C955 Applied Probability and Statistics - Set 4 - Part 2

Correct Answer: Small differences can be visually exaggerated

When the axis is truncated, the relative heights of bars misrepresent the true ratio between values, exaggerating small differences.

Correct Answer: Parts of a whole as proportions of a single total

A pie chart shows how a single total divides into categories, though it becomes hard to read with many slices or similar-sized segments.

Correct Answer: Observations of a variable collected at successive points in time

Time series data records a variable at ordered time points, allowing analysis of trends, seasonality, and change over time.

Correct Answer: A long-term increase or decrease in the data

A trend is the general long-term direction of movement in a time series, distinct from short-term fluctuations or seasonal cycles.

Correct Answer: A repeating pattern tied to calendar periods

Seasonality is a regular repeating pattern that recurs over fixed periods, such as higher retail sales each December.

Correct Answer: The difference between an observed value and the predicted value

A residual is the vertical distance between an actual data point and the value the regression line predicts, measuring prediction error for that point.

Correct Answer: The sum of squared residuals

Least squares chooses the line that minimizes the sum of the squared vertical distances between the observed points and the line.

Correct Answer: Whether a linear model is appropriate for the data

A residual plot reveals patterns indicating model problems. Random scatter suggests a good linear fit, while a curved pattern suggests a linear model is inappropriate.

Correct Answer: A linear model does not adequately fit the data

A systematic curve in residuals means the linear model misses a nonlinear relationship, so a different model form is needed.

Correct Answer: Predicting within the range of observed data

Interpolation makes predictions within the range of the data used to build the model, where the fitted relationship is supported by evidence.

Correct Answer: An unmeasured variable influencing the observed relationship

A lurking variable is not included in the analysis but affects the variables studied, potentially creating a misleading apparent relationship between them.

Correct Answer: A trend appearing in groups can reverse when the groups are combined

Simpson's paradox occurs when an association present within each subgroup disappears or reverses when the subgroups are aggregated, often due to a confounding variable.

Correct Answer: Aggregated data can mislead if important subgroups are ignored

Simpson's paradox warns that combining groups can conceal or reverse real patterns, so relevant subgroup structure must be considered in analysis.

Correct Answer: Identifying and correcting errors and inconsistencies before analysis

Data cleaning detects and fixes errors, missing values, and inconsistencies so that analysis is based on accurate, reliable data.

Correct Answer: Flawed input data produces flawed conclusions regardless of method

Even sophisticated analysis cannot rescue conclusions built on inaccurate or biased data, so data quality fundamentally limits the validity of results.

Correct Answer: Values that were not recorded for some observations

Missing data are absent values for some cases, which can bias results if the reason for missingness is related to the variables being studied.

Correct Answer: Distortion arising when those who do not respond differ from those who do

Nonresponse bias occurs when the people who decline to participate differ systematically from respondents, making the sample unrepresentative of the population.

Correct Answer: Leading or loaded wording can push respondents toward particular answers

Leading, emotionally charged, or confusing wording can steer respondents, producing answers that reflect the question's framing rather than genuine opinion.

Correct Answer: Systematic inaccuracy in the answers respondents provide

Response bias arises when respondents give inaccurate answers, for example due to social desirability, recall errors, or misleading question wording.

Correct Answer: It tests questions and procedures to identify problems early

A pilot study tests questions, timing, and procedures on a small scale, revealing ambiguities and logistical problems before committing to the full survey.