Category: RSCH-FPX7864

RSCH FPX 7864 Assessment 4 Data Analysis and Application Template Name Capella university RSCH-FPX 7864 Quantitative Design and Analysis Prof. Name Date Data Analysis Plan This study aims to provide a comprehensive review by examining a dataset from the “grades.jasp” file to evaluate the potential impact of review session participation on students’ final exam scores. Specifically, the study compares the final exam scores of students who attended review sessions against those who did not. The primary objective is to determine whether this difference is statistically significant (Tomasevic et al., 2020). Key study variables include “Review” and “Final.” The “Review” variable is categorical, with values representing students who attended (1) and those who did not (2). The “Final” variable is continuous and represents the total number of correct answers on the final exam. Research Question and Hypotheses The study seeks to answer the following research question: Does attending a review session improve students’ final exam performance? To test this, two hypotheses are established. The null hypothesis (H₀) states that students who attended review sessions have no significant difference in their final exam scores compared to those who did not attend. Conversely, the alternative hypothesis (H₁) suggests that attending a review session has a significant effect on students’ final exam scores. Identification of Variables The independent variable in this study is review session attendance, which categorizes students into those who attended and those who did not (Vale et al., 2020). The dependent variable is final exam scores, a continuous variable that represents the total number of correct answers. These variables are essential for determining the effect of review session participation on academic performance. The independent variable (review session attendance) is manipulated across groups, while the dependent variable (final exam score) is the measured outcome. Testing Assumptions For accurate statistical analysis, specific assumptions must be tested. This includes evaluating group variances using Levene’s test, which determines whether the assumption of homogeneity of variance is met. If Levene’s test results in a non-significant p-value (p > .05), the assumption holds, allowing for standard statistical tests. If the p-value is significant (p < .05), indicating a violation of homogeneity, alternative statistical approaches such as Welch’s t-test may be necessary (Saliya, 2022). Ensuring this assumption is met enhances the reliability of inferential statistics, particularly the validity of t-tests. If variances are significantly different, statistical outcomes may be misleading, necessitating adjustments to the analysis. Results & Interpretation The study compared final exam scores between students who attended and those who did not attend review sessions. The first group (n = 50) had an average final score of 61.545 with a standard deviation of 7.356, while the second group (n = 55) had an average final score of 62.160 with a standard deviation of 7.993. Statistical analysis using a t-test revealed no statistically significant difference between the two groups (t = -0.41, p = 0.68). While students who attended review sessions performed slightly better (M = 62.2, SD = 7.993), this difference was not statistically significant (Kuldoshev et al., 2023). These findings suggest that review sessions had only a minor and inconclusive effect on final exam performance. Statistical Conclusions The results of the t-test indicate that there was no significant difference in mean final exam scores between students who attended and those who did not attend review sessions. The two-tailed t-test produced a t-value of -0.41 and a p-value of 0.68, exceeding the typical significance threshold (p < .05) (Liu & Wang, 2020). Although students who attended review sessions had slightly higher scores, the observed difference was not statistically significant. Consequently, the null hypothesis cannot be rejected, suggesting that review session attendance did not substantially impact final exam performance. Limitations Several limitations may have influenced the study outcomes. The sample size (n = 105) may not have been large enough to detect small but meaningful differences (Tomasevic et al., 2020). Additionally, external validity concerns arise due to potential differences in students’ academic backgrounds, motivation levels, and learning habits. The study also lacks control over confounding variables, such as prior knowledge, engagement in coursework outside review sessions, and variations in instructional quality (Wysocki et al., 2022). These factors could have influenced final exam scores, limiting the study’s internal validity. Future research should consider these elements to better understand the relationship between review sessions and academic performance. Application The independent samples t-test is widely applicable in biostatistics and clinical research. For instance, in neurological research, this statistical method could compare the efficacy of two treatments for neurodegenerative disorders like Alzheimer’s disease. One group might receive a pharmaceutical intervention, while another undergoes cognitive rehabilitation therapy (Mathur et al., 2023). The dependent variable, in this case, would be a cognitive