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 and Application Template

In this article, we will explore the analysis of academic data to understand the relationship between quiz performance and overall GPA (Grade Point Average). By examining key variables such as Quiz 1, GPA, Total points, and Final exam scores, we aim to shed light on significant correlations that can inform educational strategies and student performance assessments.

Research Questions and Hypotheses

The primary objective of this study is to investigate two critical research questions regarding the relationships among academic performance variables:

1. What is the relationship between Quiz 1 scores and GPA?

   • Null Hypothesis (H0): There is no relationship between Quiz 1 scores and GPA.
   • Alternative Hypothesis (H1): There is a relationship between Quiz 1 scores and GPA.

2. What is the relationship between the total number of points in the class and the number of correct answers on the Final exam?

   • Null Hypothesis (H0): There is no relationship between the total points in the class and the Final exam scores.
   • Alternative Hypothesis (H1): There is a relationship between the total points in the class and the Final exam scores.

Data Analysis Plan

The data used in this study was sourced from a JASP file, focusing on four continuous variables: Quiz 1, GPA, Total points, and Final exam scores. The analysis aims to determine if these variables are correlated and if they support or reject the proposed hypotheses.

Testing Assumptions

Descriptive Statistics

Before delving into the correlation analysis, it is essential to assess the normality of the data. Here are the descriptive statistics for each variable:

• Quiz 1:
  • Skewness: -0.851
  • Kurtosis: 0.162
• GPA:
  • Skewness: -0.220
  • Kurtosis: -0.688
• Total Points:
  • Skewness: -0.757
  • Kurtosis: 1.146
• Final Exam Scores:
  • Skewness: -0.341
  • Kurtosis: -0.277

The skewness values for all variables range between -2 and +2, indicating that the assumption of normality is met.

Results and Interpretation

Pearson Correlation Coefficients

To investigate the relationships between the variables, we employed Pearson’s correlation analysis. The results are as follows:

• Significant correlations were observed:
  • Quiz 1 and GPA (r = 0.152, p = 0.121) indicate a weak correlation.
  • Quiz 1 and Total points (r = 0.797, p < .001) reveal a strong positive correlation.
  • Total points and Final exam scores (r = 0.875, p < .001) also indicate a robust positive relationship.

Statistical Conclusions

The findings suggest that while Quiz 1 scores exhibit a weak correlation with GPA, they show a significant and strong correlation with Total points and Final exam scores. This implies that performance in Quiz 1 could be a predictor of overall academic success when assessed alongside other performance metrics.

Implications for Educational Practices

Understanding these relationships can help educators tailor their teaching strategies to improve student outcomes. By focusing on enhancing quiz performance, institutions may positively influence overall GPA and final exam results, leading to better academic achievements.

RSCH FPX 7864 Assessment 4 Data Analysis and Application Template

References

If necessary, include references in proper APA style to support the research and data analysis presented in this study.

RSCH FPX 7864 Assessment 3 ANOVA Application and Interpretation

Name

Capella University

RSCH-FPX 7864 Quantitative Design and Analysis

Prof. Name

Date

Data Analysis and Application

In the independent T-test, the variables involved are gender, which serves as the independent variable, and GPA, which is the dependent variable. Gender is a categorical variable, while GPA is continuous. The research question guiding this analysis is: Does gender influence GPA levels? The null hypothesis posits that gender does not impact GPA levels, implying that the mean scores within the sample are not significantly different. Conversely, the alternative hypothesis suggests that gender has an effect on GPA, indicating that the mean GPA for females and males differs significantly.

Test Assumptions

Table 1. Independent Samples Test

The results from Levene’s test for the equality of variances (Levene, 1960) are examined to determine the homogeneity of variances between the dependent variable, GPA, and the independent variable, gender. The significance value obtained from Levene’s test is analyzed to check for any notable differences. A significance level below .05 would indicate that the variances are significantly different, whereas a significance level above .05 suggests that the variances are approximately equal. In this case, the reported significance level between GPA and gender is .758, which exceeds the threshold of p=.05. Therefore, equal variances are assumed, indicating that the assumption of homogeneity has been satisfied.

