Hypothesis: Classroom attire is statistically independent of degree completion.
Chi-Square Statistic (χ²):0.076
Degrees of Freedom (df):1
p-value:0.782
Empirical Verdict
Fail to Reject Null Hypothesis: Attire is statistically independent of academic completion.
Separate modeled independence, semester hazards and sample tables
Read the explanation
This cohort page generates synthetic students; it does not measure real clothing effects or establish a causal finding about academic outcomes. At default sample size one thousand and attire share seventy-five percent, seven hundred fifty records are marked casual and two hundred fifty traditional. Both groups use the same probability generator. The base score adds study hours divided by thirty times point three five, attendance divided by one hundred times point four, and support divided by one hundred times point two five, clamped between point one five and point nine eight. Default twenty-four study hours, ninety-two attendance and sixty-five support sum to point eight one zero five. Attire never appears in that formula, so independence is an assumption built into generation. Changing the attire percentage reallocates group sizes and reruns random generation rather than testing a real-world clothing intervention. These two equal-scale bars show seven hundred fifty versus two hundred fifty records. The base score is not directly the graduation probability. Each student first receives normal random variation with scale point zero eight and an individual score clamped between point zero five and point nine nine. Then eight semesters each test a dropout hazard equal to one minus that score divided by seven, times point eight plus point zero five times semester number. For an illustrative student whose individual score exactly equals point eight one zero five, the first-semester hazard is about two point three zero one percent and the eighth about three point two four nine percent. Multiplying all eight conditional survival factors gives about seventy-nine point eight four percent survival. This example isolates the code relationship; it is not the simulated cohort mean, which also contains random variation and sampling noise. The diagram compares the two hazard values on a common one hundred pixels per percentage-point scale. Every slider change generates a fresh cohort, so a change in results mixes parameter changes with a new random draw. The contingency table compares observed graduate and dropout counts with expectations derived from row and column totals. An illustrative one-thousand-student table with casual six hundred graduates and one hundred fifty dropouts, and traditional two hundred graduates and fifty dropouts, has matching expected cells and chi-square zero. Moving twenty graduates from the traditional to the casual group while holding row totals and total graduates fixed gives six hundred twenty, one hundred thirty, one hundred eighty and seventy. Expected cells remain six hundred, one hundred fifty, two hundred and fifty. The four squared differences divided by expected counts sum to thirteen point three three three. This is illustrative geometry using the source formula, not an injected app result. The source maps its approximate p value to a point zero five caption and allows significant sample anomalies; a large p value does not prove real-world independence. At an empty group endpoint, zero expected cells are skipped and the source can return chi-square zero and p one, so that caption is not evidence from two populated groups. Actual CSV and JSON downloads expose current synthetic records and summary. Offline D3 is unavailable, so the original retention chart remains missing while numerical counts and downloads can still be tested.
Understanding the Attire Independence Simulation and Chi-Square Test
How does this simulation calculate graduation persistence, and what does the chi-square test of independence evaluate?
This interactive workbench models hypothetical college cohorts over eight semesters. In the simulator's code, individual graduation persistence is determined entirely by academic effort variables (study hours, attendance rate, and socioeconomic baseline support) along with random variance. Attire grouping ('Casual' versus 'Traditional') has zero algorithmic influence on student completion. The contingency table and chi-square test then compare the observed distribution of graduates and dropouts between both groups against what would be expected under pure statistical independence.
This tool is an illustrative pedagogical Monte Carlo demonstration, not an empirical sociological survey or causal field study. Because the program's underlying code explicitly defines attire as having zero mathematical weight on persistence, the resulting finding of statistical independence reflects the model's design rather than measured real-world academic data.
Try a worked example
When the sample size is set to 1,000 students with a 75% casual attire index, the model assigns 750 students to the casual group and 250 to the traditional group. Clicking the 'Reset' button re-runs the simulation with default parameters (1,000 sample size, 75% casual index, 24 study hours, 92% attendance, and 65 support). The script calculates baseline completion probability from the effort sliders and generates random draws for each student. Because attire has zero weight in that formula, the resulting casual and traditional graduation percentages remain close to one another, producing a small chi-square statistic and a p-value that typically exceeds 0.05.
Contingency Table and Expected Frequencies
In a 2x2 contingency table comparing attire group (Casual vs. Traditional) to academic outcome (Graduated vs. Dropped), the expected count for each cell under the null hypothesis of independence is computed as (row total * column total) / grand total. NIST/SEMATECH e-Handbook of Statistical Methods: 7.4.5. Contingency Table Approach
For a contingency table with r rows and c columns, the degrees of freedom equal (r - 1)(c - 1). For a 2x2 table, degrees of freedom equal (2 - 1)(2 - 1) = 1. A test statistic below the critical alpha threshold yields a p-value greater than 0.05, failing to reject the null hypothesis of independence. NIST/SEMATECH e-Handbook of Statistical Methods: 7.4.5. Contingency Table Approach