Calculating Number Of Subjects Needed In A Study Using Mushra

Determine the optimal listener sample size for ITU-R BS.1534 Subjective Audio Tests.

MDD (Points)	Required Subjects (N=0.80)	Required Subjects (N=0.90)	Description

Table 1: Quick reference for calculating number of subjects needed in a study using mushra for common effect sizes.

What is Calculating Number of Subjects Needed in a Study Using MUSHRA?

Calculating number of subjects needed in a study using mushra is a critical statistical step in the design of subjective audio quality assessments. MUSHRA, which stands for Multiple Stimuli with Hidden Reference and Anchor, is a standardized methodology (ITU-R BS.1534) used to evaluate the quality of intermediate levels of audio degradation.

Unlike simple preference tests, MUSHRA requires listeners to rate multiple stimuli on a scale from 0 to 100. Because these tests are resource-intensive—requiring treated listening rooms, high-end equipment, and expert listeners—knowing exactly how many participants are needed is vital. Too few subjects, and your study will lack the statistical power to find real differences. Too many, and you waste time and funding.

Common misconceptions include the idea that a fixed number, like 10 or 15, is always sufficient. In reality, calculating number of subjects needed in a study using mushra depends entirely on the variance of your listeners’ scores and the magnitude of the difference you expect to find between audio codecs.

MUSHRA Sample Size Formula and Mathematical Explanation

To perform an accurate calculating number of subjects needed in a study using mushra, we primarily use the power analysis formula for a paired t-test or a repeated measures ANOVA, given that MUSHRA is a within-subjects design where every listener hears every stimulus.

The core formula used in this calculator is:

n = [(Z_α/2 + Z_β)² × σ²] / δ²

Variable	Meaning	Unit	Typical Range
α (Alpha)	Significance Level	Probability	0.01 – 0.10
1 – β (Power)	Statistical Power	Probability	0.80 – 0.95
σ (Sigma)	Standard Deviation	MUSHRA Points	5 – 20
δ (Delta/MDD)	Min Detectable Diff	MUSHRA Points	5 – 15

After calculating the base ‘n’, we must adjust for the “Post-Screening” process. ITU-R BS.1534-3 suggests that listeners who cannot consistently identify the hidden reference or who rate the anchors incorrectly should be excluded. Therefore, the final step in calculating number of subjects needed in a study using mushra is dividing the base number by (1 – Dropout Rate).

Practical Examples (Real-World Use Cases)

Example 1: High-Precision Codec Comparison

Imagine a developer testing a new lossless-mode codec. They expect the differences to be subtle, perhaps only 5 points on the MUSHRA scale. Based on previous tests, the standard deviation is 10. Using a 95% confidence level and 80% power, calculating number of subjects needed in a study using mushra yields a base of 32 subjects. After adding a 20% dropout buffer, the study should recruit 40 listeners.

Example 2: General Quality Benchmarking

In a broader study where the MDD is 15 points (detecting larger differences between low-bitrate mp3 and AAC), and the SD is 12. Calculating number of subjects needed in a study using mushra shows a base requirement of only 6 subjects. However, because ITU-R standards recommend a minimum for stability, one would likely increase this to at least 15-20 to ensure robustness against outlier behavior.

How to Use This MUSHRA Calculator

1. Set Alpha: Most academic and industrial studies use 0.05.
2. Define Power: 0.80 is the industry standard, meaning you have an 80% chance of detecting a real effect.
3. Input MDD: Decide the smallest difference that actually matters for your product. Is a 5-point difference on a 100-point scale worth the extra cost of 20 more subjects?
4. Estimate SD: If you don’t have pilot data, 10-15 is a safe starting point for MUSHRA tests.
5. Account for Dropout: Factor in how strict your screening will be. High-complexity audio usually has higher rejection rates.
6. Review Results: The calculator updates in real-time, showing the total recruitment target.

Key Factors That Affect MUSHRA Results

• Listener Expertise: Expert listeners typically have lower standard deviations (σ), which reduces the number of subjects needed.
• Audio Content: “Critical” items (like glockenspiel or castanets) might reveal differences more clearly, effectively increasing the MDD and lowering the required N.
• Room Acoustics: A high noise floor in the listening environment increases variance, significantly increasing the result when calculating number of subjects needed in a study using mushra.
• Anchor Selection: Well-chosen anchors help stabilize the scale, potentially reducing inter-subject variance.
• Fatigue: Long test sessions increase noise in the data, leading to higher SD values and the need for more participants.
• Screening Criteria: Stricter post-screening (e.g., ITU-R BS.1534-3) means you need a larger initial pool to end up with enough valid data points.

Frequently Asked Questions (FAQ)

What is the minimum number of subjects for a MUSHRA test?

While calculating number of subjects needed in a study using mushra might give a low number, ITU-R BS.1534-3 recommends at least 20 listeners for results to be considered representative of the general population.

Can I use this for non-audio studies?

The math is based on a standard power analysis for continuous scales, so it works for any multi-stimulus rating test, though the specific dropout logic is unique to MUSHRA.

How does MDD affect my sample size?

The relationship is inverse-square. If you want to detect a difference half as small, you need four times as many subjects.

What if I don’t know my standard deviation?

Perform a small pilot study with 5 people. Their variance will give you the best estimate for calculating number of subjects needed in a study using mushra for the full trial.

Is post-screening mandatory?

For compliance with ITU-R standards, yes. This is why the dropout buffer in our calculator is so important.

Does the number of stimuli change the sample size?

Directly, the formula for a t-test doesn’t change, but using many stimuli increases fatigue, which increases σ, indirectly increasing the required N.

What is a “good” power level?

0.80 is standard. 0.90 is preferred for high-stakes product launches where you cannot afford to miss a quality regression.

Why is MUSHRA better than Mean Opinion Score (MOS)?

MUSHRA provides a hidden reference and anchors, which reduces individual bias and allows for more precise calculating number of subjects needed in a study using mushra compared to the more volatile MOS.