Five Observations May Be Enough to Build Usable Category Ratings

Category ratings are everywhere. We describe people as very tall, tall, average, short or very short; we rate restaurants, films and services on numbered scales; and psychologists rely on them as one of the most common measurement tools in the discipline. The answer, according to the three studies reported in the paper, may be far smaller than an account in which people accumulate many exemplars before forming categories would imply.

The researchers combined a computer simulation with two experiments on human participants. In the Monte Carlo experiment, they tested whether categories built from the first five or ten numbers encountered in a stream of randomly generated stimuli could provide a usable way of sorting later numbers drawn from flat, normal and positively skewed distributions. Two further experiments then put the question to real people: one asked 27 participants to sort random integers, presented one at a time, into five bins on a computer screen, and the other asked 26 participants to perform the same task with arc segments of varying degrees. In both experiments, the category structure that participants established after only five or ten presentations was quite similar to the structure they ended up with after 30 presentations.

The theoretical backdrop comes from Parducci’s range-frequency theory, first proposed in 1965. On that account, the categories people create along a single dimension reflect a compromise between two things: the range of stimuli to be categorized and the frequency distribution of those stimuli along the dimension. Subsequent experiments have confirmed that both variables matter. If categories are genuinely built this way, a person would seemingly need to perceive and remember many exemplars before reasonable estimates of range and distribution could be formed. Yet the authors argue that this painstaking accumulation is unlikely to reflect what actually happens. Accumulation would demand considerable memory for individual exemplars, and until it was complete, category ratings would be impossible, which plainly contradicts how readily people produce them.

Empirical findings from other research traditions also point toward speed. Children recalling event or object classes appear to generalize quickly rather than remember specific details, and studies on prediction and concept formation suggest that reasonably accurate performance does not always require many exemplars, with some researchers describing people as intuitive Bayesians. Work on ensemble perception adds another clue: given a class of stimuli, people tend to recall summary statistics such as the mean and range rather than the individual items themselves. This suggests that people may rely on summary statistics obtained from small samples to build category structures, though the authors note there has been little research into just how small those samples might be.

The simulation study tested three simple algorithms representing broader prototype-based, boundary-based and range-based approaches. In the first, the initial five stimuli became prototypes for five categories, with later stimuli assigned to the closest prototype by linear distance. In the second, the first four stimuli served as the four boundaries separating five categories. In the third, an initial sample of 5, 10 or 20 stimuli was taken, the highest and lowest values became the outer prototypes, and the intermediate prototypes were spaced evenly between them. Each method was run against flat, normal and skewed distributions, with each simulation sorting 30 stimuli into five bins, repeated 5,000 times, and compared against control conditions in which the prototype or boundary values were known exactly from long-term sampling.

The simulation results were nuanced. Small-sample categorization always produced larger errors than the control conditions, as expected, but the increases were moderate. The first-five method produced an average error just under double that of the control condition, while the highest-and-lowest method with an initial sample of ten produced errors roughly 50 percent higher. Extending the initial sample from ten to 20 stimuli brought almost no further benefit, suggesting that a ceiling on the error was reached after about ten observations. The four-boundaries method produced a higher average absolute error than the first-five method, an apparently odd result the authors attribute to the fact that the first-five method’s cut points arise from averaging two prototypes rather than being completely unconstrained.

The human experiments told a complementary story. Participants in Experiment 2 saw 270 integer stimuli across nine conditions, drawn from three flat distributions, three normal distributions and three positively skewed exponential distributions, with ranges spanning from small to very large, so that at the start of each condition they could have little idea what they would encounter. They assigned each integer to one of five bins using keys 1 through 5, could swap the positions of bins after ten trials, and saw the running average and count of stimuli in each bin updated in real time, a feedback design borrowed from ensemble research. Analysis of variance revealed significant bin-by-distribution interactions after five, ten and 30 trials, meaning that even after only five integers had been observed, participants’ responses already varied with the distribution in the theoretically expected direction: more stimuli in the middle bin for normal distributions and more in the first bin for skewed ones.

Not everything matched the simple algorithms. Empty bins were the norm early on: in 234 of 243 participant-condition combinations, at least one bin was unused after five trials, and only nine instances showed the first five trials evenly spread across all five bins. Participants also rarely committed to the outer bins early, which the highest-and-lowest method would require, and on average more of the outer bins were empty after five trials than middle bins. Only a minority of participants used the bin-swapping option. The authors conclude that participants, even after five or ten trials, often seemed to be applying categorization methods other than the simple algorithms examined in the simulation, and that early categorization focused more on filling inner categories than outer ones. Nevertheless, correlations between bin counts at five, ten and 30 trials showed that the placement pattern from the first five trials tended to persist until the thirtieth.

Experiment 3, using arc segments bounded between 0 and 360 degrees, replicated the core finding: averages after five, ten and 30 trials were generally similar, and the bin-by-distribution interactions were again significant at every checkpoint. Empty bins persisted even longer here, and fewer participants swapped bins, but the correlations between early and late bin usage were, if anything, stronger than in Experiment 2. The difference between the unbounded integers of Experiment 2 and the bounded arcs of Experiment 3 suggests participants did make some use of prior knowledge about stimulus ranges, consistent with the idea that different processes may be combined in a single categorization strategy.

The authors are careful about limits. Their experiments do not reveal how the categories are actually formed, and the predictions tested were weak because there were no consequences for producing different categorizations. They note that in high-stakes settings, such as medical diagnosis, categories based on small samples would not be expected to be adequate, whereas casual everyday ratings might tolerate the extra error. Still, the overall conclusion is striking: usable category ratings, reflecting a compromise between range and frequency in line with Parducci’s theory, can often be established from about ten observations of random stimuli, even when the range and distribution of those stimuli are initially unknown.

Subject of Research: How people form category ratings from small samples of stimuli

Article Title: Early impressions count: Category ratings established from small samples

Article References: Zhang, C., Kemp, S., & Grace, R. C. (2026). Early impressions count: Category ratings established from small samples. Attention, Perception, & Psychophysics, 88(8), Article 211. https://doi.org/10.3758/s13414-026-03364-y

Image Credits: AI Generated

DOI: 10.3758/s13414-026-03364-y

Keywords: categorization, category ratings, small samples, range-frequency theory, Monte Carlo simulation, psychophysics, ensemble perception, decision making, cognitive psychology, stimulus distributions, Early, impressions