Inter-item correlations → Spearman-Brown Correction
Hover any cell to see where each correlation comes from
Split-Half Correlations
Items were randomly assigned to Half 1 or Half 2. The two colored averages are what get correlated in split-half reliability.
Split-half → Spearman-Brown correction
r (split-half correlation)
—
cor(avg₁, avg₂)
→
r (SB-corrected)
—
2r / (1 + r)
≈
Cronbach's α
—
k · r̄ / (1 + (k−1) · r̄)
●r (split-half correlation) This value represents the raw correlation between the two half-averages. It is necessarily lower than true reliability because each half has only half the items.
●r (SB-corrected) The Spearman-Brown formula adjusts for length of the half-scale, estimating what the full-scale reliability would be if the values used in the correlations were more precise/less noisy (i.e., calculated with twice as many items). The formula below this value is derived by plugging k = 2 into the Spearman-Brown formula.
●Cronbach's α This value estimates full-scale reliability using a different route than the split-half approach. Here, the avg inter-item r from the slider (the same r̄ averaged in the heatmap above) is plugged directly into the Spearman-Brown formula. r (SB-corrected) and α are estimating the same thing—full-scale reliability—just via different routes. Small differences are normal: α uses the slider's r̄ exactly, while r (SB-corrected) is derived from the actual simulated split-half correlation, which varies due to sampling.
Reliability ceiling on validity
Scale variance breakdown
Reliability of hypothetical outcome variable