3. Inferential Statistics
3.1 Chi-Square: Kitchen Access × % Processed Meals
Kitchen access groups: ['Limited Access', 'Yes']
χ²(3) = 4.649, p = 0.199 ns
Tests whether access to a kitchen is associated with the percentage of processed food consumed.
| Statistic | Value |
|---|
| χ²-statistic | 4.649 |
| Degrees of freedom | 3 |
| p-value | 0.199 |
| Significance | ns |
3.2 Independent T-Test: Kitchen Access vs. % Processed Meals (Ordinal)
Full kitchen (n=42): mean % score = 1.88
No/Limited kitchen (n=5): mean % score = 2.40
Welch's t = -1.822, p = 0.110 ns
Higher score indicates higher percentage of processed food (1=0-25%, 4=76-100%).
| Full Kitchen | No/Limited |
|---|
| Group | Full Kitchen | No/Limited Kitchen |
| n | 42 | 5 |
| Mean % score | 1.88 | 2.40 |
| Statistic | Value |
|---|
| t-statistic | -1.822 |
| p-value | 0.110 |
| Significance | ns |
3.3 T-Test: Food Program Enrollment vs. Cooking Confidence
Enrolled in food program (n=16): mean confidence = 3.06
Not enrolled (n=32): mean confidence = 3.31
Welch's t = -0.901, p = 0.375 ns
| Statistic | Value |
|---|
| t-statistic | -0.901 |
| p-value | 0.375 |
| Significance | ns |
3.4 T-Test: On-Campus vs. Off-Campus Living → % Processed Meals
On-campus (n=8): mean = 1.62 | Off-campus (n=18): mean = 1.94
Welch's t = -0.882, p = 0.389 ns
| Statistic | Value |
|---|
| t-statistic | -0.882 |
| p-value | 0.389 |
| Significance | ns |
3.5 Chi-Square: Food Budget × Typical Processed Food Frequency
χ²(9) = 4.266, p = 0.893 ns
| processed_freq_typical |
Daily |
Often (5-6 times per week) |
Rarely (1-2 times per week) |
Sometimes (3-4 times per week) |
| food_budget |
|
|
|
|
| Adequate |
2 |
7 |
7 |
6 |
| Comfortable |
0 |
4 |
2 |
5 |
| Somewhat limited |
1 |
3 |
1 |
3 |
| Very limited |
0 |
2 |
1 |
3 |
| Stat | Value |
|---|
| χ² | 4.266 |
| df | 9 |
| p | 0.893 |
| Sig. | ns |
3.6 Kruskal-Wallis: Food Budget → % Processed Meals
H(3) = 1.230, p = 0.746 ns
| Budget Group | Mean % Score | n |
|---|
| Very limited | 2.00 | 6 |
| Somewhat limited | 2.00 | 8 |
| Adequate | 1.82 | 22 |
| Comfortable | 2.09 | 11 |
| Stat | Value |
|---|
| H-statistic | 1.230 |
| p-value | 0.746 |
| Significance | ns |
3.7 Spearman Correlation: Cooking Confidence × % Processed Meals
Spearman ρ = -0.515, p = <0.001 ***
A negative ρ indicates more confident cooks eat fewer processed foods.
| Stat | Value |
|---|
| Spearman ρ | -0.515 |
| p-value | <0.001 |
| Significance | *** |
3.8 Spearman Correlation: Meal Prep Frequency × % Processed Meals
Spearman ρ = -0.670, p = <0.001 ***
A negative ρ indicates students who cook more often eat fewer processed meals.
