Principles of Experimental Design and Summarizing Data

Vocabulary flashcards covering principles of experimental design, observational studies, numerical summaries, distribution shape features, robust statistics, and linear modeling concepts.

Control (Experimental Design)

The principle of experimental design that requires comparing a treatment group of interest to a baseline control group.

Randomization

The experimental design principle of randomly assigning subjects to treatment groups and taking random samples from the population whenever possible.

Replication

The principle of experimental design that involves collecting a sufficiently large sample within a study or repeating the entire study.

Blocking

The practice of grouping subjects into blocks based on variables known or suspected to affect the response variable, then randomizing subjects within each block to treatment groups.

Scope of Inference Matrix

A 2x2 framework illustrating how random sampling allows conclusions to be generalized to the population, while random assignment allows for causal conclusions.

Observational Study

A study in which researchers observe cases and measure variables without manipulating conditions or assigning treatments.

Confounding Variable

An extraneous variable that correlates with both the explanatory variable and the response variable, potentially creating a false appearance of a causal relationship.

Sample Statistic

A numerical summary value computed from sample data, which serves as a point estimate for a population parameter.

Population Parameter

A numerical summary value for an entire population, whose exact value is typically unknown because full population data are rarely available.

Sample Mean

The average value of a sample, denoted as $\bar{x}$, calculated as $\bar{x} = \frac{x_1 + x_2 + \dots + x_n}{n}$.

Median

The midpoint value (50th percentile) that splits ordered data in half; if there is an even number of observations, it is the average of the middle two values.

Histogram

A visual display of data density where higher bars represent ranges of values that are relatively more common.

Unimodal Distribution

A distribution whose histogram displays a single prominent peak.

Bimodal Distribution

A distribution whose histogram displays two prominent peaks.

Multimodal Distribution

A distribution whose histogram displays several prominent peaks.

Right-Skewed Distribution

A distribution with a long tail extending to the right, where the mean is typically greater than the median ($\text{mean} > \text{median}$).

Left-Skewed Distribution

A distribution with a long tail extending to the left, where the mean is typically less than the median ($\text{mean} < \text{median}$).

Robust Statistics

Summary metrics, such as the median and interquartile range (IQR), that are resistant to the effects of extreme outliers and skewness.

Correlation Coefficient ($R$)

A measure ranging from $-1$ to $+1$ that describes the strength and direction of the linear relationship between two numerical variables.

Residual

The difference between an observed value and the value predicted by a linear model, calculated as $\text{Residual} = \text{Data} - \text{Fit}$.