Results and Interpretation

Table 2. Group Statistics

RSCH FPX 7864 Assessment 3 ANOVA Application and Interpretation

The statistics concerning gender and GPA are presented in Table 2. Females (n=64) have a mean GPA of 2.97, with a standard deviation of 0.678, while males (n=41) show a mean GPA of 2.69 and a standard deviation of 0.739. Based on Levene’s test, equal variances are assumed, and the assumption of homogeneity has been satisfied. The calculated significance (2-tailed) value is 0.048. Since 0.048 is less than p=0.05, it indicates a slight difference between the variances for GPA and gender, although it fails to reject the null hypothesis. This suggests that the variability between the groups is not significantly different, indicating that male GPAs are lower when compared to female GPAs.

Statistical Conclusions

This analysis explored the GPA differences between genders (male and female). An equal variance t-test revealed a statistical disparity between the mean GPAs. The data gathered included a total of (N=105) students, consisting of both males and females. The results indicated that females had a mean GPA of M = 2.97 (SD = 0.68) while males had a mean GPA of M = 2.69 (SD = 0.74). The t-test was executed at a significance level of P=0.05, yielding F (1,103) = 0.95, p = .758 > 0.05, leading to the conclusion that gender does indeed influence GPA. However, several limitations were noted. Field (2018) points out that violations of assumptions related to the between-samples t-test may affect results. Additionally, the unequal sample sizes may skew results, with females being N=64 and males being N=41. Such disparities can contribute to higher GPAs among females. Future studies should focus on identifying effective support networks that enhance GPA achievement for students.

Application

An effective HR leader must consistently analyze trends that may affect the workplace. Such trends might include time and attendance, staff turnover, and benefits utilization, among others. Human Resources can utilize these insights to identify factors influencing employee performance and satisfaction, allowing them to assess the elements that contribute to different outcomes. For example, one could compare staffing initiatives against new hires, treated as the dependent variable, or examine the impact of injury and safety training programs.

References

Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics. SAGE Publications.

Levene, H. (1960). In Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling (I. Olkin et al. eds., pp. 278-292). Stanford University Press.

RSCH FPX 7864 Assessment 2 Correlation Application and Interpretation

Name

Capella University

RSCH-FPX 7864 Quantitative Design and Analysis

Prof. Name

Date

Data Analysis Plan

Understanding the interplay between historical and contemporary performance can yield valuable insights into the stability and development of student learning. Numerous elements contribute to a student’s achievement in any specific course; however, a student’s prior grade point average (GPA) serves as a broad reflection of their academic background and abilities. In this analysis, four continuous variables are examined: Quiz 1, GPA, Final Exam, and Total points.

Total-Final Correlation

• Research Question: Is there a meaningful correlation between the total points accumulated in the course and the number of correct responses on the final examination?
• Null Hypothesis (H₀): No significant correlation exists between the total points earned in the course and the number of correct answers on the final exam.
• Alternate Hypothesis (H₁): A significant correlation exists between the total points earned in the course and the number of correct answers on the final exam.

GPA-Quiz 1 Correlation

• Research Question: Is there a significant correlation between a student’s prior GPA and their performance on Quiz 1?
• Null Hypothesis (H₀): There is no significant correlation between a student’s prior GPA and the correct answers on Quiz 1.
• Alternate Hypothesis (H₁): A significant correlation exists between a student’s prior GPA and the correct answers on Quiz 1.

Testing Assumptions

The descriptive statistics presented in the table below illustrate the skewness and kurtosis values for both GPA and the final exam scores. The GPA shows a skewness of -0.22 and a kurtosis of -0.69, while the final exam reveals skewness of -0.34 and kurtosis of -0.28. Since the skewness for both measures remains within the -1 to 1 range, it indicates that the distributions are largely symmetrical. Additionally, the values falling between -0.5 and 0.5 further support the notion that the distributions of GPA and final exam scores approximate a normal distribution.

