Chapter 2: Generalization -> how broadly do the results apply?

 What is a population in statistical terms?

A population is a set of units that we are interested in studying. These units are often called

individuals, experimental units, or observational units.

What is a sample?

A sample is a subset of the units of a population used to make inferences about the entire population.

Why is a census often impractical?

A census, which measures a variable for every unit of a population, is often impractical due to

time, cost, and feasibility constraints.

What are the three primary sources of data?

1. Published sources (books, journals, newspapers), 2. Designed experiments (controlled

conditions), 3. Observational studies (natural settings, including surveys).

 What is selection bias?

Selection bias occurs when a subset of the population has little or no chance of being selected,

systematically favoring certain outcomes.This leads to inaccurate conclusions and can skew the results of a study.

What is a representative sample?

A representative sample exhibits characteristics typical of those possessed by the target population

What is a representative sample?

A representative sample exhibits characteristics typical of those possessed by the target

population.

What is voluntary response bias?

It occurs when individuals choose themselves to be part of a sample, often leading to

overrepresentation of strong opinions (e.g., online polls).

What is convenience sampling?

A non-random sampling method where individuals easiest to reach are chosen, often leading to

bias (e.g., social media surveys).

What is undercoverage bias?

It occurs when some groups in the population are left out of the sampling process, leading to an unrepresentative sample.

How can nonresponse bias be mitigated?

By using incentives, call-backs, well-trained interviewers, and assurances of confidentiality.

What is simple random sampling (SRS)?

A sampling method where every subset of a fixed size has the same chance of being selected,

ensuring fairness.

What is the Central Limit Theorem (CLT)?

The CLT states that for a sufficiently large sample size, the sampling distribution of the sample

mean will be approximately normal, regardless of the original population distribution.

What is the finite population correction factor?

A factor used to adjust the standard deviation of a sampling distribution when the sample size is a

significant fraction of the total population.

What are the measures of the center?

They describe central tendencies in data, such as mean, median, and mode, which summarize and represent the typical values in a dataset.

What are the measure of the center?

They describe central tendencies in data, including the mean, median, and mode.

How is the mean calculated?

The mean is the sum of all values divided by the total number of observations.

How is the median calculated?

The median is the middle value when data is ordered; if even, it's the average of the two middle

values.

How is the mode determined?

The mode is the most frequently occurring value in a dataset. A dataset can be unimodal,

bimodal, or multimodal.

What is the difference between mean and median?

The mean is sensitive to extreme values, while the median is more resistant to outliers, making it

a better measure for skewed data.

What is range?

The range is the difference between the maximum and minimum values in a dataset.

What is standard deviation?

A measure of data spread that quantifies the average deviation from the mean.

 What is variance?

Variance is the squared average of the deviations from the mean and is the square of the

standard deviation.

s^2 = sum (x_i - bar_x)^2 /n-1

What is the standard error of the mean?

The standard deviation of the sample mean distribution, calculated as population standard

deviation divided by the square root of the sample size.

 What is the t-distribution?

A probability distribution used instead of the normal distribution when the sample size is small

and the population standard deviation is unknown.

How do t-distributions differ from normal distributions?

T-distributions have thicker tails, allowing for more variability, and approach the normal

distribution as sample size increases.

What is bootstrapping?

A resampling method where new samples are generated from an existing sample, with

replacement, to estimate sampling variability.

What is response bias?

Response bias occurs when survey respondents provide incorrect or misleading answers, often

due to question wording, interviewer influence, or memory issues.

What are the validity conditions for the One-Sample t-Test?

The quantitative variables should have a symmetric distribution, or you should have at least 20 observations, and the sample distribution should not be strongly skewed.