Module 5 - Manley Ch 6 - Generalizations

Question 1

What is a statistical inference?

Answer 1

Using specific observations as evidence for general claims about a larger group, or vice versa.

Question 2

What is the difference between a statistical generalization and a statistical instantiation?

Answer 2

Generalization: Moves from a sample to conclusions about the whole population.

Instantiation: Moves from known facts about the population to conclusions about a sample.

Question 3

Why is forming appropriate generalizations difficult?

Answer 3

It requires careful sampling, avoiding biases, and understanding probability, which is why the field of statistics exists.

Question 4

When does a sample provide strong evidence for a hypothesis?

Answer 4

When the likelihood of observing the sample is much greater if the hypothesis is true than if it is false.

Question 5

What factors weaken the reliability of a sample?

Answer 5

Small sample size

Sampling bias (e.g., non-random or convenience sampling)

Question 6

What is sampling bias?

Answer 6

A selection effect where the method of choosing the sample skews the results, making them unrepresentative of the population.

Question 7

How can experiments be designed to reduce sampling bias?

Answer 7

By ensuring the sample is random and representative of the population.

Question 8

Why is a larger sample size important?

Answer 8

It increases the likelihood that the sample’s proportions closely resemble those of the whole population.

Question 9

What is the law of large numbers?

Answer 9

The principle that larger samples tend to reflect the true distribution of the population more accurately.

Question 10

Why do smaller samples often have more extreme proportions?

Answer 10

Because random variation has a larger effect on smaller groups, leading to greater deviations from the population average.

Question 11

Why might small counties show extreme rates of a disease compared to larger ones?

Answer 11

Small samples are more prone to random fluctuations, leading to unusually high or low rates.

Question 12

Why are the hospitals or schools with the “best” or “worst” rates often small ones?

Answer 12

Small sample sizes magnify the effects of random variation, making extreme outcomes more likely.

Question 13

What should you consider when interpreting extreme results in small samples?

Answer 13

Whether the results could be explained by random variation rather than true differences.

Question 14

How do you test the strength of evidence?

Answer 14

By comparing the likelihood of observing the evidence if the hypothesis is true versus if it is false.

Question 15

Why is it important to design experiments where evidence strongly distinguishes between hypotheses?

Answer 15

To ensure that the observations are far more likely under one hypothesis than the other, making the evidence meaningful.

Question 16

What is stratified sampling?

Answer 16

A method of sampling where the sample is divided into subgroups (strata) that match the population’s proportions for specific characteristics.

Question 17

Why does sample size matter in statistical generalizations?

Answer 17

Larger samples are more likely to reflect the true characteristics of the population and reduce the margin of error.

Question 18

What does a 95% confidence interval mean?

Answer 18

If the true population value lies outside the interval, the observed result would occur only 5% of the time.

Question 19

Why is random sampling important?

Answer 19

It minimizes selection effects and ensures that the sample is representative of the population.

Question 20

What are some common issues with non-random sampling methods?

Answer 20

Oversampling certain groups (e.g., cars on low-traffic roads).

Failing to account for relevant subgroups.

Bias from convenience sampling.

Question 21

How does stratified sampling reduce bias?

Answer 21

By ensuring the sample mirrors the population in terms of characteristics like age, gender, or car type.

Question 22

Why does stratification not replace randomization?

Answer 22

There may be unconsidered subgroups or hidden biases, so random sampling within strata is still essential.

Question 23

What is participation bias in surveys?

Answer 23

When certain groups are more likely to participate than others, skewing the sample.

Question 24

How can offering cash incentives for survey participation still lead to bias?

Answer 24

The fixed amount may motivate some groups more than others, leaving the sample unrepresentative.

Question 25

What is response bias?

Answer 25

When participants give answers that are socially acceptable, avoid embarrassment, or reflect ignorance.

Question 26

How can the wording of a survey question introduce bias?

Answer 26

Different terms or phrasings can evoke different emotional responses, leading to skewed results (e.g., “death tax” vs. “estate tax”).

Question 27

What should you do if you cannot eliminate all selection effects in sampling?

Answer 27

Use randomization and stratification to minimize bias as much as possible.

Question 28

Why are voluntary surveys particularly prone to bias?

Answer 28

They attract participants with strong opinions, skewing results toward those who care most about the topic.

Question 29

What are the two key questions we must answer when summarizing statistical data?

Answer 29

What features of the data are most important to us?

What’s the clearest way to present those features?

Question 30

Why can statistical summaries be misleading?

Answer 30

They omit some facts and can be selectively presented to make true but misleading claims.

Question 31

What are the three main measures of central tendency?

Answer 31

Mean, median, and mode.

Question 32

When is the mean most useful?

Answer 32

When calculating the total of a quantitative feature or when outliers do not significantly skew the data.

Question 33

Why might the median be preferred over the mean?

Answer 33

The median resists being skewed by outliers and better reflects the “typical” value in some cases.

Question 34

What is the mode?

Answer 34

The value that appears most frequently in a dataset.

Question 35

What is an outlier?

Answer 35

A data point that is significantly different from other values in the dataset.

Question 36

How does a truncated mean handle outliers?

Answer 36

It calculates the mean after excluding extreme outliers.

Question 37

Why is visualizing the shape of data important?

Answer 37

It helps identify patterns, distributions, and inequalities that measures like the mean or median cannot capture.

Question 38

What does the standard deviation measure?

Answer 38

The average distance of data points from the mean, giving a sense of variability in the dataset.

Question 39

What is cherry-picking data, and why is it misleading?

Answer 39

Selecting specific data points to create a false impression of a trend while ignoring the full dataset.

Question 40

What are loose generalizations?

Answer 40

Vague or unclear generalizations, often expressed as “Most Fs are Gs” or “Many Fs are Gs,” without clear evidence or definition.

Question 41

What is a stereotype?

Answer 41

A widely held loose generalization about a social group, often influenced by in-group bias.

Question 42

Why are loose generalizations problematic?

Answer 42

They can smuggle false or misleading ideas under the guise of truth and are often vague enough to evade scrutiny.

Question 43

How can even true generalizations be misleading?

Answer 43

They might imply a causal or explanatory relationship where none exists, confusing the true cause of a phenomenon.

Question 44

Give an example of a true but misleading generalization.

Answer 44

“Older women are dangerous drivers.” While true on average, it misrepresents the real cause: visual and cognitive decline that affects some seniors, regardless of gender.

Question 45

What is the representativeness heuristic?

Answer 45

A cognitive shortcut where people estimate probabilities based on how strongly two features are associated in their minds, rather than actual statistical relationships.

Question 46

What is an example of the representativeness heuristic in action?

Answer 46

Judging “Linda is a bank teller and active in the feminist movement” as more probable than “Linda is a bank teller,” despite it being statistically impossible.

Question 47

What is base rate neglect?

Answer 47

Ignoring the general prevalence of events or conditions when assessing probabilities.

Question 48

How does base rate neglect affect decision-making?

Answer 48

It leads to errors by focusing on specific details or similarities while ignoring how common each possibility is overall.

Question 49

How can we make better generalizations?

Answer 49

Ensure clarity by defining terms and specifying proportions.

Avoid causal implications unless they are supported by evidence.

Consider base rates and broader context before drawing conclusions.

Question 50

Why is clarity important in generalizations?

Answer 50

It prevents vague or misleading interpretations and forces accountability for claims.