People's ability to summarize their knowledge of an observed numerical variable has been extensively studied. However, many real-life situations require people to go beyond summary statistics and infer which process or distribution has generated a sample. The present study investigates the extent to which people can make such inferences when the experienced variable is continuous and when they have had previous experience with instances of the variable. It also tests specific predictions derived from three possible cognitive processes of how inferences about a generating distribution are made. The results indicate that participants are efficient and flexible intuitive statisticians, requiring only as little as four observations in a sample to successfully infer which distribution it came from. Further, the results indicate that the cognitive process supporting the inference uses statistical properties of both an experienced distribution and a presented test sample, as suggested by the Naïve Sampling Model (NSM).
AndersonJ. R. (1991). The adaptive nature of human categorization. Psychological Review, 98, 409–429.
2.
Bar-HillelM. (1979). The role of sample size in sample evaluation. Organizational Behavior and Human Performance, 24, 245–257.
3.
BeachL. R., WiseJ. A., & BarclayS. (1970). Sample proportions and subjective probability revisions. Organizational Behavior and Human Performance, 5, 183–190.
4.
BrunswikE. (1955). Representative design and probabilistic theory in a functional psychology.Psychological Review, 62, 193–217.
5.
BusemeyerJ. R., MyungI. J., & McDanielM. A. (1993). Cue competition effects: Empirical tests of adaptive network learning models. Psychological Science, 4, 190–195.
6.
BusemeyerJ. R. & TownsendJ. T. (1993). Decision field-theory: A dynamic cognitive approach to decision making in an uncertain environment. Psychological Review, 100, 432–459.
7.
ChesneyD. L., & ObrechtN. A. (2012). Statistical judgments are influenced by the implied likelihood that samples represent the same population. Memory & Cognition, 40, 420–433.
8.
CowanN. (2000). The magical number 4 in short-term memory: A reconsideration of mental storage capacity. Behavioral and Brain Sciences, 24, 87–114.
9.
DoughertyM. R. P., GettysC. F., & OgdenE. E. (1999). MINERVA-DM: A memory processes model for judgments of likelihood. Psychological Review, 106, 180–209.
10.
DoughertyM. R. P., & HunterJ. E. (2003). Hypothesis generation, probability judgment, and individual differences in working memory capacity. Acta Psychologica, 113, 263–282.
11.
EvansJ. S. B. T., & DusoirA. E. (1977). Proportionality and sample size as factors in intuitive statistical judgement. Acta Psychologica, 41, 129–137.
12.
EvansJ. S. B. T., & PollardP. (1985). Intuitive statistical inferences about normally distributed data. Acta Psychologica, 60, 57–71.
13.
FiedlerK. (2000). Beware of samples! a cognitive-ecological sampling approach to judgment biases. Psychological Review, 107, 659–676.
14.
FiedlerK. & JuslinP. (Eds.). (2006). Information sampling and adaptive cognition. Cambridge, UK: Cambridge University Press.
15.
FoxS., & ThorntonG. C. (1993). Implicit distribution theory: The influence of cognitive representation of differentiation on actual ratings. Perceptual and Motor Skills, 76, 259–276.
16.
GaissmaierW., SchoolerL. J., & RieskampJ. (2006). Simple predictions fueled by capacity limitations: When are they successful?. Journal of Experimental Psychology: Learning, Memory, and Cognition, 32, 966–982.
17.
GalesicM., OlssonH., & RieskampJ. (2012). Social sampling explains apparent biases in judgments of social environments. Psychological Science, 23, 1515–1523.
18.
GilovichT., GriffinD. W., & KahnemanD. (Eds.). (2002). Heuristics and biases: The psychology of intuitive judgment. New York: Krieger Publishing Company.
19.
GriffinD. W., & TverskyA. (1992). The weighing of evidence and the determinants of confidence. Cognitive Psychology, 24, 411–435.
20.
GriffithsT. L., & TenenbaumJ. B. (2006). Optimal predictions in everyday cognition. Psychological Science, 17, 767–773.
21.
GriffithsT. L., & TenenbaumJ. B. (2011). Predicting the future as bayesian inference: People combine prior knowledge with observations when estimating duration and extent. Journal of Experimental Psychology: General, 140, 725–743.
22.
GweonH., TenenbaumJ. B., & SchulzL. E. (2010). Infants consider both the sample and the sampling process in inductive generalization. Proceedings of the National Academy of Sciences, 107, 9066–9071.
23.
HanssonP., RönnlundM., JuslinP., & NilssonL.-G. (2008). Adult age differences in the realism of confidence judgments: Overconfidence, format dependence, and cognitive predictors. Psychology and Aging, 23, 531–544.
24.
HertwigR., BarronG., WeberE. U., & ErevI. (2004). Decisions from experience and the effect of rare events in risky choice. Psychological Science, 15, 534–539.
25.
HertwigR. & PleskacT. J. (2010). Decisions from experience: Why small samples?. Cognition, 115, 225–237.
26.
HogarthR. M. & EinhornH. J. (1992). Order effects in belief updating: The belief-adjustment model. Cognitive Psychology, 24, 1–55.
27.
JakoR. A. & MurphyK. R. (1990). Distributional ratings, judgment decomposition, and their impact on interrater agreement and rating accuracy. Journal of Applied Psychology, 75, 500–505.
28.
JuslinP., KarlssonL., & OlssonH. (2008). Information integration in multiple cue judgment: A division of labor hypothesis. Cognition, 106, 259–298.
29.
JuslinP., NilssonH., WinmanA., & LindskogM. (2011). Reducing cognitive biases in probabilistic reasoning by the use of logarithm formats. Cognition, 120, 248–267.
