Student Outcomes Study

N = 40 · Dataset: survey.csv

Statistical Tests Used

Methods

All statistical analyses were performed in Python using the SciPy and statsmodels libraries via thericerca's deterministic analysis engine (v0.1.0). Statistical significance was evaluated at α = .05 (a 95% confidence level). Descriptive statistics were computed to summarise the study's variables. To assess monotonic associations between variables, a Spearman rank-order correlation was used (Spearman, 1904). To assess associations between continuous variables, a Pearson product–moment correlation was used (Pearson, 1895). To assess differences in a continuous outcome across three or more groups, a one-way analysis of variance (ANOVA) was used (Fisher, 1925). To assess associations between categorical variables, a Pearson chi-square test of independence was used (Pearson, 1900). For each inferential test, the appropriate effect size is reported with its 95% confidence interval, alongside the achieved statistical power to detect the observed effect (Cohen, 1988).

Results

To describe the age, study_hours, gpa, and satisfaction of the respondents.

This simply summarises the data — the average, spread, and range of each variable are in the table above.

To describe the age, study_hours, gpa, and satisfaction of the respondents.

This shows how the responses are distributed: how many people fall into each category, and what share of the total that is.

To determine the relationship between study_hours and gpa.

We looked at whether study hours and GPA move together. They do — as one goes up, the other tends to go up too. The strength of this pattern is medium.

Statistically: ρ = .36, p = .022, achieved power = 0.63

⚠ Spearman Rank Correlation was used instead of the Pearson Correlation because the latter's assumption(s) were not met (Normality of study_hours (Shapiro-Wilk)).

To determine the relationship between age and gpa.

We looked at whether age and GPA are related. We found no clear connection: in this sample, knowing one tells us little about the other.

Statistically: r(38) = .08, p = .614, 95% CI [-.24, .38], achieved power = 0.08

To determine whether gpa differs across the program groups.

We compared GPA across the program groups. They were broadly similar — no group clearly stood out.

Statistically: F(2, 37) = 0.02, p = .977, η² = .00, achieved power = 0.05

To determine whether study_hours differs across the program groups.

We compared study hours across the program groups. They were broadly similar — no group clearly stood out.

Statistically: F(2, 37) = 0.24, p = .784, η² = .01, achieved power = 0.09

To determine the association between gender and civil_status.

We checked whether gender and civil status are linked — for example, whether knowing someone's gender tells you anything about their civil status. In this sample they appear unrelated.

Statistically: χ²(2, N = 40) = 0.15, p = .926, V = .06, achieved power = 0.06

To determine the association between gender and program.

We checked whether gender and program are linked — for example, whether knowing someone's gender tells you anything about their program. In this sample they appear unrelated.

Statistically: χ²(2, N = 40) = 0.15, p = .926, V = .06, achieved power = 0.06

Discussion

The relationship between study hours and GPA. The analysis of study hours and GPA revealed a statistically reliable medium positive relationship. In practical terms, higher values of study hours tend to accompany higher values of GPA. An association of this strength indicates the two measures share a substantial amount of common variation, though a correlation on its own cannot establish that one variable causes the other.

The relationship between age and GPA. The analysis of age and GPA did not reveal a statistically reliable relationship. The two measures appear to vary largely independently in this sample, and the small association observed sits well within the range expected by chance. This is not evidence that no relationship exists — only that the present data give no clear sign of one.

Differences in GPA across program. Comparing GPA across the program groups did not reveal a statistically reliable overall difference. The groups were broadly similar on GPA, so no single group stands out and no pairwise follow-up interpretation is warranted.

Differences in study hours across program. Comparing study hours across the program groups did not reveal a statistically reliable overall difference. The groups were broadly similar on study hours, so no single group stands out and no pairwise follow-up interpretation is warranted.

The association between gender and civil status. Gender and civil status were not significantly associated. The two categorical variables appear to be independent in this sample, so a case's gender tells us little about its civil status.

The association between gender and program. Gender and program were not significantly associated. The two categorical variables appear to be independent in this sample, so a case's gender tells us little about its program.

