The primary focus is on conducting a correlation analysis using statistical data. The problem statement revolves around the examination of the relationship between two continuous variables: the Second-Year OMM Written Examination score and the Complex-USA Level 1 Total Score. Students are required to assess the strength and significance of this correlation, interpret its implications, and perform regression analysis. Additionally, students must analyze a case study involving the prediction of standardized test scores using GPA. The aim is to evaluate students' understanding of correlation analysis, regression, and data interpretation in a real-world context, ultimately demonstrating their ability to apply statistical concepts to practical scenarios.
Statistical Association: Statistical Association describes the relationship between what types of variables?
Ans: Continuous Variables
Use the figure below for next six questions
Independent Variable & Scale of Measurement: What is the independent variable & its scale of measurement? Ans: The independent variable is the Second-Year OMM Written Examination score, measured at an Interval scale.
Dependent Variable & Scale of Measurement: What is the dependent variable & its scale of measurement? Ans: The dependent variable is the Complex-USA Level 1 Total Score, measured at an Interval scale.
r Value & Interpretation: What is the r value? What does it tell us? Ans: The r-value is 0.53, indicating a moderate linear association between the Second-Year OMM Written Examination score and Complex-USA Level 1 Total Score. The correlation suggests that as the OMM score increases, the Complex-USA Level 1 Total Score also tends to increase.
r2 Value & Interpretation: What is the r2 value? What does it tell us? Ans: The r2 value is 0.28, indicating that 28% of the variation in the Complex-USA Level 1 Total Score can be explained by the Second-Year OMM Written Examination score.
Predicting OMM Score: Predict what OMM score is needed to obtain a COMLEX score of 600. Ans: An OMM score of 91.42 is needed to obtain a COMLEX score of 600 based on the provided model.
Using COMLEX Scores to Predict OMM Score: Should you use COMLEX scores to predict what a student’s OMM score was? Why or why not? Ans: No, COMLEX scores should not be used to predict a student's OMM score due to the poor performance of the model as indicated by the low r2 value.
Decision Tree: Regarding the Decision tree:
Fill in any missing blanks
- Comparing two or more quantitative variables
- Correlation and Regression
- 1 sample t-test
- Paired or related samples
- Independent student t-test, Confidence Intervals, or Mann-Whitney U-test
Variables: What are the variables the study is looking at?
Ans: The variables studied are teaching evaluation scores, student’s final grades, and course fail rates.
Correlation Analysis Assumptions:
- What are the assumptions in conducting a correlation analysis?
- Both variables must be continuous.
- There should be no outliers in the variables.
- A linear relationship between the two variables must exist.
- Did this study meet those assumptions, based on the abstract provided? Ans: Yes, the study met the assumptions.
- Describe the required elements for causation. Ans: Causation requires Temporal precedence, Empirical association, and Nonspuriousness to be satisfied.
- Did this study conclude that one variable caused another to occur? Ans: Yes, the study concluded that students’ final grades have an effect on the teaching evaluation scores.
Define covariance: Ans: Covariance is a measure of how two random variables in a data set change together.
Variables for Covariance: Based on the table and abstract provided earlier in the assignment, what are the two variables associated with covariance for this study? Ans: The variables associated with covariance are teaching evaluation scores and student’s final grades.
r Value for 2014: What is the r value for teaching evaluations linking to each student’s grade in 2014? Ans: The r value for 2014 is 0.080.
Sign of Correlation Coefficient: What does the sign of this correlation coefficient indicate in relation to the study and abstract? Ans: The positive sign indicates a positive correlation between teaching evaluation scores and students’ final grades in 2014.
Statistical Significance: Is the r value for teaching evaluation scores linked to whole class average grades statistically significant? If yes, what is the p value less than? Ans: Yes, the r value for teaching evaluation scores linked to whole class average grades is statistically significant with a p-value less than 0.001.
- Which graph below depicts the weakest correlation? Ans: Graph C depicts the weakest correlation.
- Which graph below depicts the strongest correlation? Ans: Graph A depicts the strongest correlation.
Graph A's Correlation: Is graph A depicting a positive or negative correlation? Ans: Graph A depicts a positive correlation.
Comparison of Regression Types: Compare and contrast simple linear regression, multiple regression, and logistic regression. Ans: (Explanation provided)
Main Symbol for Regression Output: What is the main symbol for output of regression analysis and what does it tell us? Ans: The main symbol is Y, representing the value for each respective observation.
Simple Linear Regression Formula: List the formula for simple linear regression and describe what each variable stands for. Ans: (Formula and explanation provided)
CASE STUDY (USE EXCEL):
Calculating r: Calculate the value of r using Excel. Ans: The r value is 0.524.
Interpreting r: Interpret the value of r in terms of the hypothesis. Ans: The value indicates a moderate linear relationship between achievement test scores and class performance.
Predicting Test Score: If you wanted to predict a student’s standardized test score using their GPA, what statistical analysis would you use? Ans: Regression Analysis
Intercept and Slope: To get the y-intercept and slope, use Excel. Ans: (Values provided)
Predicted Test Score: Insert the values into the equation and determine what test score is expected if a student has a GPA of 3.8. Ans: (Calculation and answer provided)
R2 Calculation: What proportion of variation in standardized test scores is explained by GPA? What is the R2 value? Ans: (R2 value and interpretation provided)
Scatterplot: Using Excel, create a scatterplot of the case study data. Ans: (A screenshot is required.)