RSCH FPX 7864 Assessment 2 Correlation Application and Interpretation

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Capella university

RSCH-FPX 7864 Quantitative Design and Analysis

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Date

Correlation Application and Interpretation

The study’s dependent variables are the students’ final grade, grade point average, first quiz score, and total grade. Data on student demographics, academic performance on standardized tests, and instructors’ use of formative evaluations across all three units will be considered. This inquiry primarily aims to determine the extent to which students’ final grades mirror their grade point averages. The cumulative mark and final grade are both continuous variables, meaning they are open to any possible value (Sayyed et al., 2023). The students’ Quiz 1 scores are static, but their sexual orientation is hypothetical. This correlational analysis used a 105-person sample with a 0.05 significance level.

RSCH FPX 7864 Assessment 2 Correlation Application and Interpretation

Correlation Analysis	Research Question	Null Hypothesis (H₀)	Alternative Hypothesis (Hₐ)
Total Final Correlation	Does a student’s final score reflect their cumulative grade?	A student’s final grade is not directly proportional to their cumulative grade.	A student’s final grade is positively correlated with the sum of their grades.
GPA-Quiz 1 Correlation	Does this research show that students’ grade point averages correlate significantly with their performance on Quiz 1?	There is no clear correlation between students’ GPAs and their performance on Quiz 1.	A linear relationship exists between students’ GPAs and their performance on Quiz 1.

Testing Assumption

Figure 1: Descriptive Statistics

Final exam scores and grade point averages can be seen in the descriptive table, along with their skewness and kurtosis values. Through the computation of skewness and kurtosis for each component, we were able to confirm that the data followed a normal distribution. Distributions for the first quiz and the GPA were normal, as shown by skewness and kurtosis values that were within acceptable ranges (Verostek et al., 2021). However, there was a slight deviation from the ideal values, causing the overall grade distributions to not follow a normal distribution. The skewness and kurtosis values are within acceptable levels, indicating that the GPA distribution is normal. The kurtosis value is -0.688, and the skewness value is -0.220. 

RSCH FPX 7864 Assessment 2 Correlation Application and Interpretation

The data follows a normal distribution, as the skewness and kurtosis values are within acceptable ranges, according to the final test findings. The kurtosis value is -0.277, and the skewness value is -0.341. However, the normal interpretation impacted both the first quiz and the final grades. A little negative skew and negative kurtosis were indicated by the initial exam, which fell inside the permissible range for skewness and kurtosis, with values of -0.5 and -1.2, respectively. Thus, it is reasonable to assume that Quiz 1 has a normal distribution. Total grade skewness = 0.8 and kurtosis = 2.1, which are somewhat beyond the ideal range but nevertheless show a positive skew and positive kurtosis, respectively.

RSCH FPX 7864 Assessment 2 Correlation Application and Interpretation

As a result, we may state that the distribution of grades is not 100% normal (Endleman et al., 2021). To complete my responsibility of assessing the normality of the distributions of all four variables, I will incorporate these interpretations in the report. The skewness score of -0.220 and kurtosis value of -0.688 show that the GPA distribution is significantly negatively skewed. However, given both the skewness and kurtosis values are within the acceptable range, it appears that the GPA distribution is normal.

Similarly, the kurtosis value is -0.277, and the skewness value is -0.341 for the distribution of the final test results, suggesting that the data is somewhat skewed to the negative. The distribution of final test scores is normal, as shown by these figures, and they are also within the permissible range (Ozcan et al., 2021). Upon examination of all four variables, it can be inferred that the final test scores and GPA adhere to normal distributions, as their skewness and kurtosis values fall within the given ranges. The last two variables in the report—the first quiz score and total grade—will be analyzed for skewness and kurtosis values so that you can get a complete picture.

Analysis of Decision-Making Process

Importantly, categorical variables are distinct from continuous ones. The final grade, grade point average, and cumulative grade are all variables that indicate numerical values at meaningful intervals; they are considered continuous in this examination. However, the initial quiz score only displays discrete categories (such as the total number of right answers) and does not contain any numerical value. Framing hypotheses within that framework is vital when undertaking a correlation study. It is important that the hypothesis explicitly states that the variables have a linear connection (Thompson, 2021).