Results & Interpretation

Table 2 shows a weak positive correlation between GPA and Quiz 1, represented by a correlation coefficient (r) of 0.152. With 104 degrees of freedom (df = n-1) and a significance threshold of P=0.01, the calculated P-value is 0.212, which exceeds 0.01. The effect size is 0.152², equal to 0.023104, indicating that Quiz 1 explains only 2% of the variability in GPA. These results lack statistical significance, meaning the null hypothesis cannot be rejected.

RSCH FPX 7864 Assessment 2 Correlation Application and Interpretation

Conversely, the strongest correlation in the matrix is identified between the final and total variables, which demonstrate a significant linear relationship with r=0.875, a P-value of 0.000, and 104 degrees of freedom. The effect size of 0.875², amounting to 0.765625, indicates that the final exam accounts for 76% of the variation in the total score. This relationship is statistically significant with an alpha of 0.05, prompting rejection of the null hypothesis. Furthermore, a moderate linear correlation between GPA and the final score is also apparent, with r=0.379. The associated P-value of 0.000, alongside 104 degrees of freedom, indicates that the effect size of 0.379² equals 0.143641, suggesting that the final exam explains 14% of the variability in GPA. Given the significance of the findings, the null hypothesis is rejected, affirming that a substantial linear relationship exists between GPA and the final score.

Statistical Conclusions

While there is insufficient evidence to substantiate a significant correlation between GPA and Quiz 1 scores, significant relationships have been identified between final and total scores, as well as between GPA and final scores. The following conclusions can be drawn regarding these correlations:

• The correlation between GPA and Quiz 1 is relatively weak, with a coefficient of r = 0.152.
• Although a slight positive correlation exists, the statistical significance is not upheld since the observed P-value (0.212) exceeds the selected significance level (0.01).
• The effect size indicates that only 2% of GPA variability can be attributed to Quiz 1 scores.

Conversely, there is strong evidence for a significant relationship between final and total scores based on this dataset:

• A robust linear correlation is present between final and total scores, indicated by a correlation coefficient of r = 0.875.
• This relationship is statistically significant, as the observed P-value (0.000) is below the alpha level of 0.05.
• The substantial effect size implies that 76% of the variability in the total score is explained by the final exam results.

Furthermore, data supports a statistically significant linear relationship between GPA and final scores:

• A moderate correlation exists between GPA and final score, with a coefficient of r = 0.379.
• This relationship is statistically significant, with the P-value (0.000) being lower than the alpha level of 0.05.
• The effect size reveals that 14% of the variability in GPA is explained by final exam scores.

Application

In the realm of veterans’ healthcare, correlation analysis serves as a powerful method for exploring the relationships between experiences during military service and the development of specific medical conditions. By rigorously examining health outcome patterns among veterans, researchers can ascertain whether certain illnesses or conditions are more prevalent within this population compared to the general public or other comparable groups. For instance, if veterans exposed to particular environments or chemicals during their service display higher incidence rates of a specific condition than those who were not exposed, a positive correlation could imply a potential service-related connection. When such correlations are robust, consistent across various studies, and control for other potential causal factors, it strengthens the argument for designating these conditions as “presumptive.” Recognizing conditions as presumptive streamlines the process for affected veterans to secure benefits and treatment, as they are no longer required to provide proof that their condition is directly linked to their military service. Instead, the service connection is presumed based on the statistical relationships established through comprehensive research.

References

Betancourt, J. A., Granados, P. S., Pacheco, G. J., Reagan, J., Shanmugam, R., Topinka, J. B., Beauvais, B. M., Ramamonjiarivelo, Z. H., & Fulton, L. V. (2021). Exploring health outcomes for U.S. veterans compared to non-veterans from 2003 to 2019. Healthcare (Basel, Switzerland), 9(5), 604. https://doi.org/10.3390/healthcare9050604

Creswell, J. W. (2014). Research design: Qualitative, quantitative, and mixed methods approaches (4th ed.). SAGE Publications.

