Test Rating (Technical)

Cronbach’s Alpha Reliability Analysis

This Assessment Analysis visualization displays internal consistency reliability measurements using Cronbach’s alpha (α) coefficients, comparing local test reliability against established state standards for psychometric evaluation.

Technical Components

1. Reliability Coefficient Display

My Test Reliability: α = 0.66

• Indicates “questionable” internal consistency reliability
• Displayed as green bar showing current assessment instrument reliability
• Falls below acceptable psychometric standards (α ≥ 0.70)

State Standard Reliability: α = 0.93 (2023)

• Represents “excellent” internal consistency reliability benchmark
• Displayed as red bar indicating target reliability standard
• Exceeds excellent reliability threshold (α ≥ 0.90)

2. Cronbach’s Alpha Calculations

Standard Cronbach’s Alpha Formula:

α = (k/(k-1)) × (1 - (Σσ²ᵢ/σ²ₜ))

Where:
k = number of test items
Σσ²ᵢ = sum of individual item variances
σ²ₜ = total test variance

Reliability Gap Analysis:

Reliability Deficit = State Standard - My Test
Reliability Deficit = 0.93 - 0.66 = 0.27

Relative Reliability Index:

Reliability Ratio = My Test α / State Standard α
Reliability Ratio = 0.66 / 0.93 = 0.710 (71% of benchmark reliability)

3. Psychometric Interpretation Standards

Reliability Classification Scale:

• α ≥ 0.90: Excellent reliability (State Standard: 0.93 ✓)
• α ≥ 0.80: Good reliability
• α ≥ 0.70: Acceptable reliability
• α ≥ 0.60: Questionable reliability (My Test: 0.66)
• α < 0.60: Poor reliability

4. Item Analysis Calculations

Minimum Items Needed for Acceptable Reliability: Using Spearman-Brown prophecy formula:

k₂ = k₁ × (α₂(1-α₁))/(α₁(1-α₂))

Where α₁ = current reliability (0.66)
      α₂ = desired reliability (0.70)

Standard Error of Measurement (SEM):

SEM = SD × √(1-α)
SEM = SD × √(1-0.66) = SD × 0.583

Reliability Assessment Status

• Current Reliability: Questionable (α = 0.66)
• Target Reliability: Excellent (α = 0.93)
• Improvement Needed: 0.27 coefficient points
• Risk Level: High – may compromise score validity and precision

Recommended Actions

Immediate Interventions:

1. Item Review: Analyze individual item-total correlations
2. Item Deletion: Remove items with correlations < 0.30
3. Item Addition: Increase test length using Spearman-Brown formula
4. Content Validation: Review items for clarity and relevance

Quality Assurance Metrics:

• Inter-item Correlation Range: Target 0.20-0.40
• Item-Total Correlation: Minimum 0.30
• Factor Loading: Minimum 0.40 for unidimensional scales

This Cronbach’s alpha analysis enables OnTarget users to evaluate measurement precision, identify reliability deficits, and implement targeted improvements to achieve psychometrically sound assessment instruments that meet state reliability standards.