Week 4- Assignment 2

1. The Data Analysis Plan Descriptive Statistics In this analysis, we are considering four continuous variables: GPA, Quiz1, Total, and Final. We aim to explore the relationships between these variables through two research questions. The first question asks if there is a significant correlation between students’ total scores and their final exam scores. The null hypothesis for this question is that there is no significant correlation between these two variables, while the alternate hypothesis proposes that a significant correlation exists. The second research question investigates whether there is a significant correlation between students’ GPA and their scores on Quiz1. Similarly, the null hypothesis suggests no significant correlation between these variables, and the alternate hypothesis posits that a significant correlation does exist. We will test these hypotheses using Pearson’s correlation coefficient, which will provide insights into the strength and direction of the linear relationship between the variables. Descriptive Statistics   quiz1 gpa total final Skewness -0.851 -0.220 -0.757 -0.341 Std. Error of Skewness 0.236 0.236 0.236 0.236 Kurtosis 0.162 -0.688 1.146 -0.277 Std. Error of Kurtosis 0.467 0.467 0.467 0.467

2. Testing Assumptions Correlation Pearson's Correlations Variable   quiz1 gpa total final 1. quiz1 Pearson's r — p-value —       2. gpa Pearson's r 0.152 — p-value 0.121 —     3. total Pearson's r 0.797 ** * 0.318*** — p-value < .001 < .001 —   4. final Pearson's r 0.499 ** * 0.379*** 0.875*** — p-value < .001 < .001 < .001 — * p < .05, ** p < .01, *** p < .001 In assessing the normality of the variables GPA, quiz1, total, and final, we examined the skewness and kurtosis values. The skewness values for GPA, quiz1, total, and final indicated a slight to moderate leftward skew, while the kurtosis values suggested a range from platykurtic (lighter tails) to leptokurtic (heavier tails) distributions. These values are within the acceptable range for assuming normality, typically where the absolute value of skewness is less than 2 and kurtosis is less than 7. Therefore, we can conclude that the assumption of normality is not violated for these variables, and it is appropriate to proceed with Pearson’s correlation analysis. However, it’s worth noting that these values only suggest normality, and additional confirmation could be obtained through visual inspections such as histograms or Q-Q plots. 3.Results and Interpretations Descriptive Statistics   gpa quiz1 total final Valid 105 105 105 105 Missing 0 0 0 0 Mean 2.862 7.467 100.086 61.838 Std. Deviation 0.713 2.481 13.427 7.635 Minimum 1.080 0.000 54.000 40.000 Maximum 4.000 10.000 123.000 75.000

5. Application Correlation analysis is a powerful tool in the field of clinical psychology, particularly in forensic psychology. It allows us to understand the relationships between different variables and can help in predicting one variable based on the other. For instance, consider the variables ‘Severity of Mental Illness’ and ‘Risk of Recidivism’. Studying the correlation between these two variables could provide valuable insights. If a significant positive correlation is found, it would suggest that as the severity of mental illness increases, so does the risk of recidivism. This could have profound implications for treatment plans and risk management strategies for individuals in the criminal justice system. Understanding such relationships is crucial in the field of forensic psychology. It can guide the development of effective interventions, inform judicial decisions, and contribute to a safer society.