Question

Question 5. (twenty marks)

(a) How does the ‘law of small numbers’ affect the interpretation of data? (six marks, maximum 100 words)

(b) Two alternatives to buffer against psychological frailties in the interpretation of data are • use of a specified p-value for the Type I error rate (typically 0.05), or • routine use of confidence intervals. Which of these two alternatives is better in your opinion? Why? (twelve marks, maximum 250 words)

(c) A p-value is the probability of observing a particular data set given a hypothesis, Pr (data | hypothesis). Bayesian statisticians use Bayes’ theorem and prior information to calculate a different quantity. Describe the quantity Bayesian statisticians use, in one sentence. (two marks)

Answer 1

A) the law of small numbers refers to a cognitive bias of generalising a set of findings based on a small sample as true for a large set of scores or population. It is also called hasty generalisation in statistics as one may derive a broad and rushed conclusion from insufficient evidence without considering all of the variables. As such, the results based on small sets of data are likely to be misleading and not representative of the true state of affairs in the population. . According to social psychologist Daniel Kahneman, this is reinforced by a common misconception that random numbers don’t generate patterns or form clusters. But In reality they often do.

Often enough, Researchers don’t pay enough attention to calculating the required sample size and instead use rules of thumb. The law of small numbers raises problems for the correct interpretation of data in research as firstly it makes the researchers prone to select too small a sample size which may lead to a potentially large sampling error in the final results. This makes the people more prone to jumping conclusions and to construct a vision of reality that appears coherent and believable. Thus, the law of small numbers leads to exaggerating the consistency and meaning of what the researchers see. When it goes unchecked, it increases the tendency for causal thinking that is to see a statistically significant relationship when there isn’t one.