Understanding the effects of sample size on the variability of the mean

In the first three experiments, we attempted to learn more about subjects' understanding of the importance of sample size by systematically changing aspects of the problems we gave to subjects. In a fourth study, understanding of the effects of sample size was tested as subjects went through a computerassisted training procedure that dealt with random sampling and the sampling distribution of the mean. Subjects used sample size information more appropriately for problems that were stated in terms of the accuracy of the sample average or the center of the sampling distribution than for problems stated in terms of the tails of the sampling distribution. Apparently, people understand that the means of larger samples are more likely to resemble the population mean but not the implications of this fact for the variability of the mean. The fourth experiment showed that although instruction about the sampling distribution of the mean led to better understanding of the effects of sample size, subjects were still unable to make correct inferences about the variability of the mean. The appreciation that people have for some aspects of the law of large numbers does not seem to result from an in-depth understanding of the relation between sample size and variability.     

Relative judgments affect assessments of stimulus duration

Humans were trained on two independent temporal discriminations, with correct choice dependent on the initial stimulus duration. In Experiment 1, the durations were 1.0 and 4.0 sec, with one set of choice stimuli, and 2.0 and 8.0 sec, with a different set of choice stimuli. The 2.0- and 4.0-sec values were selected to be the geometric mean of the two values in the other discrimination. In Experiment 2, the durations were 2.0 and 5.0 sec for one discrimination and 3.5 and 6.5 sec for the other. The 3.5- and 5.0-sec values were selected to be the arithmetic mean of the two values in the other discrimination. In both experiments, participants showed evidence for relational coding of the duration pairs. That is, the test durations were selected to be at the presumed bisection point (i.e., they should have produced indifferent choice), but instead the shorter test duration from the longer duration pair produced a “short” bias (in both experiments), whereas the longer duration from the shorter duration pair produced a “long” bias (in the second experiment). Results were similar to those from Zentall, Weaver, and Clement (2004) with pigeons.     

大学生对穷人的消极刻板印象及猜测偏向

主要考察大学生对穷人的消极刻板印象及猜测偏向。实验1中的两个单类内隐联想测验结果与前人研究基本一致：虽然被试对穷人热情的评价相对积极,但总体上认为穷人低能力、低热情。实验2通过源监测任务发现,在忘记特质词来源的情况下,被试倾向于猜测消极特质词来自贫困者,积极特质词来自小康者。研究不仅证实了大学生对穷人的消极刻板印象,而且进一步发现大学生存在对穷人的消极猜测偏向。     

Subjective probability intervals: how to reduce overconfidence by interval evaluation

Format dependence implies that assessment of the same subjective probability distribution produces different conclusions about over- or underconfidence depending on the assessment format. In 2 experiments, the authors demonstrate that the overconfidence bias that occurs when participants produce intervals for an uncertain quantity is almost abolished when they evaluate the probability that the same intervals include the quantity. The authors successfully apply a method for adaptive adjustment of probability intervals as a debiasing tool and discuss a tentative explanation in terms of a naive sampling model. According to this view, people report their experiences accurately, but they are naive in that they treat both sample proportion and sample dispersion as unbiased estimators, yielding small bias in probability evaluation but strong bias in interval production.     

Perceiving numbers affects the subjective temporal midpoint

Temporal experience can be modulated by several environmental factors. There is increasing evidence that numerical quantity may also influence temporal processes. Here, it is shown that merely looking at numbers causes a bias in a time-bisection task that depends on its magnitude. In the first experiment, a group of healthy subjects was submitted to a time-bisection task in which numerical cues were blocked (blocked design). In the second experiment, a new group of participants performed a time-bisection task in which the previous numbers were all randomly arranged in the same block (intermingled design). Results show that temporal performance is biased when numbers of different magnitude are arranged in an intermingled design. These findings argue for a functional interaction between time and numbers, depending on the implicit extrapolation of the size difference between the displayed numbers rather than on the numerical size itself.     

Belief bias in the perception of sample size adequacy

In two experiments participants were instructed to set aside their own, complete knowledge of a statistical population parameter and to take the perspective of an agent whose knowledge was limited to a random sample. Participants rated the appropriateness of the agent's conclusion about the adequacy of the sample size (which, objectively, was more than adequate). They also rated the agent's intelligence. Whereas previous work suggests that unbelievable statistical conclusions impact reasoning by provoking critical thought which enhances the detection of research flaws, the present studies presented participants an unflawed scenario designed to assess effects of believability on bias. The results included the finding that participants’ complete knowledge did indeed bias their perceptions not only of the adequacy of the sample size, but also of the rationality of the agent drawing the conclusion from the sample. The findings were interpreted in the context of research on belief bias, social attribution, and Theory of Mind.     