improvement score measured through standardized cognitive assessments. Understanding the effectiveness of different treatment approaches through statistical analysis can help optimize patient care and therapeutic strategies in clinical practice (Kumar et al., 2023). Table Representation Section Key Information Reference(s) Data Analysis Plan Compares final exam scores between students who attended review sessions and those who did not. Evaluates statistical significance of differences. Tomasevic et al., 2020 Research Question Does attending a review session improve students’ final exam performance? – Hypotheses H₀: No significant difference in scores between attendees and non-attendees. H₁: Attending review sessions significantly impacts exam performance. – Variables Independent: Review session attendance (Yes/No). Dependent: Final exam score (Total correct answers). Vale et al., 2020 Testing Assumptions Evaluates homogeneity of variance using Levene’s test (p > .05 = assumption met; p < .05 = assumption violated). Uses t-test or Welch’s t-test. Saliya, 2022 Results Mean final scores: – Attendees: 62.2 (SD = 7.993) – Non-attendees: 61.545 (SD = 7.356). No significant difference (t = -0.41, p = 0.68). Kuldoshev et al., 2023 Statistical Conclusions The t-test showed no significant improvement in final scores due to review sessions. The null hypothesis is not rejected. Liu & Wang, 2020 Limitations Small sample size, external validity concerns, uncontrolled confounding variables (e.g., motivation, prior knowledge, teaching quality). Tomasevic et al., 2020; Wysocki et al., 2022 Application Uses t-test in clinical research (e.g., comparing Alzheimer’s treatments). Helps determine cognitive improvement and guide patient care. Mathur et al., 2023; Kumar et al., 2023 References Kuldoshev, R., Nigmatova, M., Rajabova, I., & Raxmonova, G. (2023). Mathematical, statistical analysis of attainment levels

RSCH FPX 7864 Assessment 3 ANOVA Application and Interpretation Name Capella university RSCH-FPX 7864 Quantitative Design and Analysis Prof. Name Date Data Analysis Plan This study aims to provide a comprehensive review by examining a dataset from the “grades.jasp” file to evaluate the potential impact of review session participation on students’ final exam scores. Specifically, the study compares the final exam scores of students who attended review sessions against those who did not. The primary objective is to determine whether this difference is statistically significant (Tomasevic et al., 2020). Key study variables include “Review” and “Final.” The “Review” variable is categorical, with values representing students who attended (1) and those who did not (2). The “Final” variable is continuous and represents the total number of correct answers on the final exam. Research Question and Hypotheses The study seeks to answer the following research question: Does attending a review session improve students’ final exam performance? To test this, two hypotheses are established. The null hypothesis (H₀) states that students who attended review sessions have no significant difference in their final exam scores compared to those who did not attend. Conversely, the alternative hypothesis (H₁) suggests that attending a review session has a significant effect on students’ final exam scores. Identification of Variables The independent variable in this study is review session attendance, which categorizes students into those who attended and those who did not (Vale et al., 2020). The dependent variable is final exam scores, a continuous variable that represents the total number of correct answers. These variables are essential for determining the effect of review session participation on academic performance. The independent variable (review session attendance) is manipulated across groups, while the dependent variable (final exam score) is the measured outcome. Testing Assumptions For accurate statistical analysis, specific assumptions must be tested. This includes evaluating group variances using Levene’s test, which determines whether the assumption of homogeneity of variance is met. If Levene’s test results in a non-significant p-value (p > .05), the assumption holds, allowing for standard statistical tests. If the p-value is significant (p < .05), indicating a violation of homogeneity, alternative statistical approaches such as Welch’s t-test may be necessary (Saliya, 2022). Ensuring this assumption is met enhances the reliability of inferential statistics, particularly the validity of t-tests. If variances are significantly different, statistical outcomes may be misleading, necessitating adjustments to the analysis. Results & Interpretation The study compared final exam scores between students who attended and those who did not attend review sessions. The first group (n = 50) had an average final score of 61.545 with a standard deviation of 7.356, while the second group (n = 55) had an average final score of 62.160 with a standard deviation of 7.993. Statistical analysis using a t-test revealed no statistically significant difference between the two groups (t = -0.41, p = 0.68). While students who attended review sessions performed slightly better (M = 62.2, SD = 7.993), this difference was not statistically significant (Kuldoshev et al., 2023). These findings suggest that review sessions had only a minor and inconclusive effect on final exam