To make a point, let’s say we have two competing hypotheses about the relationship between cumulative and final grades. One could argue that the null hypothesis (H0) is: “There is no linear correlation between total and final grades.” In contrast, the alternative hypothesis (H1) would state: “There is a linear correlation between total and final grades.” This methodology would also be used to investigate a linear relationship between quiz 1 scores and GPA. This is how we frame the hypotheses such that they are clear, testable, and relevant to the correlation analysis. This will help to cement the study’s findings.

Results and Interpretation

Figure 2: Correlation between variables

The association matrix examined four factors: grade point average, overall GPA, quiz 1 score, and final grade. The results of the statistical analysis and the correlation matrix show a positive association between higher final grades and better outcomes, thereby rejecting the null hypothesis. The statistical analysis was conducted at a significance level of 0.05.

The study discovered a highly significant linear association between overall and final grades, with a Pearson correlation coefficient of R=0.88 and p=0.001. This shows a strong positive connection between total and final grades, implying that the two are closely related (Wu et al., 2021). The data contradict the null hypothesis and support the alternative hypothesis, which holds that there is a high link between overall and final grades.

RSCH FPX 7864 Assessment 2 Correlation Application and Interpretation

A connection of 0.152 between the grade point average and the first quiz was found (103 degrees of freedom, p-value of 0.112). According to these findings, the association between the first quiz and GPA should be stronger, but it is only weak. The 105-person sample size is too large to have a statistically significant p-value of 0.121, even at the less strict 0.05 level. Since the evidence does not support the hypothesis that the first quiz significantly correlates with the grade point average, we must maintain Ho (Westrick et al., 2020). These results are highly dependent on the analyses and alpha level utilized. Therefore, additional study may be needed to validate them.

Statistical Conclusions

The investigation uncovered significant correlations among specific characteristics. Higher final grades are indicative of superior performance since there was a positive association between students’ total grades and their final grades. The first quiz’s link with the grade point average needed to be stronger so that it did not reach statistical significance. Excluding the possibility that the two are unconnected, statistical tests with a significance threshold of 0.05 support the hypothesis that Final and Total grades are directly correlated (Rand et al., 2020). With the information we have at the moment, we still can’t say that there isn’t a connection between GPA and Quiz 1.

Regardless of the results, it is critical to approach them with caution due to their inherent limits. Through statistical testing, issues related to sample size, potential bias in sampling, measurement accuracy, and confounding variables are meticulously considered. If the community is well-represented and delicate correlations are difficult to uncover, then a sample size of 105 should be plenty (Wiernik & Dahlke, 2020).

However, unexplored traits or features may still impact the reported linkages.  Furthermore, 0.05 is a generally used alpha level, although it isn’t necessarily optimal because it increases the likelihood of Type I errors, also called false positives. To replicate these results and ensure their reliability and practicality, future research should employ bigger samples, random sampling methods, and tight controls for confounding variables. This would be a good direction for future studies to go in order to validate and expand upon the discovered links.

Application

Relationships between factors and their effects on various biological states are complex; therefore, biostatisticians depend largely on correlations (Moriarity & Alloy, 2021). By monitoring patterns, medical professionals and researchers can gain a better understanding of the elements that influence brain health and the emergence of disorders.

The Ageing Brain and Cognitive Loss

Further research on the link between aging and cognitive loss can better understand the normal course of neurodegenerative diseases like Alzheimer’s and dementia. Examining this link can teach us more about the causes and possible remedies for age-related neurological disorders (Azam et al., 2021). Based on these findings, individualized treatment programs and early intervention tactics can be created to enhance patients’ well-being.

RSCH FPX 7864 Assessment 2 Correlation Application and Interpretation

How Motor Skills Are Rooted in the Body?

Researchers can learn about the neurological underpinnings of motor functions and movement disorders by undertaking neuroimaging studies that look at the relationship between brain structure and motor skills. This research helps fill gaps in our knowledge about the roles played by various brain areas and neural networks in motor control and coordination.