Right visual field advantage for perceived contrast: Correlation with an auditory bias and handedness

Studies have suggested that supramodal attentional resources are biased rightward due to asymmetric spatial fields of the two hemispheres. This bias has been observed especially in right-handed subjects. We presented left and right-handed subjects with brief uniform grey visual stimuli in either the left or right visual hemifield. Consistent with the proposed asymmetry in attentional resources, right-handed subjects estimated right hemifield targets as having a higher contrast than physically identical stimuli presented in the left hemifield. Left-handed participants did not show a systematic rightward or leftward bias. However, the group of left-handed participants also took part in a dichotic listening experiment whose results showed that visual bias score correlated positively with ear-advantage in dichotic listening. Our results are consistent with the view that supramodal processing resources are biased towards the right hemispace, and that this bias is influenced by handedness.     

Right visual field advantage for perceived contrast: correlation with an auditory bias and handedness

Studies have suggested that supramodal attentional resources are biased rightward due to asymmetric spatial fields of the two hemispheres. This bias has been observed especially in right-handed subjects. We presented left and right-handed subjects with brief uniform grey visual stimuli in either the left or right visual hemifield. Consistent with the proposed asymmetry in attentional resources, right-handed subjects estimated right hemifield targets as having a higher contrast than physically identical stimuli presented in the left hemifield. Left-handed participants did not show a systematic rightward or leftward bias. However, the group of left-handed participants also took part in a dichotic listening experiment whose results showed that visual bias score correlated positively with ear-advantage in dichotic listening. Our results are consistent with the view that supramodal processing resources are biased towards the right hemispace, and that this bias is influenced by handedness.     

Hindsight bias around the world

Hindsight bias refers to the tendency to overestimate in hindsight what one has known in foresight. Recently, two experiments extended the research to include samples from different cultures (Choi & Nisbett, 2000; Heine & Lehman, 1996). Asking their participants what they would have guessed before they knew the outcome ("hypothetical design"), Choi and Nisbett (2000) found that Koreans, in comparison to North Americans, exhibited more hindsight bias. Heine and Lehman (1996), however, reported that Japanese people in comparison to Canadians showed marginally less hindsight bias. In a second study, in which participants were asked to recall what they had estimated before they knew the outcome ("memory design"), the latter authors found no difference in hindsight bias between Japanese people and Canadians. We extended these studies with 225 Internet participants, in a hypothetical design, from four different continents (Asia, Australia, Europe, and North America). Hindsight bias was large and similar for all samples except for German and Dutch participants who showed no hindsight bias at all. While the latter effect may be based on peculiarities of the material and of the participants, the former underscores the worldwide stability of the phenomenon. In addition a follow-up surprise rating (paper and pencil) in China (35 participants) and Germany (20 participants) revealed that only less surprising items led to hindsight bias while more surprising ones did not. We suggest that the basic cognitive processes leading to hindsight bias are by-products of the evolutionary-evolved capacity of adaptive learning. On top of these basic processes, individual meta-cognitions (e.g., elicited by surprise) or motives (e.g., a self-serving motive) may further moderate the amount of bias, thus explaining the diverging results of Choi and Nisbett (2000), Heine and Lehman (1996), and our own study.     

Physical similarity (and not quantity representation) drives perceptual comparison of numbers: evidence from two Indian notations

Numerical quantity seems to affect the response in any task that involves numbers, even in tasks that do not demand access to quantity (e.g., perceptual tasks). That is, readers seem to activate quantity representations upon the mere presentation of integers. One important piece of evidence in favor of this view comes from the finding of a distance effect in perceptual tasks: When one compares two numbers, response times (RTs) are a function of the numerical distance between them. However, recent studies have suggested that the physical similarity between Arabic numbers is strongly correlated with their numerical distance, and that the former could be a better predictor of RT data in perceptual tasks in which magnitude processing is not required (Cohen, 2009a). The present study explored the Persian and Arabic versions of Indian numbers (Exps. 1 and 2, respectively). Na?ve participants (speakers of Spanish) and users of these notations (Pakistanis and Jordanians) participated in a physical same–different matching task. The RTs of users of the Indian notations were regressed on perceptual similarity (estimated from the Spanish participants’ RTs) and numerical distance. The results showed that, regardless of the degree of correlation between the perceptual similarity function and the numerical distance function, the critical predictor for RTs was perceptual similarity. Thus, participants do not automatically activate Indian integers’ quantity representations, at least not when these numbers are presented in simple perceptual tasks.     

