Balanced presentation-order randomizer
Generate balanced AAB, ABA, BAA, BBA, BAB, and ABB sequences with blind codes and an administrator answer key.
| Judgment | Sequence | Code 1 | Code 2 | Code 3 | Odd position | Odd product |
|---|---|---|---|---|---|---|
| Generate a plan to display randomized sequences. | ||||||
Individual assessor data
Record assessor, session, sequence, selected sample, response time, confidence, comments, and exclusions.
| Assessor ID | Session | Sequence | Selected | Correct sample | Status | Seconds | Confidence | Excluded | Reason | Comments |
|---|
Formula used
P(X ≥ x) = Σ C(n,k)(1/3)k(2/3)n−k, from k = x through n.
pd = (3pc − 1) / 2, bounded between zero and one.
plimit = 1/3 + (2/3)pd,max. The calculator uses an exact lower-tail test against this selected limit.
How to use this calculator
- Enter the test identity, products, objective, assessor count, and number of trials.
- Enter valid judgments, correct judgments, exclusions, alpha, and confidence level.
- Choose planning assumptions for discriminator proportion, power, missing rate, and similarity limit.
- Add chemistry context so the report records sample preparation and comparison conditions.
- Select Analyze triangle test to calculate exact probabilities, intervals, power, and recruitment requirements.
- Generate balanced presentation sequences and record individual assessor responses when needed.
- Export the result, randomized plan, assessor data, or printable PDF report.
Example data table
| Input | Example | Purpose |
|---|---|---|
| Valid judgments | 36 | Total usable forced-choice responses |
| Correct responses | 22 | Assessors identifying the odd sample |
| Alpha | 0.05 | Maximum Type I error probability |
| Expected discriminator proportion | 0.35 | Alternative used for power planning |
| Desired power | 0.80 | Target probability of detecting the planned effect |
| Maximum similarity discriminator | 0.20 | Largest tolerable true discriminator proportion |
Interpretation and limitations
The triangle method compares three coded samples where two are identical. Each assessor selects the sample believed to be different. Chance performance equals one correct response in three.
A statistically significant difference result supports a perceptible distinction. A non-significant difference result does not automatically prove equivalence. Similarity requires a defined maximum acceptable difference and a suitable one-sided design.
Repeated judgments from one assessor may be correlated. Pooled binomial analysis assumes independent judgments and should be interpreted carefully. Use assessor-level or mixed-effects methods when dependence materially affects the study.
Strong flavours, odours, irritation, adaptation, or carryover can impair validity. Neutral coding, balanced presentation, controlled preparation, and independent assessor responses remain essential. Document exclusions and protocol deviations before analysis.
Frequently asked questions
Why is chance probability one-third?
The assessor chooses one odd sample from three coded samples. Only one selection is correct, so random guessing succeeds one-third of the time.
Which p-value is primary?
For difference testing, the calculator reports the exact upper-tail binomial p-value. For similarity, it reports an exact lower-tail p-value against the selected maximum acceptable discriminator limit.
Does a non-significant result prove similarity?
No. Failure to detect a difference may result from insufficient power. A similarity objective needs an explicit similarity limit and adequate study design.
What is the discriminator proportion?
It estimates the fraction of assessors who can genuinely distinguish products, assuming non-discriminators guess randomly.
Why use balanced sequences?
Balanced AAB, ABA, BAA, BBA, BAB, and ABB orders reduce position and presentation-order bias.
Can assessors complete repeated trials?
Yes, but repeated judgments may be dependent. Review assessor-level consistency and avoid assuming complete independence without justification.
How are missing responses handled?
Excluded or missing responses are removed from valid judgments. Their reasons should remain documented in the assessor table and report.
What does statistical power mean?
Power is the probability that the selected design reaches its critical boundary when the planning alternative is true.
Can chemistry measurements be entered?
Yes. pH, concentration, serving temperature, storage, preparation, and instrumental measurements provide scientific context but do not automatically change the binomial model.