STP 231 - Chapter 2

Undercoverage

A type of sampling bias where some groups are excluded or rarely selected.

Nonresponse

A type of sampling bias when selected individuals fail or refuse to respond.

Self-selection

A type of sampling bias where individuals choose for themselves whether to participate.

Response bias

A type of sampling bias where answers are inaccurate or influenced by how the question was asked.

Leading wording

A cause of response bias whereby the way a question is phrased biases the response.

Variable types: Categorical

A variable that can be divided into categories, such as blood type.

Variable types: Quantitative

A variable that represents numerical amounts, such as number of doctor visits.

Dotplot

A graphical display that plots individual data points.

Histogram

A graphical display that shows the frequency of data within specified intervals.

Mean

The average of a set of observations calculated by summing the observations and dividing by the number of observations.

Median

The middle value of an ordered data set.

Standard deviation

A measure of the amount of variation or dispersion in a set of values.

Interquartile range (IQR)

The difference between the first (Q1) and third (Q3) quartiles, measuring the spread of the middle 50% of the data.

Outlier

An observation that lies outside the overall pattern of a distribution.

1.5 x IQR Rule

A method for identifying suspected outliers by calculating lower and upper fences.

Boxplot

A graphical display of the five-number summary: minimum, first quartile (Q1), median, third quartile (Q3), and maximum.

Five-number summary

A summary that includes the minimum, first quartile (Q1), median, third quartile (Q3), and maximum values.

Degrees of freedom

The number of values in a calculation that are free to vary, usually calculated as n-1 for sample statistics.

Percentiles

Values below which a certain percentage of observations fall.

Sampling bias

The bias that occurs when the sample selected is not representative of the population.

Response bias

Bias that occurs due to inaccuracies in responses due to question wording or other influences.

Self-selection bias

Bias that occurs when individuals decide whether to participate in a study.

Undercoverage bias

Bias that arises when certain groups in the population are inadequately represented in the sample.

Undercoverage

A type of sampling bias where some groups in the population are left out or underrepresented in the process of choosing the sample.

Nonresponse

A type of sampling bias that occurs when an individual chosen for the sample cannot be contacted or refuses to participate.

Self-selection

A type of sampling bias occurring when individuals voluntarily choose whether to join a study or sample.

Response bias

A type of sampling bias that occurs when respondents provide inaccurate answers due to question phrasing, interviewer behavior, or social desirability.

Leading wording

A cause of response bias where the phrasing of a question subtly influences respondents toward a specific answer.

Categorical variable

A variable that places an individual into one of several groups or categories, such as blood type or eye color.

Quantitative variable

A variable that takes numerical values for which arithmetic operations such as adding and averaging make sense.

Dotplot

A simple graphical display where each data value is shown as a point above its location on a number line.

Histogram

A display for quantitative data that shows the frequency or relative frequency of values falling within consecutive, equal-width bins.

Mean

The arithmetic average of a quantitative data set, calculated by dividing the sum of all observations by the sample size $n$.

Median

The physical midpoint of an ordered set of quantitative data, dividing the observations into two equal halves.

Standard deviation

A measure of the average distance of quantitative observations from their mean.

Interquartile range (IQR)

The range of the middle $50\%$ of quantitative observations, calculated as $IQR = Q_3 - Q_1$.

1.5 x IQR Rule

A criterion for identifying suspected outliers: values falling below $Q_1 - 1.5 \times IQR$ or above $Q_3 + 1.5 \times IQR$.

Five-number summary

A summary set for quantitative data consisting of Minimum, $Q_1$, Median, $Q_3$, and Maximum.

Simple Random Sample (SRS)

A sampling design in which every group of $n$ individuals in the population has an equal chance of being selected as the sample.

Stratified random sample

A sampling method formed by dividing the population into homogenous groups called strata and taking a random sample from each stratum.

Cluster sample

A sampling method created by dividing the population into heterogeneous groups called clusters, then randomly selecting entire clusters to sample.

Systematic sample

A sampling method in which individuals are chosen at a fixed interval from an ordered population list, such as every $k^{\text{th}}$ person.

Convenience sample

A non-random sampling method that selects individuals who are easiest to reach, leading to unrepresentative data.

Observational study

A study that gathers data on individuals without attempting to influence or manipulate any treatment or condition.

Experiment

A study that intentionally imposes a treatment on subjects to observe and measure the resulting responses.

Confounding variable

A variable related to both the explanatory and response variables, making it difficult to isolate the true cause of the effect.

Explanatory variable

A variable whose changes help explain or predict changes in the response variable.

Response variable

A variable that measures an outcome or result of a study.

Z-score

A measure of how many standard deviations an observation falls above or below the mean, calculated as $z = \frac{x - \mu}{\sigma}$.

Right-skewed distribution

A quantitative distribution shape where the right tail (higher values) is longer than the left tail, typically causing the mean to be greater than the median.

Left-skewed distribution

A quantitative distribution shape where the left tail (lower values) is longer than the right tail, typically causing the mean to be less than the median.

Variance

A measure of spread equal to the average squared distance of observations from their mean, denoted as $s^2$ or $\sigma^2$.