Statistical Assumptions as Empirical Commitments (original) (raw)

Beliefs underlying random sampling

Memory & Cognition, 1984

In Experiment 1, subjects estimated {1) the mean of a random sample of 10 scores consisting of 9 unknown scores and 1 known score that was divergent from the population mean and {2} the mean of the 9 unknown scores. The modal answer {about 40% of the responses} for both sample means was the population mean. The results extend the work of Tversky and Kahneman {1971} by demonstrating that subjects hold a passive, descriptive view of random sampling rather than an active-balancing model. This result was explored further in in-depth interviews {Experiment 2}, wherein subjects solved the problem while explaining their reasoning. The interview data replicated Experiment 1 and further showed: {1} that subjects' solutions were fairly stable--when presented with alternative solutions, including the correct one, few subjects changed their answers; !2} little evidence of a balancing mechanism; and {3} that acceptance of both means as 400 is largely a result of the perceived unpredictability of "random samples."

Conceptions of sample and their relationship to statistical inference

Educational studies in mathematics, 2002

We distinguish two conceptions of sample and sampling that emerged in the context of a teaching experiment conducted in a high school statistics class. In one conception 'sample as a quasi-proportional, small-scale version of the population' is the encompassing image. This conception entails images of repeating the sampling process and an image of variability among its outcomes that supports reasoning about distributions. In contrast, a sample may be viewed simply as 'a subset of a population'-an encompassing image devoid of repeated sampling, and of ideas of variability that extend to distribution. We argue that the former conception is a powerful one to target for instruction.

The randomization mode of statistical inference.

2010

Abstract How should one estimate and test comparative effects from a field experiment of only 8 units? What does statistical inference mean in this context? In a randomized experiment the most basic and important inference is between the treatments: after all, the point of randomizing is to allow us to say how the treatment group would have behaved had treatment been withheld.

Repeated Sampling as a step towards Informal Statistical Inference

2018

Recent literature suggests that secondary school students should learn about informal statistical inference (ISI) as preparation for formal statistical inference. Not enough is known, however, how to realize this. The design study reported here aimed at developing a theoretically and empirically grounded learning trajectory (LT) on ISI for 9th-grade 14-year-old students. The LT focused on sampling, the frequency distribution of results from repeated samples, and sampling distribution. The current paper reports on the part of the LT on using the frequency distribution of repeated samples as tested with twenty students. The results showed that these students could imagine and sketch the frequency distribution of repeated samples, which indicates a step forward in their understanding of variation and uncertainty in drawing informal statistical inferences.

The Virtues and Limitations of Randomized Experiments

Acta Analytica, 2021

Despite the consensus promoted by the Evidence Based Medicine framework, many authors con-tinue to express doubts about the superiority of Randomized Controlled Trials. This paper evalu-ates four objections targeting the legitimacy, feasibility, and extrapolation problems linked to the experimental practice of random allocation. I argue that random allocation is a methodologically sound and feasible practice contributing to the internal validity of controlled experiments dealing with heterogeneous populations. I emphasize, however, that random allocation is solely designed to ensure the validity of causal inferences at the level of groups. By itself, random allocation can-not enhance test precision, doesn’t contribute to external validity, and limits the applicability of causal claims to individuals.