performance. Statistical Conclusions The results of the t-test indicate that there was no significant difference in mean final exam scores between students who attended and those who did not attend review sessions. The two-tailed t-test produced a t-value of -0.41 and a p-value of 0.68, exceeding the typical significance threshold (p < .05) (Liu & Wang, 2020). Although students who attended review sessions had slightly higher scores, the observed difference was not statistically significant. Consequently, the null hypothesis cannot be rejected, suggesting that review session attendance did not substantially impact final exam performance. Limitations Several limitations may have influenced the study outcomes. The sample size (n = 105) may not have been large enough to detect small but meaningful differences (Tomasevic et al., 2020). Additionally, external validity concerns arise due to potential differences in students’ academic backgrounds, motivation levels, and learning habits. The study also lacks control over confounding variables, such as prior knowledge, engagement in coursework outside review sessions, and variations in instructional quality (Wysocki et al., 2022). These factors could have influenced final exam scores, limiting the study’s internal validity. Future research should consider these elements to better understand the relationship between review sessions and academic performance. Application The independent samples t-test is widely applicable in biostatistics and clinical research. For instance, in neurological research, this statistical method could compare the efficacy of two treatments for neurodegenerative disorders like Alzheimer’s disease. One group might receive a pharmaceutical intervention, while another undergoes cognitive rehabilitation therapy (Mathur et al., 2023). The dependent variable, in this case, would be a cognitive improvement score measured through standardized cognitive assessments. Understanding the effectiveness of different treatment approaches through statistical analysis can help optimize patient care and therapeutic strategies in clinical practice (Kumar et al., 2023). Table Representation Section Key Information Reference(s) Data Analysis Plan Compares final exam scores between students who attended review sessions and those who did not. Evaluates statistical significance of differences. Tomasevic et al., 2020 Research Question Does attending a review session improve students’ final exam performance? – Hypotheses H₀: No significant difference in scores between attendees and non-attendees. H₁: Attending review sessions significantly impacts exam performance. – Variables Independent: Review session attendance (Yes/No). Dependent: Final exam score (Total correct answers). Vale et al., 2020 Testing Assumptions Evaluates homogeneity of variance using Levene’s test (p > .05 = assumption met; p < .05 = assumption violated). Uses t-test or Welch’s t-test. Saliya, 2022 Results Mean final scores: – Attendees: 62.2 (SD = 7.993) – Non-attendees: 61.545 (SD = 7.356). No significant difference (t = -0.41, p = 0.68). Kuldoshev et al., 2023 Statistical Conclusions The t-test showed no significant improvement in final scores due to review sessions. The null hypothesis is not rejected. Liu & Wang, 2020 Limitations Small sample size, external validity concerns, uncontrolled confounding variables (e.g., motivation, prior knowledge, teaching quality). Tomasevic et al., 2020; Wysocki et al., 2022 Application Uses t-test in clinical research (e.g., comparing Alzheimer’s treatments). Helps determine cognitive improvement and guide patient care. Mathur et al., 2023; Kumar et al., 2023 References Kuldoshev, R., Nigmatova, M., Rajabova, I., & Raxmonova, G. (2023). Mathematical, statistical analysis of attainment levels of

RSCH FPX 7864 Assessment 2 Correlation Application and Interpretation Name Capella university RSCH-FPX 7864 Quantitative Design and Analysis Prof. Name Date Correlation Application and Interpretation The study’s dependent variables include students’ final grades, grade point averages (GPAs), first quiz scores, and total grades. Additionally, data related to student demographics, standardized academic performance, and instructors’ use of formative assessments across three units are considered. The primary objective of this research is to analyze the relationship between students’ final grades and their overall GPAs. Both the cumulative mark and final grade are continuous variables, meaning they can take any value within a range (Sayyed et al., 2023). While Quiz 1 scores remain fixed, students’ gender identities are hypothetical variables. The correlational analysis involved a sample size of 105 participants, with a significance level set at 0.05. Correlation Analysis A correlation analysis was conducted to examine the relationships between academic performance indicators. The research focuses on two primary questions: (1) whether a student’s final grade reflects their cumulative grade, and (2) whether students’ GPAs significantly correlate with their performance on Quiz 1. The hypotheses were structured as follows: Null Hypothesis (H₀): There is no linear correlation between the final grade and the cumulative grade. Alternative Hypothesis (Hₐ): A positive correlation exists between the final grade and cumulative grade. Null Hypothesis (H₀): No significant relationship exists