| Stat | Value |
|---|
| Spearman ρ | -0.670 |
| p-value | <0.001 |
| Significance | *** |
3.9 Spearman Correlation: Age × % Processed Meals
Spearman ρ = -0.031, p = 0.834 ns
| Stat | Value |
|---|
| Spearman ρ | -0.031 |
| p-value | 0.834 |
| Significance | ns |
3.10 Chi-Square: Interest in Workshop × Food Choice Description
χ²(4) = 6.076, p = 0.194 ns
| food_choice_desc |
A balance of whole foods and processed foods |
Mostly processed foods |
Mostly whole foods (fruits, vegetables, whole grains, fresh meats) |
| interest_workshop |
|
|
|
| Maybe |
19 |
3 |
4 |
| No |
2 |
1 |
1 |
| Yes |
7 |
2 |
8 |
| Stat | Value |
|---|
| χ² | 6.076 |
| df | 4 |
| p | 0.194 |
| Sig. | ns |
3.11 T-Test: High vs. Low Work Hours → % Processed Meals
High work hours ≥21h/wk (n=13): mean = 2.38
Low work hours ≤10h/wk (n=21): mean = 1.86
Welch's t = 1.648, p = 0.111 ns
| Stat | Value |
|---|
| t-statistic | 1.648 |
| p-value | 0.111 |
| Significance | ns |
5. Conclusions
Key Findings
Out of eleven inferential tests conducted on n=48 SFSU students, two emerged as statistically significant, both pointing to the same underlying theme: behavioral habits around cooking are the strongest predictors of processed food consumption, outweighing structural factors such as kitchen access, food budget, or living situation.
Significant Results
| Finding | Statistic | Interpretation |
|---|
| Cooking confidence × % processed meals |
ρ = −0.515, p < 0.001 |
Students with greater confidence in preparing healthy meals consume a significantly lower proportion of processed foods. Moderate-to-strong negative relationship. |
| Meal prep frequency × % processed meals |
ρ = −0.670, p < 0.001 |
Students who cook more frequently eat substantially less processed food. This is the strongest correlation in the analysis, suggesting meal preparation habits are the most actionable lever. |
Non-Significant Findings
The following variables showed no statistically significant association with processed food consumption: kitchen access, food program enrollment, on- vs. off-campus living, food budget, age, work hours, and interest in nutrition workshops. While small sample size (n≈47) reduces statistical power — meaning some true effects may have gone undetected — the effect sizes in these tests were generally small, suggesting these structural factors are weaker predictors even if the sample were larger.
Descriptive Context
Processed food consumption is prevalent in this sample: 29.2% of students report eating processed food every day, and only 27.1% describe their diet as mostly whole foods. The top three self-reported reasons for choosing processed food are convenience (83.3%), limited time (70.8%), and cost (56.2%). These motivations are consistent with the statistical finding that cooking frequency — a behavior directly tied to time and effort — is the strongest predictor.
Overall Conclusion
The data suggest that simply having a kitchen or a food budget is not sufficient to reduce processed food intake among SFSU students. Rather, whether students use those resources — by actually cooking and building confidence in the kitchen — is what matters most. This points to a behavioral gap: students may have the infrastructure but lack the habit, motivation, or skill to translate access into action.
Practical Recommendations
Given that 91.7% of respondents expressed openness to nutrition workshops (yes or maybe), there is a strong foundation for intervention. However, interest alone does not predict current behavior (test 3.10, p=0.194), so programming should focus on hands-on skill-building and routine formation rather than awareness campaigns. Specific recommendations include:
- Batch cooking and meal prep workshops — directly address the time/convenience barrier while building the habits most associated with lower processed food consumption.
- Quick, affordable recipe resources — cost was cited by 56.2% of students; recipes that are fast and budget-friendly could reduce reliance on processed options.
- Longitudinal follow-up — with a larger sample (n > 100), future studies would have the power to better detect effects of budget, work hours, and living situation, and to track whether workshop participation translates to lasting dietary change.
Limitations
This study is limited by its small convenience sample (n=48) drawn from a single institution, which restricts generalizability and statistical power. All measures are self-reported, introducing potential response and social desirability bias. Cross-sectional design prevents causal inference — while cooking confidence and meal prep frequency are strongly correlated with lower processed food intake, the direction of causality cannot be determined from this data alone.
