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Category Number Generators

Randomization Method Block methods ensure balanced allocation.

Total Subjects Range: 2 – 10,000

Allocation Ratio (A:B)

Block Size Must be a multiple of (ratio + 1).

Arm A Label

Arm B Label

Subject ID Prefix

Starting ID Number

Quick Presets:

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About

Improper randomization in a two-arm study introduces selection bias. This corrupts your treatment effect estimate and can invalidate months of data collection. Regulatory bodies (FDA, EMA) require documented, reproducible allocation sequences that demonstrate concealment. Simple coin-flip methods produce unacceptable imbalance in small samples. A study with n = 30 using pure random assignment has roughly a 10% chance of a split worse than 20/10. This tool uses permuted block randomization with cryptographically secure entropy from the Web Crypto API, not Math.random(). It supports allocation ratios from 1:1 to 3:1, variable block sizes to prevent prediction, and exports audit-ready CSV files. Note: this tool does not replace a validated IWRS system for Phase III trials. It is appropriate for investigator-initiated studies, pilot trials, and educational use.

Formulas

In permuted block randomization with allocation ratio r:1, each block contains b subjects. Within a block of size b, the number of subjects assigned to Arm A and Arm B is fixed:

n_A = r × k n_B = 1 × k b = n_A + n_B = k(r + 1)

where k is the block multiplier (a positive integer). The block is then shuffled using a Fisher-Yates permutation seeded by cryptographic entropy. The number of possible permutations within one block is:

b!n_A! ⋅ n_B!

For a 1:1 ratio with block size 4: 4!2! ⋅ 2! = 6 possible arrangements. For block size 6: 20 arrangements. Variable block sizes are drawn uniformly from a user-specified set to prevent sequence prediction.

where r = allocation ratio (Arm A : Arm B), k = block multiplier, b = block size, n_A = subjects per block assigned to Arm A, n_B = subjects per block assigned to Arm B.

Reference Data

Randomization Method	Balance Guarantee	Predictability Risk	Best Use Case	Minimum Sample Size
Simple (Coin Flip)	None	None	Large trials (n > 200)	200+
Fixed Block	Within each block	High (if block size known)	Small balanced trials	10
Variable Block	Within each block	Low	Most RCTs	20
Stratified Block	Within stratum & block	Low	Multi-site or covariate-adjusted	30
Minimization	Adaptive	Moderate	Small trials with many covariates	50
Biased Coin	Probabilistic	Low	Moderate sample sizes	40
Urn (Wei)	Adaptive	Low	Sequential enrollment	30
Block Size 2 (1:1)	Every 2 subjects	Very High	Not recommended (too predictable)	-
Block Size 4 (1:1)	Every 4 subjects	Moderate	Common default	12
Block Size 6 (1:1)	Every 6 subjects	Low	Preferred for open-label	18
Block Size 4 (2:1)	Every 6 subjects (4A+2B)	Moderate	Unequal allocation	18
Block Size 8 (1:1)	Every 8 subjects	Very Low	Large single-site trials	24
ICH E9 Recommendation	Block-based	-	Regulatory submission trials	-
CONSORT Requirement	Documented method	-	All published RCTs	-

Frequently Asked Questions

Simple randomization guarantees equal allocation only asymptotically. For a study with n = 20, there is approximately a 17% probability of an imbalance of 12/8 or worse. Block randomization forces balance within every block, so maximum possible imbalance at any point equals half the block size. Use block sizes of 4 or 6 for studies under 100 subjects.

With a fixed block size of 4 (1:1 ratio), an investigator who has enrolled 3 subjects (e.g., A, B, A) knows the 4th must be B. Variable blocks (e.g., randomly choosing between sizes 2, 4, 6) eliminate this certainty because the investigator does not know when a block boundary occurs. ICH E9 guidelines recommend variable block sizes specifically for open-label or single-blind studies.

The Web Crypto API provides cryptographically secure pseudorandom numbers sourced from OS-level entropy pools. This exceeds the quality of most legacy IWRS systems that used linear congruential generators. However, for a pivotal Phase III trial, regulatory bodies expect a validated, 21 CFR Part 11 compliant system with audit trails. This tool is appropriate for investigator-initiated, pilot, and academic studies.

This tool supports 1:1, 2:1, and 3:1 ratios. Unequal allocation (e.g., 2:1) is used when you need more safety data on the experimental arm, when the control treatment is well-characterized, or in dose-finding studies. Note that a 2:1 ratio requires roughly 12% more total subjects than 1:1 to achieve equivalent statistical power.

The results panel displays the count and percentage for each arm. For block randomization, the counts will satisfy the allocation ratio exactly at every block boundary. You can verify by checking that after every b subjects (where b is your block size), the cumulative ratio matches your target. The exported CSV includes a block number column for this audit.

No. The minimum block size equals r + 1 (for ratio r:1) multiplied by the block multiplier k ≥ 1. For a 2:1 ratio, the smallest valid block is 3 (containing 2 A and 1 B). The tool enforces this constraint and will warn you if an invalid block size is entered.