between students’ GPA and their Quiz 1 performance. Alternative Hypothesis (Hₐ): A significant linear relationship exists between students’ GPA and their Quiz 1 performance. Statistical assumptions were verified through descriptive statistics, including skewness and kurtosis values. The analysis confirmed that while the distributions of the first quiz and GPA were within normal ranges, the overall grade distribution deviated slightly from normality (Verostek et al., 2021). The GPA’s skewness was -0.220, and its kurtosis was -0.688, indicating a normal distribution. The final exam results followed a similar trend, with a skewness of -0.341 and a kurtosis of -0.277. However, minor deviations in Quiz 1 and total grades suggested a slight departure from normality. Analysis of Decision-Making Process Understanding the distinction between categorical and continuous variables is crucial in correlation analysis. Variables such as final grades, GPA, and cumulative grades are continuous, meaning they can take any value within a defined range. In contrast, Quiz 1 scores are categorical, representing specific correct-answer counts rather than numerical values. The hypothesis framework must clearly define the expected linear relationships among variables (Thompson, 2021). For example, two competing hypotheses regarding the relationship between total and final grades were evaluated. The null hypothesis posited that no linear correlation existed between these variables, while the alternative hypothesis suggested a direct correlation. Similarly, the relationship between Quiz 1 scores and GPA was examined under the same methodological approach. By structuring these hypotheses in a clear and testable format, the study aimed to reinforce its findings through robust statistical analysis. Correlation Application and Interpretation Correlation Analysis Research Question Hypothesis Final Grade vs. Cumulative Grade Does a student’s final grade reflect their cumulative grade? H₀: No linear correlation between final and cumulative grades. Hₐ: A positive correlation exists between final and cumulative grades. GPA vs. Quiz 1 Score Is there a significant correlation between GPA and Quiz 1 performance? H₀: No significant relationship between GPA and Quiz 1 score. Hₐ: A linear relationship exists between GPA and Quiz 1 score. Statistical Assumptions Skewness Value Kurtosis Value Normality Assessment GPA Distribution -0.220 -0.688 Normal distribution Final Test Scores -0.341 -0.277 Normal distribution Quiz 1 Scores -0.5 -1.2 Minor negative skew; near-normal distribution Total Grade 0.8 2.1 Slight positive skew and kurtosis Results and Interpretation The correlation matrix analyzed four primary variables: grade point average, total GPA, Quiz 1 score, and final grade. The statistical findings revealed a strong positive correlation between total and final grades, leading to the rejection of the null hypothesis. The Pearson correlation coefficient was R = 0.88, with a p-value of 0.001, indicating a significant linear relationship between the two variables (Wu et al., 2021). However, the relationship between GPA and Quiz 1 scores was weaker. The correlation coefficient for GPA and Quiz 1 was 0.152, with 103 degrees of freedom and a p-value of 0.112. This suggests that the association between GPA and Quiz 1 performance is not statistically significant at the 0.05 alpha level. Given the large sample size of 105 participants, the evidence does not support a strong link between GPA and Quiz 1 performance, necessitating the retention of the null hypothesis (Westrick et al., 2020). Future research with refined methodologies may be required to verify these results. Statistical Conclusions The findings indicated that higher final grades were positively associated with superior academic performance. However, the correlation between Quiz 1 scores and GPA was weak, failing to reach statistical significance. Given the 0.05 significance threshold, the study confirmed a direct relationship between final and total grades while leaving the GPA-Quiz 1 correlation inconclusive (Rand et al., 2020). Although a sample size of 105 participants was statistically robust, limitations such as potential biases, measurement accuracy, and confounding variables should be considered. Application in Biostatistics Correlation analysis is widely utilized in biostatistics to examine relationships between variables influencing biological and psychological states (Moriarity & Alloy, 2021). For instance, investigating the link between aging and cognitive decline aids in understanding neurodegenerative diseases like Alzheimer’s and dementia. By analyzing these correlations, researchers can develop early intervention strategies to enhance patient well-being (Azam et al., 2021). Another application involves exploring the neurological basis of motor functions. Neuroimaging studies assessing brain structure and motor skills can improve the diagnosis and treatment of movement disorders (Newell, 2020). Understanding these relationships enhances patient care, facilitates early diagnosis, and enables the development of targeted interventions. Overall, correlation analysis remains a critical tool for advancing medical research and improving patient outcomes. References Azam, S., Haque, M. 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 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 Rand, K.

