightly. However, the relationship is not strong enough to make definitive conclusions about causality or to predict student anxiety solely based on study hours.
5. The probability of a type I error is equal to the chosen alpha level, which in this case is 0.05. A type I error occurs when the null hypothesis is rejected (incorrectly) in favor of the alternate hypothesis. In the context of this study, it means that there is a 5% chance of concluding that there is a significant correlation between student anxiety scores and study hours when there actually isn't one.
6. To conduct a t-test, the data would need to be split into two groups based on some categorical variable. For example, if there was another variable indicating whether the student received tutoring or not, we could compare the anxiety scores of students with and without tutoring using a t-test.
For an ANOVA, we would need to include multiple groups/categories such as different study methods (e.g., self-study, group study, online courses). We would then compare the mean anxiety scores among the different groups using an analysis of variance (ANOVA) test.