Introduction
This paper focuses on the analysis of correlations between four variables, including the number of correct answers in Quiz 1(‘quiz1’), grade point average (‘GPA’), total number of points earned in class (‘total’), and number of correct answers in the final exam (‘final’). First, the paper provides a data analysis plan by listing the variables and stating research the research question and the hypotheses. Second, the paper tests assumption of Pearson’s correlation analysis. Third, the results of the analysis are provided and interpreted. Fourth, the statistical conclusions are drawn. The paper is concluded with a discussion of the application of the methods for psychology discussed.
Data Analysis Plan
This paper analyzes four variables including ‘quiz1’, ‘gpa’, ‘total’, ‘final. All four of the variables are continuous that include integers except for ‘gpa’, which is a number that has two digits after the decimal point. The primary research question answer during the analysis of the four variables is:
- RQ1: What is the correlation between the number of correct answers in Quiz 1 and number of correct answers in the final exam?
The null and alternative hypotheses are provided below:
- H0: There is no significant correlation between the number of correct answers in Quiz 1 and number of correct answers in the final exam.
- HA: There is no significant correlation between the number of correct answers in Quiz 1 and number of correct answers in the final exam.
Testing Assumptions
In order to conduct correlation analysis, it is crucial to test for the statistical assumption to ensure that no bias is present in the analysis. According to Field (2018), normality is one of the central assumptions required for Pearson’s correlation test. The assumption of normality can be assessed by the analysis descriptive statistics. In particular, if the skewness and kurtosis for the variables are close to zero, the distribution is seen as normal (Field, 2018). The descriptive statistics for the four variables under analysis are provided in Table 1 below.
Table 1. Descriptive Statistics
The analysis of the descriptive statistics for the variables demonstrated that there were no violations of the assumption of normality. Skewness of the ‘gpa’ variable of -0.22 the kurtosis was 0.688 which is classified as almost a perfect fit. The kurtosis for the ‘quiz1’ variable is 0.162 and the skewness was -0.851, which signified almost a perfect fit with the normal distribution curve. The kurtosis and skewness of the ‘final’ variable were both close to zero with values of -0.341 and -0.277 correspondingly, which implies that that the assumption of normality holds for the variable. Similarly, the distribution of the ‘total’ variable was normally distributed, as both skewness and kurtosis were close to zero with values of -0.757 and 1.146 correspondingly. However, it should be noted that the variable’s kurtosis was in the ‘acceptable’ range, as it was above the value of 1. In summary, the assumption of normality is true only for the ‘final’ variable.
Results and Interpretation
Pearson’s correlation coefficient was used to assess the correlation between the variables. According to Field (2018), Person’s correlation coefficient quantifies the inter-relationships between two variables on a scale from -1 to 1, where ‘0’ stands for no correlation, ‘1’ stands for perfect positive correlation, and ‘-1’ stand for perfect negative correlation. The correlation matrix for the four variables under analysis are provided in Table 2 below.
Table 2. Correlation matrix
The correlation with the lowest magnitude was between GPA and Quiz 1. The correlation between the number of correct answers in Quiz 1 and GPA was with r(103) = 0. 152, p = 0.121, which an insignificant correlation. The effect size was small with Cohen’s d = 0.308. Since the p value was above the threshold of 0.05, there was no significant evidence to reject the null hypothesis. Therefore, the null hypothesis was accepted and the alternative hypothesis was rejected.
The correlation with the highest magnitude was between the number of correct answers in the final exam and the total number of points earned in class is close with Person’s r(103) = 0.875, p < 0.001, which demonstrated a very high correlation. The effect size was very high with Cohen’s d = 3.615. Since the p value was below the threshold of 0.05, there was significant evidence to reject the null hypothesis. Therefore, the null hypothesis was rejected and the alternative hypothesis was accepted.
The correlation between the number of correct answers in Quiz 1 and the number of correct answers for the final exam was r(103) = 0.499, p < 0.001, which demonstrates a moderate correlation. The effect size was high with Cohen’s d = 1.152. Since the correlation between ‘quiz1’ and ‘final’ is statistically significant with p < 0.001, the null hypothesis should be rejected.
Statistical Conclusions
The statistical analysis of the variables revealed there was a significant correlation all the variables under analysis except for the relationship between ‘quiz1’ and ‘gpa’. Hypothesis test demonstrated that the null hypothesis should be rejected, meaning that there was a significant correlation between the number of correct answers in Quiz 1 and the number of correct answers for the final exam. This implies that the results for Quiz 1 can be used to predict the performance of a student during the final test.
There are two major limitations to the findings that should be acknowledged. On the one hand, the results can be applied only to the population under analysis, which is not mentioned in the dataset. This implies that the correlation may be not universal for all courses in all schools and universities. Second, the analysis of assumptions revealed violations of the assumption of normality. Therefore, the results of the analysis may be biased.
There is one alternative explanation of the findings that should be mentioned. In particular, the results of the analysis suggest that the performance on the final exam differs from the performance during the first quiz, as the correlation was not perfect. In other words, the performance of students may improve or worsen during the semester. Future research should focus on determining what factors affect the success rate during the final exam apart from the results of Quiz 1.
Application
There may be numerous uses of correlation analysis in psychology. For instance, psychologists can measure the relationships between traits of character of people and their susceptibility to psychological conditions. In particular, researchers may measure neuroticism score among a certain population as an independent variable and the severity of depression symptoms as the dependent variable. The results of may have significant implications for psychology. In particular, such knowledge can determine risk factors of depression, which can help to apply prevention strategies to improve psychological health of the population. Therefore, using correlation analysis in psychology research is important.
Reference
Field, A. (2018). Discovering statistics using SPSS: North American edition (5th ed.). Sage.