30.
JuslinP., WinmanA., & HanssonP. (2007). The naïve intuitive statistician: A naïve sampling model of intuitive confidence intervals. Psychological Review, 114, 678–703.
31.
KacelnikA., & BatesonM. (1996). Risky theories—the effects of variance on foraging decisions. American Zoologist, 36, 402–434.
32.
KahnemanD., & MillerD. T. (1986). Norm theory: Comparing reality to its alternatives. Psychological Review, 93, 136–153.
33.
KahnemanD., SlovicP., & TverskyA. (1982). Judgment under uncertainty: Heuristics and biases. New York: Cambridge University Press.
34.
KahnemanD. & TverskyA. (1972). Subjective probability: A judgment of representativeness. Cognitive Psychology, 3, 430–454.
35.
KareevY., ArnonS., & Horwitz-ZeligerR. (2002). On the misperception of variability. Journal of Experimental Psychology: General, 131, 287–297.
36.
LichtensteinS., SlovicP., FischhoffB., LaymanM., & CombsB. (1978). Judged frequency of lethal events. Journal of Experimental Psychology: Human Learning and Memory, 4, 551–578.
37.
LindskogM., WinmanA., & JuslinP. (2013a). Calculate or wait: Is man an eager or a lazy intuitive statistician?. Journal of Cognitive Psychology, 25, 994–1014.
38.
LindskogM., WinmanA., & JuslinP. (2013b). Naïve point estimation. Journal of Experimental Psychology: Learning, Memory, and Cognition, 39, 782–800.
39.
LinvilleP. W., FischerG. W., & SaloveyP. (1989). Perceived distributions of the characteristics of in-group and out-group members: Empirical evidence and a computer simulation. Journal of Personality and Social Psychology, 57, 165–188.
40.
LipkusI. M. & PetersE. (2009). Understanding the role of numeracy in health: Proposed theoretical framework and practical insights. Health Education & Behavior, 36, 1065–1081.
41.
LipkusI. M., SamsaG., & RimerB. K. (2001). General performance on a numeracy scale among highly educated samples. Medical Decision Making, 21, 37–44.
42.
LovieP. (1978). Teaching intuitive statistics II. aiding the estimation of standard deviations. International Journal of Mathematical Education in Science and Technology, 9, 213–219.
43.
LovieP. & LovieA. D. (1976). Teaching intuitive statistics i: Estimating means and variances. International Journal of Mathematical Education in Science and Technology, 7, 29–39.
44.
NilssonH., WinmanA., JuslinP., & HanssonG. (2009). Linda is not a bearded lady: Configural weighting and adding as the cause of extension errors. Journal of Experimental Psychology: General, 138, 517–534.
45.
NisbettR. E., KrantzD. H., JepsonC., & KundaZ. (1983). The use of statistical heuristics in everyday inductive reasoning. Psychological Review, 90, 339–363.
46.
NisbettR. E., & KundaZ. (1985). Perception of social distributions. Journal of Personality and Social Psychology, 48, 297–311.
47.
ObrechtN. A., ChapmanG. B., & GelmanR. (2007). Intuitive t-tests: Lay use of statistical information. Psychonomic Bulletin & Review, 14, 1147–1152.
48.
ObrechtN. A. & ChesneyD. L. (2013). Sample representativeness affects whether judgments are influenced by base rate or sample size. Acta Psychologica, 142, 370–382.
49.
PetersE., SlovicP., VästfjällD., & MertzC. K. (2008). Intuitive numbers guide decisions. Judgment and Decision Making, 3, 619–635.
50.
PetersE., VästfjällD., SlovicP., MertzC. K., MazzoccoK., & DickertS. (2006). Numeracy and decision making. Psychological Science, 17, 407–413.
51.
PhillipsL. D. & EdwardsW. (1966). Conservatism in a simple probability inference task. Journal of Experimental Psychology, 72, 346–354.
52.
PollardP. (1984). Intuitive judgments of proportions, means, and variances: A review. Current Psychology, 3, 5–18.
53.
SedlmeierP. (1998). The distribution matters: Two types of sample-size tasks. Journal of Behavioral Decision Making, 11, 281–301.
54.
SedlmeierP. & GigerenzerG. (1997). Intuitions about sample size: The empirical law of large numbers. Journal of Behavioral Decision Making, 10, 33–51.
55.
StewartN., ChaterN., & BrownG. D. A. (2006). Decision by sampling. Cognitive Psychology, 53, 1–26.
56.
ThomasR. P., DoughertyM. R. P., SprengerA. M., & HarbisonJ. I. (2008). Diagnostic hypothesis generation and human judgment. Psychological Review, 115, 155–185.
57.
TverskyA. & KahnemanD. (1974). Judgment under uncertainty: Heuristics and biases. Science, 185, 1124–1131.
58.
VulW., GoodmanN. D., GriffithsT. L., & TenenbaumJ. B. (2009). One and done? optimal decisions from very few samples. In TaatgenN. A. & van RijnH. (Eds.), Proceedings of the 31st annual conference of the cognitive science society (pp. 66–72). Austin, TX: Cognitive Science Society.
59.
XuF. & DenisonS. (2009). Statistical inference and sensitivity to sampling in 11-month-old infants. Cognition, 112, 97–104.
60.
XuF. & GarciaV. (2008). Intuitive statistics by 8-month-old infants. Proceedings of the National Academy of Sciences, 105, 5012–5015.
61.
ZacksR. T. & HasherL. (2002). Frequency processing: A twenty-five year perspective. In SedlmeierP. & BetschT. (Eds.), ETC. frequency processing and cognition (pp. 21–36). New York, NY, US: Oxford University Press.