By assisting in the detection of neurological disorders that cause motor skill deficiencies it may lead to better diagnosis and targeted therapy (Newell, 2020). Biostatistics cannot progress as an academic discipline without investigating the connections between these factors. It can help neurologists learn more about their patients, foresee how their illnesses might worsen, and create personalized therapy programs. Patient outcomes, research, clinical practice, and evidence-based decision-making are all enhanced when neurological illnesses are addressed through the use of biostatistical correlation analysis.

References

Azam, S., Haque, Md. E., Balakrishnan, R., Kim, I.-S., & Choi, D.-K. (2021). The ageing brain: Molecular and cellular basis of neurodegeneration. Frontiers in Cell and Developmental Biology, 9. https://doi.org/10.3389/fcell.2021.683459 

Endleman, S., Brittain, H., & Vaillancourt, T. (2021). The longitudinal associations between perfectionism and academic achievement across adolescence. International Journal of Behavioral Development, 46(2), 016502542110374. https://doi.org/10.1177/01650254211037400 

Moriarity, D. P., & Alloy, L. B. (2021). Back to basics: The importance of measurement properties in biological psychiatry. Neuroscience & Biobehavioral Reviews, 123, 72–82. https://doi.org/10.1016/j.neubiorev.2021.01.008 

RSCH FPX 7864 Assessment 2 Correlation Application and Interpretation

Newell, K. M. (2020). What are fundamental motor skills and what is fundamental about them? Journal of Motor Learning and Development, 8(2), 280–314. https://doi.org/10.1123/jmld.2020-0013 

Ozcan, N. A., Sahin, S., & Cankir, B. (2021). The validity and reliability of thriving scale in academic context: Mindfulness, GPA, and entrepreneurial intention among university students. Current Psychology. https://doi.org/10.1007/s12144-021-01590-1 

Rand, K. L., Shanahan, M. L., Fischer, I. C., & Fortney, S. K. (2020). Hope and optimism as predictors of academic performance and subjective well-being in college students. Learning and Individual Differences, 81, 101906. https://doi.org/10.1016/j.lindif.2020.101906 

Sayyed, R. A., Awwad, F. A., Itriq, M., Suleiman, D., Saqqa, S. A., & AlSayyed, A. (2023). The pass/fail grading system at Jordanian universities for online learning courses from students’ perspectives. Frontiers in Education, 8. https://doi.org/10.3389/feduc.2023.1186535 

RSCH FPX 7864 Assessment 2 Correlation Application and Interpretation

Thompson, M. E. (2021). Grade expectations: The role of first-year grades in predicting the pursuit of STEM majors for first- and continuing-generation students. The Journal of Higher Education, 1–25. https://doi.org/10.1080/00221546.2021.1907169 

Verostek, M., Miller, C. W., & Zwickl, B. (2021). Analyzing admissions metrics as predictors of graduate GPA and whether graduate GPA mediates Ph.D. completion. Physical Review Physics Education Research, 17(2). https://doi.org/10.1103/physrevphyseducres.17.020115 

Westrick, P. A., Schmidt, F. L., Le, H., Robbins, S. B., & Radunzel, J. M. R. (2020). The road to retention passes through first year academic performance: A meta-analytic path analysis of academic performance and persistence. Educational Assessment, 26(1), 35–51. https://doi.org/10.1080/10627197.2020.1848423 

RSCH FPX 7864 Assessment 2 Correlation Application and Interpretation

Wiernik, B. M., & Dahlke, J. A. (2020). Obtaining unbiased results in meta-analysis: The importance of correcting for statistical artifacts. Advances in Methods and Practices in Psychological Science, 3(1), 94–123. https://doi.org/10.1177/2515245919885611 

Wu, H., Guo, Y., Yang, Y., Zhao, L., & Guo, C. (2021). A meta-analysis of the longitudinal relationship between academic self-concept and academic achievement. Educational Psychology Review. https://doi.org/10.1007/s10648-021-09600-1