Ch 6: Generalizations

base rate: the overall proportion or probability of a feature in general or in the population at large. 

central tendency: a value meant to summarize a set of observations by reporting the typical, principal, or middle point in the distribution of value(s) observed in the dataset. Measures of central tendency include the arithmetic mean, truncated mean, median, mode, and geometric mean. These are defined in section 6.3. They differ with respect to their resistance to outliers, among other things. For example, if we are concerned about something like the average productivity of a large group, because we're interested in what the group can achieve taken together, we may not want to be resistant to outliers. So, in this case, the arithmetic mean would be appropriate. But in other contexts, we might be concerned about something like the wealth of a normal person in a group where a very small number of people have enormous wealth. Here the median is likely a better measure.

confidence interval: roughly, the interval such that there is a low probability (less than .05, in the case of a 95 percent confidence interval) that if the true percentage in the population were outside the interval, a sample like this would have yielded the value it did. The size of this interval in either direction from the given value is called the margin of error. 

convenience sample: a set of observations that is small and carelessly selected. Such samples generally do not provide much evidence for hypotheses because small samples can easily fail to match the population as a whole. Moreover, the examples that are conveniently available to us tend to be subject to selection effects. 

geometric mean: given n values, the geometric mean is the nth root of the product of those values.

​heuristic: a cognitive shortcut used to bypass the more effortful type of reasoning that would be needed to reach an accurate answer. Heuristics are susceptible to systematic and predictable errors. 

law of large numbers: the larger a sample, the more likely it is that its proportions closely reflect those of the population as a whole. Consider tossing a coin. After only a few coins, you may have a very high or low percentage of heads. However, it would be extremely unlikely to have even 2/3 of coin tosses come up heads after many tosses. Instead, the series start to converge on the true distribution of heads and tails in the "population of coins as a whole," which is 50/50.

loose generalization: when we associate one kind of thing or person with an attribute but we are unclear what proportions we take to be involved. For example, we might believe that Canadians are polite without having much sense of what this means, statistically speaking. Loose generalizations can be expressed using bare plurals (see the chapter titled "Clarity") or with "many" as in "Many Canadians are polite." 

margin of error: see confidence interval.

outlier: an observation that is very distant from a dataset’s central tendency, conventionally three standard deviations. For more on resistance to outliers, see central tendency.

participation bias: a selection effect arising from differences in the target population with regard to willingness to participate in a survey. Those who choose to respond might be importantly different from those who choose not to respond. For example, those with strong opinions and who are less busy are more likely to take part in a survey than those who lack strong opinions or who are busier. 

​representative sample: a sample that has the same sort of variety as its target population, in respects that might affect the probability of possessing the trait being studied. That is, the proportion of every relevant subgroup in a sample matches the proportion of that subgroup in the overall population. A relevant subgroup is any subgroup defined by a feature that there is reason to think might be correlated with the property you are studying. For example, if one is conducting a national poll about political views, the sample should have a proportion of Democrats and Republicans that matches the proportion in the population as a whole. Likewise for any demographic feature that might be correlated with the views being surveyed. Evidence from an unrepresentative sample will have a lower strength factor, as these observations may still be very likely even if the target population does not match the sample.

representativeness heuristic: a heuristic used to answer questions about the statistical relationship between two or more features. Rather than answering that question, when using this heuristic, we ask ourselves about the strength of our mental association between those features. For example, we might be wondering how common a feature F is among individuals that are G and, instead of answering that question, we determine how closely we associate being F with being G.

response bias: an effect whereby responses reported by respondents to a survey differ from their true value due to their beliefs or expectations about what answers are expected of them. For example, respondents may not know the answer or may lack an opinion, but be embarrassed to say so. Another example is when respondents believe that a particular answer is expected. For these reasons, it is especially important to avoid loaded questions, which can skew participants’ expectations, and then skew results. For example, referring to a “death tax” as opposed to an “estate tax” will likely lead to more negative participant responses, which may not reflect participants’ underlying opinions.

sampling bias: a selection effect in a sample created by the way in which we are sampling the population. 

statistical generalization: an inference made about a population based on features of a sample.

statistical inference: an inference that uses specific observations as evidence for general claims of which they are instances—or vice versa.

statistical instantiation: an inference made about a sample based on features of a population.

stereotype: a widely held loose generalization about a social group. For example, “Canadians are polite.” Stereotypes can pose problems because they are often too unclear to assess for accuracy, they commonly lead to failures of communication, and they are highly subject to in-group bias.

stratified random sampling: a way of trying to achieve a representative sample by ensuring that the proportions of relevant subgroups in your sample match those of the corresponding subgroups within the population as a whole (see representative sample). First, the population to be sampled is divided into subgroups, one for each relevant feature. Then, a simple random sample is taken from each subgroup, with sizes proportional to the population in each group. These simple random samples are then combined to create the complete sample.

summary statistics: the practice of summarizing and reporting statistical data. This involves making decisions about what the most important facts are, and how best to present them.