Student Growth and Satisfaction

class: center, middle, inverse, title-slide

.title[
# Student Growth and Satisfaction
]
.subtitle[
## Survey Analysis
]
.author[
### Tyler Battaglini & Ryan Lebo
]
.date[
### 2025-05-08
]

---

## Table of Contents

<li>Introduction </li>
<li>Project Questions </li> 
<li>Data Management </li>
<li>Validity and Reliability Analyses </li>
<li>Principal Component Analysis</li>
<li>Box Cox Transformation</li>
<li>Regression Analysis</li>
<li>Conclusion</li>

</ul>

---

## Introduction

<li> Student experience/satisfaction survey </li>
<li> Goal of Project  </li>
<li>Data set provides different questionnaires </li>
<li> Purpose of our analysis </li>

</ul>

---
## Project Questions 
<ul style="font-size: 1.2em; line-height: 1.6;">

<li> How well does student engagement in inside and outside the classroom predict their overall satisfaction with their college experience? </li>

<li> Does the level of support and encouragement from the school and/or school community correlate with students reported development in areas such as critical thinking, communication, and job skills? </li>

</ul>

---
## Data Management 
<ul style="font-size: 1.2em; line-height: 1.6;">

<li>Handling missing variables </li>
<li>Computed mode of any given survey item </li>
<li>Replaced missing items with the mode </li>

</ul>

---
##

<div style="display: flex; justify-content: center; align-items: center; height: 80vh; font-size: 50px;">
  Validity and Reliability Analyses
</div>
---

## Student's Engagement
<ul style="font-size: 1.2em; line-height: 1.6;">

<li>Negatively Correlated values </li>
<li>we scaled our values into different sub sections </li>
<li>Removed technology use and negative engagement </li>
<li> High level of internal consistency </li>

</ul>

---
## Student's Engagement

---

## Student's Engagement

---

## Student's Engagement

--------------------------
  LCI     alpha     UCI   
-------- -------- --------
 0.8105   0.8302   0.8487 
--------------------------

Table: Confidence Interval of Cronbach's Alpha

---
## Encouragement and Support Questionare

<li>All positive values </li>
<li> High internal consistency between our questions </li>

</ul>

---

## Encouragement and Support Questionare

--------------------------
  LCI     alpha     UCI   
-------- -------- --------
 0.7851   0.8083   0.8298 
--------------------------

Table: Confidence Interval of Cronbach's Alpha

---
## Growth and Development

<li>All values are positively correlated </li>
<li>High internal consistency between our questions. </li>

</ul>

---

## Growth and Development

-------------------------
  LCI    alpha     UCI   
------- -------- --------
 0.936   0.9426   0.9488 
-------------------------

Table: Confidence Interval of Cronbach's Alpha

---

<div style="display: flex; justify-content: center; align-items: center; height: 80vh; font-size: 50px;">
  Principal Component Analysis
</div>

---

## Student Engagement in Learning PC

<li>Proceed with 2 principal components  </li>

</ul>

---

## Student Engagement in Learning PC

<li>First PC explains 43% while PC2 only explains 17%   </li>
<li>Proceed with one principal component </li>

</ul>

<table class="table" style="font-size: 30px; color: black; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;">  </th>
   <th style="text-align:right;"> PC1 </th>
   <th style="text-align:right;"> PC2 </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Standard deviation </td>
   <td style="text-align:right;"> 1.967 </td>
   <td style="text-align:right;"> 1.242 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Proportion of Variance </td>
   <td style="text-align:right;"> 0.430 </td>
   <td style="text-align:right;"> 0.171 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Cumulative Proportion </td>
   <td style="text-align:right;"> 0.430 </td>
   <td style="text-align:right;"> 0.601 </td>
  </tr>
</tbody>
</table>

---

## Student Engagement in Learning PC

<li>Skewed to the right   </li>
<li>Perform Box Cox Transformation  </li>

</ul>

---

## Encouragement and Support PC

<li>Proceed with 2 principal components  </li>

</ul>

---

## Encouragement and Support PC

<li>First PC explains 48%, while PC2 only explains 17%  </li>
<li>Proceed with one principal components  </li>

</ul>

<table class="table" style="font-size: 30px; color: black; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;">  </th>
   <th style="text-align:right;"> PC1 </th>
   <th style="text-align:right;"> PC2 </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Standard deviation </td>
   <td style="text-align:right;"> 1.832 </td>
   <td style="text-align:right;"> 1.102 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Proportion of Variance </td>
   <td style="text-align:right;"> 0.480 </td>
   <td style="text-align:right;"> 0.173 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Cumulative Proportion </td>
   <td style="text-align:right;"> 0.480 </td>
   <td style="text-align:right;"> 0.653 </td>
  </tr>
</tbody>
</table>