Estimating averages from distributions of tone durations

We examined whether estimating average duration was influenced by the distribution peak location. We presented participants with samples of various tone durations and then presented comparison tone durations. Participants judged whether each comparison duration was longer than the average sample duration. Estimates of the averages were inferred from the psychophysical functions. The durations were sampled from three distributions: one positively skewed, one symmetric, and one negatively skewed. In Experiment 1, every participant was presented with every distribution. Estimates of the averages were unbiased for the symmetric distribution but were biased toward the long tail of each skewed distribution. This would occur if participants combined the sample to be judged with the previous, irrelevant samples, or with the comparison durations. In Experiment 2, each participant was presented with samples from only one of the distributions. Estimates of the averages were still biased toward the long tails of the skewed distributions. This would occur if participants combined the sample to be judged with the comparison durations, which were the same for the three distributions. In Experiment 3, each participant was presented with only one distribution, and each distribution was tested with its own comparison durations, selected as percentiles from the distribution. The estimates were accurate for the smallest population mean (positively skewed distribution) but underestimated the larger means. These results could be explained by subjective shortening of the durations in memory, with a simple equation from scalar timing theory. This equation correctly predicted two results: The estimated averages were a linear function of the stimulus means, and the variances were a linear function of the squared stimulus means. Neither prediction was dependent on the skewness of the stimulus durations.     

Biases in the perceived prevalence and motives of severe acute respiratory syndrome prevention behaviors among Chinese high school students in Hong Kong

In two studies conducted in Hong Kong during and immediately after the outbreak of severe acute respiratory syndrome (SARS), participants displayed several social cognitive biases when they estimated the prevalence of and inferred the motives underlying SARS preventive behaviors. First, participants who practiced preventive behaviors (practicers) consistently estimated that more people practiced such behaviors than did non-practicers (false consensus bias). Second, for some preventive behaviors, participants believed that their own behaviors were more motivated by prosocial concerns (relative to self-interest) than were other practicers (pluralistic ignorance). Finally, non-practicers underestimated the importance of prosocial concerns underlying some preventive behaviors (actor-observer bias). We discussed the relevance of these social cognitive biases to health education and to Hong Kong people's psychological reactions to SARS.     

The spatial representation of numerical and non-numerical ordered sequences: Insights from a random generation task

It is widely believed that numbers are spatially represented from left to right on the mental number line. Whether this spatial format of representation is specific to numbers or is shared by non-numerical ordered sequences remains controversial. When healthy participants are asked to randomly generate digits they show a systematic small-number bias that has been interpreted in terms of “pseudoneglect in number space”. Here we used a random generation task to compare numerical and non-numerical order. Participants performed the task at three different pacing rates and with three types of stimuli (numbers, letters, and months). In addition to a small-number bias for numbers, we observed a bias towards “early” items for letters and no bias for months. The spatial biases for numbers and letters were rate independent and similar in size, but they did not correlate across participants. Moreover, letter generation was qualified by a systematic forward direction along the sequence, suggesting that the ordinal dimension was more salient for letters than for numbers in a task that did not require its explicit processing. The dissociation between numerical and non-numerical orders is consistent with electrophysiological and neuroimaging studies and suggests that they rely on at least partially different mechanisms.     

知觉场理论对面孔知觉年龄偏差效应的解释

使用融合面孔范式和倒置面孔范式来研究面孔知觉的年龄偏差效应,检验知觉场能否作为面孔整体加工的指标,并以此发展年龄偏差的整体加工解释。结果发现：（1）成人和儿童在加工正立面孔时的知觉场均大于加工倒置面孔时的知觉场;（2）在加工正立面孔时,成人加工本年龄面孔比加工他年龄面孔的知觉场更大。上述结果表明：（1）知觉场大小可以作为面孔整体加工的指标,且受面孔朝向的影响;（2）知觉场假设可以解释面孔的年龄偏差效应。     

When you don't have to be exact: Investigating computational estimation skills with a comparison task

The present study is the first systematic investigation of computational estimation skills of multi-digit multiplication problems using an estimation comparison task. In two experiments, participants judged whether an estimated answer to a multi-digit multiplication problem was larger or smaller than a given reference number. Performance was superior in terms of speed and accuracy for smaller problem sizes, for trials in which the reference numbers were smaller vs. larger than the exact answers (consistent with the size effect) and for trials in which the reference numbers were numerically far compared to close to the exact answers (consistent with the distance effect). Strategy analysis showed that two main strategies were used to solve this task—approximate calculation and sense of magnitude. Most participants reported using the two strategies. Strategy choice was influenced by the distance between the reference number and exact answer, and by the interaction of problem size and reference number size. Theoretical implications as to the nature of numerical representations in the ANS (approximate number system) and to the estimation processes are suggested.     

