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?
To determine why correlation is the most appropriate statistic for this study, we need to consider the research question and the nature of the variables being examined. In this case, the study aims to examine the relationship between student anxiety scores and the number of hours studied. Both variables, anxiety scores, and study hours, are continuous in nature. Correlation is used to measure the strength and direction of the linear relationship between two continuous variables. Therefore, correlation is the most appropriate statistic to analyze the relationship between student anxiety scores and study hours.
The null hypothesis (H0) states that there is no relationship between student anxiety scores and the number of hours studied. The alternate hypothesis (Ha) states that there is a relationship between student anxiety scores and the number of hours studied.
To calculate the correlation coefficient, we can use statistical software or a calculator. The correlation coefficient ranges from -1 to +1. A positive value indicates a positive relationship, while a negative value indicates a negative relationship. A value of 0 suggests no linear relationship. To interpret the correlation coefficient:
- If the correlation coefficient is close to +1, it indicates a strong positive relationship between student anxiety scores and study hours.
- If the correlation coefficient is close to -1, it indicates a strong negative relationship between student anxiety scores and study hours.
- If the correlation coefficient is close to 0, it suggests no significant linear relationship between the two variables.
Alpha (α) is the significance level used to determine the probability of making a type I error. Commonly used values for alpha are 0.05 or 0.01. To interpret the findings, we compare the p-value to the chosen alpha level:
- If the p-value is less than the chosen alpha level (e.g., p < 0.05), we reject the null hypothesis and conclude that there is a significant relationship between student anxiety scores and study hours.
- If the p-value is greater than the chosen alpha level, we fail to reject the null hypothesis and conclude that there is no significant relationship between student anxiety scores and study hours.
The effect size in correlation is typically measured by the absolute value of the correlation coefficient (|r|). If the correlation is statistically significant, a large effect size (close to +1 or -1) indicates a stronger relationship between student anxiety scores and study hours.
The probability of a type I error is equal to the chosen alpha level (e.g., 0.05). A type I error occurs when we reject the null hypothesis when it is actually true. In this study, it would mean concluding that there is a relationship between student anxiety scores and study hours when the actual relationship is due to chance alone.
To conduct a t-test using this information, we would need to separate the data into two groups based on a categorical variable. For example, we could compare the anxiety scores for students who studied more than a certain number of hours versus those who studied less. This would allow us to determine if there is a significant difference in anxiety scores between the two groups.
To conduct an ANOVA, we would need to have multiple groups or levels of study hours. For example, we could categorize the study hours into low, medium, and high, and then compare the mean anxiety scores between these groups using an analysis of variance (ANOVA) test.