---

## Encouragement and Support PC

<li>Normal Distribution  </li>
<li>No transformation needed </li>

</ul>

---

## Growth and Development PC

<li>Proceed with 2 principal components  </li>

</ul>

---

## Growth and Support PC

<li>First PC explains 56% while PC2 explains 8%   </li>
<li>Proceed with 1 principal component  </li>

</ul>

<table class="table" style="font-size: 30px; color: black; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;">  </th>
   <th style="text-align:right;"> PC1 </th>
   <th style="text-align:right;"> PC2 </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Standard deviation </td>
   <td style="text-align:right;"> 2.905 </td>
   <td style="text-align:right;"> 1.109 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Proportion of Variance </td>
   <td style="text-align:right;"> 0.563 </td>
   <td style="text-align:right;"> 0.082 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Cumulative Proportion </td>
   <td style="text-align:right;"> 0.563 </td>
   <td style="text-align:right;"> 0.645 </td>
  </tr>
</tbody>
</table>

---

## Growth and Development PC

<li>Skewed to the right   </li>
<li>Need to perform a Box Cox Transformation  </li>

</ul>

---

## Box Cox Transformation Engagement

<li>Lamda value at zero  </li>
<li>Proceed with Box Cox transformation  </li>
<li>Relatively normal distribution </li>

</ul>

---

## Box Cox Tranformation Growth and Development

<li>Lamda value at zero  </li>
<li>Proceed with Box Cox transformation  </li>
<li>Relatively normal distribution </li>

</ul>

---

## Principal Component Regression Engagement vs Growth

<li>Assume Normality </li>
<li>Constant variance </li>

</ul>

---

## Principal Component Regression

<li>For each one-unit increase in the engagement index the growth/development index decreases by approximately 1.02 units </li>
<li>The model explains about 18.34% of the variance in growth/development outcomes. </li>
<li> Engagement PC1 is significantly and negatively associated with growth/development </li>

</ul>

```

Call:
lm(formula = Growth ~ ., data = df_pcr)

Residuals:
    Min      1Q  Median      3Q     Max 
-6.2317 -0.3778 -0.3778  0.4513  9.6142

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  5.88604    0.08373   70.29   <2e-16 ***
engage_PC   -1.02186    0.08380  -12.19   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 2.158 on 662 degrees of freedom
Multiple R-squared:  0.1834,    Adjusted R-squared:  0.1822 
F-statistic: 148.7 on 1 and 662 DF,  p-value: < 2.2e-16
```

---

## Principal Component Analysis Encouragement vs Growth

<li>Assume Normality </li>
<li>Constant variance </li>

</ul>

---

## Principal Component Regression

<li>For each one-unit increase in the encouragement index the growth/development index increases by approximately .87 units </li>
<li>The model explains about 45% of the variance in growth/development outcomes. </li>
<li> Encouragement PC1 is significantly and positively associated with growth/development </li>

</ul>

```

Call:
lm(formula = Growth ~ Encouragement, data = df_enc)

Residuals:
    Min      1Q  Median      3Q     Max 
-7.7402 -0.1070 -0.1070  0.2927  7.6013

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)    5.88604    0.06865   85.74   <2e-16 ***
Encouragement  0.87470    0.03750   23.32   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.769 on 662 degrees of freedom
Multiple R-squared:  0.4511,    Adjusted R-squared:  0.4503 
F-statistic: 544.1 on 1 and 662 DF,  p-value: < 2.2e-16
```

---

## Conclusion

<li> The coefficient for engagement was 1.02, suggests that higher engagement was associated with lower growth/development index scores</li>
<li>The negative direction may imply  that engagement may reflect overinvolvement, stress, or poor balance </li>
<li> Encouragement PC1, the coefficient was +.87, indicating that encouragement significantly predicts greater growth and development </li>
<li> Supportive academic environments play a critical role in fostering key student outcomes like critical thinking, communication, and job readiness</li>

</ul>

---

## Limitations

<li> Students taking particular classes and/or minors have different outlooks  </li>
<li> No specification on what regions were surveyed</li>
<li> Voluntary engagement in the survey, could sway certain surveys </li>

</ul>
---

<div style="display: flex; justify-content: center; align-items: center; height: 80vh; font-size: 50px;">
  Thank You
</div>---

---

## Contributors

<li> Ryan Lebo - Slides Beginning to Correlation Matrix  </li>
<li> Tyler Battaglini - Slides Principal Components to  Conclusion </li>

</ul>