Data Analysis Scenario

Suppose you serve on a university’s committee that seeks to improve teaching. Your university is considering providing incentives for faculty who strive to improve their teaching methods through adopting various untraditional teaching methods. They are considering providing stipends for faculty members who adopt one of the following teaching methods: flipped classrooms, student-centered, and content-centered classes. They want to compare these methods to a control (lecture teaching). The committee acquires a national dataset of 543 students that contains information about the success of each method (flipped, student-centered, content-centered, and lecture). Specifically, this dataset measures students’ performance on a standardized exam in classes that use each of the four methods. The dataset also records the average number of dollars spent per student on teaching improvement. You have been asked to analyze this dataset to make recommendations about how the university ought to proceed with deciding which method to sponsor.

Based on an analysis of the data, answer the following questions:

Results

Model Info

Model Information
Value
\(R^2\) 0.07
Adjusted \(R^2\) 0.06
df (residual) 539
F 12.95
p <0.001

Descriptive Statistics

Descriptive Statistics for Variable GPA
instruction.method N Mean Median SD Min Max Skew
lecture 389 74.23 74.44 10.20 46.46 99.97 0.05
content 44 73.29 73.13 9.04 55.94 92.26 0.20
flipped 44 68.14 70.40 9.01 49.75 83.04 -0.19
student 66 67.16 68.04 9.77 45.69 86.10 -0.02

ANOVA Summary Table and Parameter Estimates

ANOVA Summary Table
df SS MS F p semi-partial R Squared
instruction.method 3 3861.44 1287.15 12.95 <0.001 0.07
Residuals 539 53555.13 99.36
Parameter Estimates
B Lower Upper \(\beta\) t p
(Intercept) 74.22889 73.238306 75.219474 0.00000 146.87288 <0.001
instruction.methodcontent -0.93676 -4.044222 2.170702 -0.02486 -0.59085 0.55
instruction.methodflipped -6.08809 -9.195552 -2.980628 -0.16156 -3.84001 <0.001
instruction.methodstudent -7.07152 -9.672401 -4.470639 -0.22471 -5.32902 <0.001

Post-Hoc Tests

Post-Hoc Tests using Tukey HSD
Difference Lower Limit Upper Limit p Cohen’s d
content-lecture -0.9368 -5.0225 3.149 0.935 -0.09
flipped-lecture -6.0881 -10.1739 -2.0023 <0.001 -0.71
student-lecture -7.0715 -10.4912 -3.6518 <0.001 -0.61
flipped-content -5.1513 -10.628 0.3254 0.074 -0.62
student-content -6.1348 -11.1343 -1.1352 0.009 -0.52
student-flipped -0.9834 -5.983 4.0161 0.957 0.10

Univariate Graphics

Plots of the Model

Correlation Results

Test of Correlation Coefficient
Value
Correlation Coefficient 0.53
df 541
p <0.001
Regression Estimates
variables estimate lower upper std.estimate t p
(Intercept) 65.145 63.866 66.425 0.000 99.819 <0.001
funding 0.230 0.199 0.262 0.525 14.354 <0.001

Questions

  1. For each of the following scenarios, identify the appropriate statistical procedure.
    1. You have three treatment conditions (control, medication, and therapy) and want to see which condition reduces depression the most
    2. You want to study the relationship between the amount of fertilizer (measured in ounces) and plant height (measured in inches)
    3. You want to see if males and females differ in emotional intelligence
    4. You want to compare the mean cholestero of those who exercise versus those who do not
  2. Which method had the largest sample?
    1. lecture
    2. flipped
    3. student
    4. content
  3. What was the mean difference between flipped and student-centered?
    1. -0.0894
    2. -0.0693
    3. -.1587
    4. 0.426
  4. According to the mean, which teaching method was most effective?
    1. lecture
    2. flipped
    3. student
    4. content
  5. Which of the following statements are true of the variables in our dataset (circle all that apply)?
    1. funding is positively skewed
    2. gpa.change is bimodal
    3. instruction method is skewed
    4. gpa change is approximately normal
    5. instruction method has very different sample sizes in each group
  6. Which of the following statements are true of the ANOVA test of statistical significance?
    1. There is a 0.001 probability that the null hypothesis is true
    2. There is less than a 0.001 probability that the null hypothesis is true
    3. Given our data, there is less than a 0.001 chance the null hypothesis is true
    4. If the mean differences were all zero, there is less than a 0.001 chance of observing our data
  7. Which of the following statements are true of the relationship between funding and gpa.change (circle all that apply)?
    1. more funding leads to a higher gpa change
    2. the relationship is moderately strong
    3. the relationship is quite weak
    4. more funding leads to smaller gpa changes
    5. outliers are affecting the relationship

  8. Based on the graph, how much money would you recommend the university invest per student?

  9. What proportion of the money would you invest in each method
    1. lecture: ___%
    2. flipped: ___%
    3. student: ___%
    4. content:___%

  10. Based on this analysis, What is your overall recommendation to your sponsor with regard to teaching method?

  11. Based on this analysis, What is your overall recommendation to your sponsor with regard to investing in teaching?