知觉场理论对面孔知觉年龄偏差效应的解释

使用融合面孔范式和倒置面孔范式来研究面孔知觉的年龄偏差效应,检验知觉场能否作为面孔整体加工的指标,并以此发展年龄偏差的整体加工解释。结果发现：（1）成人和儿童在加工正立面孔时的知觉场均大于加工倒置面孔时的知觉场;（2）在加工正立面孔时,成人加工本年龄面孔比加工他年龄面孔的知觉场更大。上述结果表明：（1）知觉场大小可以作为面孔整体加工的指标,且受面孔朝向的影响;（2）知觉场假设可以解释面孔的年龄偏差效应。     

Attentional bias towards angry faces is moderated by the activation of a social processing mode in the general population

ABSTRACT

Dot-probe studies usually find an attentional bias towards threatening stimuli only in anxious participants, but not in non-anxious participants. In the present study, we conducted two experiments to investigate whether attentional bias towards angry faces in unselected samples is moderated by the extent to which the current task requires social processing. In Experiment 1, participants performed a dot-probe task involving classification of either socially meaningful targets (schematic faces) or meaningless targets (scrambled schematic faces). Targets were preceded by two photographic face cues, one angry and one neutral. Angry face cues only produced significant cueing scores (i.e. faster target responses if the target replaced the angry face compared to the neutral face) with socially meaningful targets, not with meaningless targets. In Experiment 2, participants classified only meaningful targets, which were either socially meaningful (schematic faces) or not (schematic houses). Again, mean cueing scores were significantly moderated by the social character of the targets. However, cueing scores in this experiment were non-significant in the social target condition and significantly negative in the non-social target condition. These results suggest that attentional bias towards angry faces in the dot-probe task is moderated by the activation of a social processing mode in unselected samples.     

Outcome-Desirability Bias in Resource Management Problems

Sequences of numbers representing prior resource size were presented to participants in a common-pool resource dilemma. The numbers were sampled from uniform probability distributions with either a low variance (low resource uncertainty) or a high variance (high resource uncertainty). Presentations were both sequential and simultaneous. Three groups of 16 undergraduates either estimated the size of the resource when it did not represent value to them; requested an amount from the resource, identified with a sum of money, when the outcome of the requests only depended on resource size; or requested from the resource (sum of money) when the outcome of the requests depended on both resource size and how much others in a group requested. In support of an individual outcome-desirability bias due to selective recall of the number sequences, after sequential presentation larger requests were observed when resource uncertainty was high than when it was low. No effects of resource uncertainty or presentation were found on the estimates of resource size. Whether or not the outcome of the requests depended on others' requests made little difference.     

差数显著性t检验与元分析方法的模拟对比

利用计算机程序构造被试总体、模拟实验研究程序进行抽样研究 ,探讨差数显著性t检验方法与元分析方法在检验实验结果数据和进行实际应用方面的差异。模拟实验结果表明 ,差数显著性t检验与总体效果大小和样本容量有明显关系 ,但与随机抽样分布样本数目基本无关 ;抽样分布样本效果大小的平均值可以作为总体效果大小的估计值 ,它与样本容量和抽样样本数目有密切关系 ;本研究提供的实际应用数据结果可以作为研究者进行元分析方法实验研究的参考依据     

A solution to the effect of sample size on outlier elimination

Results from a Monte Carlo study demonstrate how a non-recursive, a simple recursive, a modified recursive, and a hybrid outlier elimination procedure are influenced by population skew and sample size. All the procedures are based on computing a mean and a standard deviation from a sample in order to determine whether an observation is an outlier. Miller (1991) showed that the estimated mean produced by the simple non-recursive procedure can be affected by sample size and that this effect can produce a bias in certain kinds of experiments. We extended this result to the other three procedures. We also create two new procedures in which the criterion used to identify outliers is adjusted as a function of sample size so as to produce results that are unaffected by sample size.