First-year proficiency on binomial/normal distributions: coded exam responses (ODL university, N=120)

Research hypothesis
(H1) Students’ conceptual framing of a probability-distribution task (Conceptual Understanding, CU) is positively associated with procedural success (Applying Statistical Methods, ASM) within the same response; (H2) Primary error types are concept-specific across binomial exact-probability, normal between-probability, and inverse-normal (percentile→cutoff) items.

What the data are
A de-identified, item-level dataset created from 120 invigilated exam scripts in an open-distance learning (ODL) statistics module. Only three sub-questions were coded (one per concept): Binomial (exact), Normal (between), Inverse-Normal (percentile→cutoff). Each response is scored on CU and ASM (0–3), flagged Attempt (Y/N), and assigned a mutually exclusive primary error: MODEL/PARAM, EVENT, Z/QUANT, COMPUTE/TABLE, BACK-TRANSFORM, or NOERROR. Non-attempts are recorded separately.

How the data were gathered
Scripts were written under exam conditions (no software; tables + non-programmable calculators). After consent and de-identification, responses were double-coded on a calibration set; Cohen’s κ=0.83. The researcher then applied the finalized rubric to all 120 scripts. Ethics approval: CREC Ref 003/EGM/2014.

Files & structure (key variables)

Coding.xlsx (one row per ScriptID × item). Fields: ScriptID (pseudonymous), Item (Binomial/Normal/InverseNormal), Attempt (Y/N), CU (0–3), ASM (0–3), PrimaryError (MODEL|EVENT|Z/QUANT|COMPUTE/TABLE|BACK|NOERROR). Optional admin columns may include Notes or brief anonymised excerpts.

Codebook.pdf (or .docx): variable definitions, scoring anchors, examples.

Rubric.pdf (CU/ASM level descriptors).

What the data show (headline results to orient users)

Non-attempt: 16% (binomial; 19/120), 20% (normal; 24/120), 49% (inverse-normal; 59/120).

Means on attempted: CU—1.60 (bin), 2.29 (norm), 1.05 (inv); ASM—0.88 (bin), 1.67 (norm), 0.20 (inv).

CU–ASM correlations (attempted): r≈0.80, 0.73, 0.78 (bin, norm, inv).

Dominant errors: Binomial—MODEL/PARAM (46/101); Normal—COMPUTE/TABLE (21/96) and Z/QUANT (9/96); Inverse-Normal—EVENT (24/61) and Z/QUANT (24/61).

How to interpret/use

Unit of analysis is the item response, not the student. Compute CU/ASM summaries on attempted responses only; report non-attempts separately for transparency.

PrimaryError is mutually exclusive and reflects the issue most proximal to an incorrect result (tie-breaker rule).

Appropriate uses: learning analytics; error-profiling; assessment design; replication of CU↔ASM association; building targeted teaching interventions (e.g., binomial model-checks; normal table-literacy; inverse-normal percentile→event→z→x routine).

Limitations
Single institution, three items, manual/table context; interpretations should not be generalized to software-based assessments without caution.