Raw Scores vs. Percentiles
A raw reaction time of 220ms cannot be judged as 'fast' or 'slow' in isolation. Meaning emerges only from relative position within a group measured under identical conditions. A percentile indicates 'what percentage of people score below you'; the 75th percentile means you rank above 75% of the population. The advantage of percentiles is their applicability regardless of whether the original score distribution is normal. Even for distributions with long right tails like reaction time (approximating log-normal), percentiles enable intuitive interpretation. However, differences between percentiles are not equidistant. Improving from the 50th to 60th percentile and from the 90th to 95th percentile represent vastly different magnitudes of actual ability difference, with the latter being far greater.
Practical Understanding of Normal Distribution and Standard Deviation
Many cognitive abilities approximate normal distribution at the population level. In a normal distribution, the entire distribution is described by just two parameters: mean (μ) and standard deviation (σ). Approximately 68% of people fall within ±1σ of the mean, 95% within ±2σ, and 99.7% within ±3σ. IQ tests are standardized with mean 100 and standard deviation 15, so IQ 130 corresponds to +2σ (top 2.3%). Similarly with Bench tests, understanding how many σ your score deviates from the mean provides more precise understanding of your position within the group. Reaching the top 1% requires +2.33σ, a level demanding considerable combination of training and aptitude.
| Distance from the mean | Share of people | IQ equivalent (mean 100, SD 15) | How to read it |
|---|---|---|---|
| ±1σ | About 68% in this range | 85 to 115 | The band where the majority sits; ups and downs here are hard to tell from measurement scatter |
| ±2σ | About 95% in this range | 70 to 130 | IQ 130 sits at +2σ, which corresponds to the top 2.3% |
| ±3σ | About 99.7% in this range | 55 to 145 | Almost everyone falls inside; suspect your test conditions first if you land outside |
| +2.33σ | The boundary of the top 1% | About 135 | A level demanding a considerable combination of training and aptitude |
The IQ equivalents are computed from the definition of mean 100 and SD 15. Bench scores work the same way: look at how many σ you are from the mean.
Measurement Error and Confidence Intervals
All measurements contain error. Primary sources of measurement error in cognitive tests include physical condition fluctuation, arousal level variation, practice effects, and environmental noise. Equating a single measurement result with 'true ability' is statistically inappropriate; results should be interpreted with confidence intervals. For a test with test-retest reliability of 0.85, the standard error is approximately 39% of the standard deviation. This means if your score is at the 75th percentile on a given day, your true ability likely falls within the 65th-85th percentile range. For reliable assessment, using the median of multiple measurements or using mean rather than best score as the indicator is recommended.
Practice Effects and Establishing Baselines
Cognitive tests exhibit practice effects. During initial attempts, unfamiliarity with the test format tends to produce scores below true ability. For most tests, practice effects level off after a few attempts, with subsequent scores stabilizing. Scores during this stable period constitute the baseline. Evaluating training effects without establishing a baseline risks misidentifying practice effects as ability improvement. Accurate evaluation requires first establishing a baseline through approximately 5 measurements, then tracking changes from subsequent training interventions. Additionally, intervals that are too short introduce fatigue effects, while intervals that are too long are affected by diurnal variation. Spacing measurements at least 24 hours apart while testing at the same time of day is ideal.
Beware of ceiling and floor effects
In reading test results, it is worth knowing the pitfalls of ceiling and floor effects. A ceiling effect is the phenomenon where a task is so easy that many people cluster near full marks and differences in ability among top performers can no longer be measured. Conversely, a floor effect is where a task is so hard that many sink near the lowest score and differences among lower performers become invisible. In such tests, true ability is hard to show in the number. When your score is near the edge of a test's measurement range, it is desirable not to judge ability by that number alone but to also use tests of different difficulty.
Score Changes Over Time and Determining Significant Improvement
Determining training effectiveness requires evaluating whether score changes exceed measurement error range. Statistics uses the Reliable Change Index (RCI), calculated by dividing the change amount by the standard error. Values exceeding 1.96 indicate true change with 95% probability. Practically, improvement exceeding 1.5 times the baseline standard deviation can be taken as a benchmark for improvement beyond measurement error. Conversely, smaller variations likely fall within normal daily fluctuation range. For tracking long-term training effects, weekly moving averages smooth daily variations and visualize trends. Bench stores your personal best for each test on your device, which gives you a fixed reference point for comparisons across weeks. To follow the trend in more detail, keep your own log of test dates and scores.