The investigation revealed meaningful insights into what influences academic performance, showing a clear distinction between factors that relate to student grades and those that do not. Most notably, the inquiry established a reliable link between the number of hours students spend studying and their overall grade point average. In practical terms, this demonstrates that dedicating more time to independent academic preparation is associated with better academic outcomes. In statistical terms, this finding is considered statistically significant, meaning the observed connection is strong enough that it is very unlikely to be the result of random chance. In contrast, several other variables examined in the research showed no clear link or detectable pattern. Specifically, there was no noticeable relationship between a student's age and their grade point average, suggesting that maturity or age alone does not dictate academic success in this context. Furthermore, when comparing students across different academic programs, the analysis revealed no meaningful differences in grade point averages or in the average number of hours students spent studying; students across distinct fields of study appear to perform and allocate study time at similar levels. Finally, the analysis evaluated demographic background characteristics and found no clear association between gender and civil status, nor between gender and program choice. These non-significant findings mean that any subtle differences observed in the sample were too small to be distinguished from normal, random variation. Importantly, a lack of statistical evidence for these relationships should be interpreted as an absence of detectable pattern in this specific group rather than absolute proof that no relationship exists in broader settings. Consequently, the firm link between study hours and performance stands as the primary substantiated finding from this dataset.

Conclusions

In summary, the evidence collected yields a well-defined picture regarding academic achievement, supporting some initial expectations while finding no support for others. The firmly established finding—that study hours are positively tied to grade point average—provides a trustworthy, evidence-based insight that can be confidently integrated into educational discussions and future academic planning. This key finding highlights personal study time as a key area for supporting student achievement. Conversely, the absence of detectable effects regarding age, academic program, gender, and civil status indicates that these specific demographic and structural factors did not meaningfully differentiate student performance or study habits within this group. Maintaining a clear distinction between confirmed relationships and unproven ones is essential for drawing measured, defensible conclusions that neither overstate the influence of demographic background nor ignore the demonstrated value of dedicated study effort.

Recommendations

Based on these outcomes, several practical and research-focused steps are recommended. First, because the reliable connection between study time and academic performance offers the strongest basis for action, future research should aim to confirm this pattern in independent and larger student groups to ensure it applies broadly. To better understand how study habits influence grades, researchers should consider longitudinal designs that track students over extended periods or experimental interventions that test specific study strategies, allowing for a clearer understanding of cause and effect rather than simple association. Second, the areas that showed no clear link—such as program-level differences, age, and demographic distributions—should not be discarded prematurely; they warrant re-examination in larger, more diverse samples to determine whether very small, subtle patterns exist that this evaluation could not detect. Throughout future work, emphasis should be placed on evaluating the real-world significance and practical magnitude of every finding, ensuring that educational decisions are guided by meaningful impacts rather than mathematical probability alone. Finally, maintaining consistent data collection methods and screening for inconsistencies will preserve data integrity in subsequent studies.

Limitations

Several important boundaries should be kept in mind when interpreting these conclusions. First, no major data-quality issues were identified during processing, which supports the internal consistency of the findings. However, the study design is purely observational, meaning it captures patterns as they occur naturally without direct intervention. As a result, even the statistically reliable relationship between study hours and grade point average cannot prove that increased studying directly causes higher grades; unmeasured background factors, such as individual motivation, prior academic preparation, or effective learning techniques, could also account for the observed success. Second, these insights describe the specific group of individuals evaluated in this study. Extending these conclusions to broader student populations or different institutional contexts depends entirely on how closely this group reflects those wider populations.

References

1. Fisher, R. A. (1925). Statistical Methods for Research Workers. Oliver and Boyd.
2. Pearson, K. (1895). Notes on regression and inheritance in the case of two parents. Proceedings of the Royal Society of London, 58, 240–242.
3. Pearson, K. (1900). On the criterion that a given system of deviations… Philosophical Magazine, 50(302), 157–175.
4. Spearman, C. (1904). The proof and measurement of association between two things. American Journal of Psychology, 15(1), 72–101.
5. Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum Associates.
6. Seabold, S., & Perktold, J. (2010). statsmodels: Econometric and statistical modeling with Python. Proceedings of the 9th Python in Science Conference, 92–96.
7. Virtanen, P., Gommers, R., Oliphant, T. E., et al. (2020). SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods, 17, 261–272.

Python Code Appendix

Descriptive Statistics

df[['study_hours', 'gpa']].describe()

Frequency & Percentage Distribution

df['satisfaction'].value_counts(normalize=True)

Spearman Rank Correlation

r, p = stats.spearmanr(df['study_hours'], df['gpa'])

Pearson Correlation

r, p = stats.pearsonr(df['age'], df['gpa'])

One-Way ANOVA

groups = by_level(df, 'gpa', 'program')
F, p = stats.f_oneway(*groups)

Chi-Square Test of Independence

table = pd.crosstab(df['gender'], df['civil_status'])
chi2, p, dof, expected = stats.chi2_contingency(table)

Numeric-claim validation: PASSED (44 numbers checked). Engine v0.1.0 · Registry v0.2.0. Prose source: llm:gemini.