RSCH FPX 7864 Assessment 1 Descriptive Statistics Name Capella university RSCH-FPX 7864 Quantitative Design and Analysis Prof. Name Date Descriptive Statistics Lower Division The histogram illustrates the final exam results distribution for a cohort of 49 lower-division students, showing the relationship between their scores and the corresponding score ranges. The exam results serve as the independent variable, while the lower-division category acts as the dependent variable. The data reveals that two students scored between 40 and 45, while three students obtained scores between 45 and 50. Additionally, seven students fell within the 55 to 60 range, and eight students scored between 50 and 55. The most frequently occurring score range is between 60 and 65, where twelve students achieved scores. Further analysis shows that seven students scored between 65 and 70, while ten students secured scores ranging from 70 to 75. The concentration of scores in the higher range suggests that many students performed well in their final assessments (Yağcı, 2022). With the highest number of students (12) scoring between 60 and 65, this range represents the most common performance level. The left-skewed distribution, where the longer tail extends toward the lower score range, indicates that a majority of students scored closer to the higher end of the distribution (Liu et al., 2024). This observation is further confirmed by the median score (62.5) being slightly higher than the mean (61.469), which signifies that while most students performed well, a smaller subset obtained significantly lower scores, thereby reducing the average. Understanding this distribution pattern is essential for assessing performance trends among lower-division students and can help shape future exam preparation strategies. Upper Division The histogram depicting the final test scores for 56 upper-division students effectively captures the relationship between exam results and student performance categories. The data reveals that eleven students scored between 50 and 55, while twelve students fell within the 55 to 60 range. Furthermore, fourteen students scored between 60 and 65, indicating a solid understanding of the course material. A closer examination shows that thirteen students scored between 65 and 70, representing strong performance, whereas six students excelled by achieving scores between 70 and 75. The highest concentration of students is observed in the 60 to 65 range, signifying that most upper-division students attained their scores in this interval (Dhal et al., 2020). The histogram exhibits a bell-shaped curve, suggesting a normal distribution, with a peak frequency at the center and a gradual decrease at both extremes. The calculated average score of 62.161 aligns closely with the median score of 62.5, reinforcing the notion of a normally distributed dataset. The symmetry of the distribution, along with the alignment of the mean and median, indicates that student performance follows a typical bell curve pattern, with most students scoring within the middle range and fewer students positioned at the extremes. Data Set Interpretation The GPA distribution exhibits skewness values ranging from -0.220 to 0.220, suggesting a slight negative skew. This minor leftward skew implies that lower GPA values are marginally more prevalent but not to a significant extent. The kurtosis values, ranging from -0.688 to 0.688, indicate that the distribution is flatter than a normal curve, meaning that GPA values are more dispersed rather than tightly concentrated around the mean (Jammalamadaka et al., 2020). Despite these small deviations from perfect normality, the skewness and kurtosis values remain within the acceptable range for normality, typically considered -1 to +1 for skewness and -2 to +2 for kurtosis. This suggests that the GPA distribution is approximately normal, with only slight asymmetry and a relatively flat shape. These insights are valuable for analyzing GPA trends, indicating that while the distribution is not perfectly normal, it remains within acceptable statistical limits. For Quiz 3, the distribution’s skewness is negative, ranging from -0.078 to 0.078, signifying a minor asymmetry in the dataset. Additionally, the kurtosis values, which range from -0.149 to 0.149, indicate that the distribution is slightly more peaked than a standard normal curve. While these deviations are minimal, the distribution still largely conforms to normality. The skewness and kurtosis values remain within the standard thresholds for normality (-1 to +1 for skewness and -2 to +2 for kurtosis), confirming that the distribution maintains an overall normal shape (Mohammed et al., 2020). Although the distribution exhibits slight deviations from a perfectly normal shape, the combined skewness and kurtosis analysis offers a deeper understanding of the dataset’s overall characteristics. These statistical indicators are crucial for determining whether the data aligns with the expectations of normality, which is essential for accurate data interpretation and analysis. Table Representation Category Findings Interpretation Lower Division – Most common score range: 60-65 (12 students) – Skewness: Left-skewed – Mean: 61.469 – Median: 62.5 The left-skewed distribution suggests that while most students performed well, a small number scored significantly lower, affecting the overall average. The highest concentration of scores was in the 60-65 range. Upper Division – Most common score range: 60-65 (14 students) – Distribution: Bell-shaped, normal – Mean: 62.161 – Median: 62.5 The normal distribution suggests that students’ scores were evenly spread, with most students scoring near the average. The symmetry between the mean and median supports this observation. GPA Distribution – Skewness: -0.220 to 0.220 (minor negative skew) – Kurtosis: -0.688 to 0.688 (flatter than normal) The data distribution is close to normal but slightly flatter and negatively skewed. This suggests that lower GPAs are slightly more common, but the deviation is within acceptable limits. Quiz 3 – Skewness: -0.078 to 0.078 (minor negative skew) – Kurtosis: -0.149 to 0.149 (slightly more peaked) The distribution is nearly normal, with minor asymmetry and slightly increased peak concentration. These variations do not significantly affect overall data interpretation. References Dhal, K. G., Das, A., Ray, S., Gálvez, J., & Das, S. (2020). Histogram equalization variants as optimization problems: A review. Archives of Computational Methods in Engineering, 28(3), 1471–1496. https://doi.org/10.1007/s11831-020-09425-1 Jammalamadaka, S. R., Taufer, E., & Terdik, G. H. (2020). On multivariate skewness and kurtosis. Sankhya A, 83. https://doi.org/10.1007/s13171-020-00211-6 Liu, A., Cheng, W., & Guan,