Field, A. (2018). Discovering statistics using IBM SPSS statistics (5th ed.). SAGE.

RSCH FPX 7864 Assessment 2 Correlation Application and Interpretation

Gravetter, F. J., & Wallnau, L. B. (2016). Statistics for the behavioral sciences (10th ed.). Cengage Learning.

McHugh, M. L. (2013). The Chi-square test of independence. Biochemia Medica, 23(2), 143-149.

RSCH FPX 7864 Assessment 1 Descriptive Statistics

Name

Capella University

RSCH-FPX 7864 Quantitative Design and Analysis

Prof. Name

Date

Descriptive Statistics

The following table presents the descriptive statistics for the final exam scores among lower and upper division students.

Distribution Plots

The histogram for the final exam results of 49 lower division students reveals the following distribution: Two students scored between 40 and 45, three students between 45 and 50, eight students between 50 and 55, seven students between 55 and 60, twelve students between 60 and 65, seven students between 65 and 70, and ten students scored between 70 and 75. This analysis indicates that the majority of lower division students scored between 60.1 and 65 on their final exams, with the histogram exhibiting a left skew. According to Glen (2022), “left skewed histograms are histograms with long tails on the left.” In the lower division, the mean score is 61.469, while the median, calculated as (60 + 65)/2, is 62.5. Since the median is higher than the mean, it confirms that the histogram is indeed skewed to the left.

RSCH FPX 7864 Assessment 1 Descriptive Statistics

Similarly, the histogram for the final exams of 56 upper division students shows that eleven students scored between 50 and 55, twelve students between 55 and 60, fourteen students between 60 and 65, thirteen students between 65 and 70, and six students between 70 and 75. The distribution for the upper division indicates that most students scored between 60.11 and 65. This histogram aligns with a normal distribution, characterized by a bell-shaped curve where data is symmetrically distributed around the mean, with frequency counts peaking in the center and tapering off on either side. The mean score for the upper division is 62.161, while the median remains the same as that of the lower division at (60 + 65)/2 = 62.5. The mean and median being nearly equal signifies a typical normal distribution. The National Institute of Health (n.d.) notes, “a variable that is normally distributed has a histogram (or ‘density function’) that is bell-shaped, with only one peak, and is symmetric around the mean.”

Descriptive Statistics of GPA and Quiz 3

In this analysis, the GPA indicates a slight right skew and a distribution that is somewhat flatter than normal. Conversely, Quiz 3 reveals a minor skew, with its distribution appearing more peaked than usual. A skewness value falling between -0.5 and 0.5 suggests a relatively symmetric distribution. Thus, both GPA and Quiz 3 scores fall within the normal skewness range. Furthermore, regarding kurtosis, both distributions deviate from normality. Skewness and kurtosis can provide insights into the nature of the distribution.

Muhammad (2021) states, “The skewness of the distribution is used to determine whether it is normal, left-tailed, or right-tailed, while the kurtosis is applied to check the height of the distribution” (p. 1227). The skewness for GPA is -0.220, indicating a slight leftward tilt, while Quiz 3 shows a skewness of -0.078, suggesting near symmetry. The kurtosis for GPA is -0.688, indicating a flat distribution, whereas Quiz 3, with a kurtosis of 0.149, reflects a peak distribution. Notably, values closer to zero indicate a normal kurtosis; thus, Quiz 3 displays characteristics more aligned with a normal distribution compared to GPA.

References

Glen, S. (2022). Skewed distribution: Definition, examples. Statistics How To. https://www.statisticshowto.com/probability-and-statistics/skewed-distribution/

Muhammad, A. (2021). A study on skewness and kurtosis estimators of wind speed distribution under indeterminacy. Theoretical and Applied Climatology, 143(3-4), 1227-1234. https://doi.org/10.1007/s00704-020-03509-5

National Institute of Health. (n.d.). Learn more about normal distribution. Dietary assessment primer. https://dietassessmentprimer.cancer.gov/learn/distribution.html#:~:text=The%20%22normal%2 0distribution%22%20is%20the