Book contents
- Frontmatter
- Contents
- List of Contributors
- PART I INTRODUCTION
- PART II THE PSYCHOLOGICAL LAW OF LARGE NUMBERS
- 2 Good Sampling, Distorted Views: The Perception of Variability
- 3 Intuitive Judgments about Sample Size
- 4 The Role of Information Sampling in Risky Choice
- 5 Less Is More in Covariation Detection – Or Is It?
- PART III BIASED AND UNBIASED JUDGMENTS FROM BIASED SAMPLES
- PART IV WHAT INFORMATION CONTENTS ARE SAMPLED?
- PART V VICISSITUDES OF SAMPLING IN THE RESEARCHER'S MIND AND METHOD
- Index
- References
3 - Intuitive Judgments about Sample Size
Published online by Cambridge University Press: 02 February 2010
Book contents
- Frontmatter
- Contents
- List of Contributors
- PART I INTRODUCTION
- PART II THE PSYCHOLOGICAL LAW OF LARGE NUMBERS
- 2 Good Sampling, Distorted Views: The Perception of Variability
- 3 Intuitive Judgments about Sample Size
- 4 The Role of Information Sampling in Risky Choice
- 5 Less Is More in Covariation Detection – Or Is It?
- PART III BIASED AND UNBIASED JUDGMENTS FROM BIASED SAMPLES
- PART IV WHAT INFORMATION CONTENTS ARE SAMPLED?
- PART V VICISSITUDES OF SAMPLING IN THE RESEARCHER'S MIND AND METHOD
- Index
- References
Summary
Suppose a state election is coming up in a certain European country and somebody asks you if you would bet on whether the Social Democrats will beat the Christian Democrats again as they did in the last election. Shortly before Election Day, you are presented the results of two opinion polls, based on random samples of either 100 or 1,000 voters. In the smaller sample, the Social Democrats have an advantage of 4 percentage points whereas in the larger sample, the Christian Democrats lead by the same amount. Would you take the bet? You probably would not and I assume that this would be the choice of most people asked this question. As we will see later, your choice would be justified on both empirical and theoretical grounds.
This chapter offers an explanation for how and when the “naïve intuitive statistician” (Fiedler & Juslin, this volume) understands the impact that the size of a sample should have on estimates about population parameters such as proportions or means. I will argue that, in general, people know intuitively that larger (random) samples yield more exact estimates of population means and proportions than smaller samples and that one should have more confidence in these estimates the larger the size of the sample. My main claim is that the size-confidence intuition – an intuition that properly captures the relationship between sample size and accuracy of estimates – governs people's judgments about sample size. This intuition can be regarded as the result of associative learning.
- Type
- Chapter
- Information
- Information Sampling and Adaptive Cognition , pp. 53 - 71Publisher: Cambridge University PressPrint publication year: 2005
References
(1979). Robust locally weighted regression and smoothing scatterplots. Journal of the American Statistical Association, 74, 829–836CrossRefGoogle Scholar
(1962). The statistical power of abnormal-social psychological research. Journal of Abnormal and Social Psychology, 65, 145–153CrossRefGoogle ScholarPubMed
, & (2004). Zum Verständnis von Zufall und Variabilität in empirischen Daten bei Schülern. [School students' understanding of chance and variability in empirical data]Unterrichtswissenschaft, 32, 169–191Google Scholar
(1964). Absolute judgments of discrete quantities randomly distributed over time. Journal of Experimental Psychology, 57, 475–482CrossRefGoogle Scholar
, & (1977). Proportionality and sample size as factors in intuitive statistical judgement. Acta Psychologica, 41, 129–137CrossRefGoogle Scholar
, & (1985). Intuitive statistical inferences about normally distributed data. Acta Psychologica, 60, 57–71CrossRefGoogle Scholar
(1991). The tricky nature of skewed frequency tables: An information loss account of distinctiveness-based illusory correlations. Journal of Personality and Social Psychology, 60, 24–36CrossRefGoogle Scholar
(1996). Explaining and simulating judgment biases as an aggregation phenomenon in probabilistic, multiple-cue environments. Psychological Review, 103, 193–214CrossRefGoogle Scholar
(2000). Beware of samples! A cognitive–ecological sampling approach to judgment biases. Psychological Review, 107, 659–676CrossRefGoogle ScholarPubMed
, , , & (2000). A sampling approach to biases in conditional probability judgments: Beyond baserate neglect and statistical format. Journal of Experimental Psychology: General, 129, 1–20Google Scholar
, , , & (2002). Judgment biases in a simulated classroom – A cognitive-environmental approach. Organizational Behavior and Human Decision Processes, 88, 527–561CrossRefGoogle Scholar
(1975). The intuitive sources of probabilistic thinking in children. Reidel: Dordrecht-HollandCrossRefGoogle Scholar
Haberstroh, S., & Betsch, T. (2002). Online strategies versus memory-based strategies in frequency estimation. In & (Eds.), Etc. Frequency processing and cognition (pp. 205–220). Oxford: Oxford University PressCrossRefGoogle Scholar
, & (1976). Illusory correlation in interpersonal perception: A cognitive basis of stereotypic judgments. Journal of Experimental Social Psychology, 12, 392–407CrossRefGoogle Scholar
, & (1972). Subjective probability: A judgment of representativeness. Cognitive Psychology, 3, 430–454CrossRefGoogle Scholar
, & (1989). Hypothesis testing in rule discovery: Strategy, structure and content. Journal of Experimental Psychology: Learning, Memory and Cognition, 15, 596–604Google Scholar
, & (2003). Imagination can create false autobiographical memories. Psychological Science, 14, 186–188CrossRefGoogle ScholarPubMed
, , , & (1983). The use of statistical heuristics in everyday inductive reasoning. Psychological Review, 90, 339–363CrossRefGoogle Scholar
(1986). Statistical inference: A commentary for the social and behavioral sciences. New York: WileyGoogle Scholar
(1989). Variations on a seminal demonstration of people's insensitivity to sample size. Organizational Behavior and Human Decision Processes, 43, 52–57CrossRefGoogle Scholar
(2003). Comparing Bayes's theorem to frequency-based approaches to teaching Bayesian reasoning. Teaching of Psychology, 30, 325–328Google Scholar
(1998). The distribution matters: Two types of sample-size tasks. Journal of Behavioral Decision Making, 11, 281–3013.0.CO;2-U>CrossRefGoogle Scholar
(1999). Improving statistical reasoning: Theoretical models and practical implications. Mahwah, NJ: Lawrence ErlbaumGoogle Scholar
Sedlmeier, P. (2002). Associative learning and frequency judgments: The PASS model. In & (Eds.), Etc. Frequency processing and cognition (pp. 137–152). Oxford: Oxford University PressCrossRefGoogle Scholar
Sedlmeier, P. (2003). Simulation of estimates of relative frequency and probability for serially presented patterns. Unpublished raw data
Sedlmeier, P. (2005). From associations to intuitive judgment and decision making: Implicitly learning from experience. In & (Eds.), Experience-based decision making (pp. 83–99). Mahwah, NJ: Lawrence ErlbaumGoogle Scholar
, & (1989). Do studies of statistical power have an effect on the power of studies?Psychological Bulletin, 107, 309–316CrossRefGoogle Scholar
, & (1997). Intuitions about sample size: The empirical law of large numbers. Journal of Behavioral Decision Making, 10, 33–513.0.CO;2-6>CrossRefGoogle Scholar
, & (2000). Was Bernoulli wrong? On intuitions about sample size. Journal of Behavioral Decision Making, 13, 133–1393.0.CO;2-H>CrossRefGoogle Scholar
, & (2001). Teaching Bayesian reasoning in less than two hours. Journal of Experimental Psychology: General, 130, 380–400CrossRefGoogle ScholarPubMed
, , & (1998). Are judgments of the positional frequencies of letters systematically biased due to availability?Journal of Experimental Psychology: Learning, Memory, and Cognition, 24, 754–770Google Scholar
, & (2004). The hazards of underspecified models: the case of symmetry in everyday predictions. Psychological Review, 111, 770–780CrossRefGoogle ScholarPubMed
, & (2001). Wahrscheinlichkeiten im Alltag: Statistik ohne Formeln. [Probabilities in everyday life: statistics without formula]. Braunschweig: Westermann (textbook with CD)Google Scholar
, & (2004). Attentional processes and judgments about frequency: Does more attention lead to higher estimates? Manuscript submitted for publicationGoogle Scholar
(1995). The psychology of associative learning. Cambridge, UK: Cambridge University PressCrossRefGoogle Scholar
, & (1971). Belief in the law of small numbers. Psychological Bulletin, 73, 105–110CrossRefGoogle Scholar
, , & (2002). Entscheidungsfindung unter Unsicherheit als fächerübergreifende Kompetenz. Zeitschrift für Pädagogik, 45 (Suppl.), 35–50Google Scholar
, & (2000). Subitizing and its subprocesses. Psychological Research, 64, 81–92CrossRefGoogle ScholarPubMed
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