Sample Surveys, Experiments, and Regression Review

Flashcards covering key statistical concepts from chapters on sample surveys, experimental design, displaying categorical and quantitative data, distributions, and linear regression.

What is the difference between a population and a sample in statistics?

A population is the entire group of individuals that we want information about, whereas a sample is a subset of the population that is actually examined to gather information.

How is a Simple Random Sample ($SRS$) defined?

A sampling design in which each member of the population has an equal chance of being included.

Under what condition is a sample defined as biased?

A sample is biased if each member of the population does not have an equal chance of being selected.

What is the difference between undercoverage and non-response in sample surveys?

Undercoverage occurs when the entire targeted population is not included in the design of the sample, whereas non-response occurs when a selected individual cannot be contacted or refuses to cooperate.

What are the two types of observational studies based on their temporal direction?

Retrospective studies look backward in time, whereas prospective studies look forward in time.

What are the five principles of experimental design outlined in the notes?

1. Control experimental conditions to ensure lurking variables do not bias results; 2. Randomly assign experimental units to treatments; 3. Use replication to reduce chance variation; 4. Use a placebo or control as one treatment; 5. Use double-blinding for medical experiments.

What is the distinction between a lurking variable and a confounding variable?

A lurking variable is a variable that is not among the explanatory or response variables but influences the interpretation of their relationship. A confounding variable is an additional explanatory variable that affects the response variable but is not considered when exploring the explanatory/response relationship.

What is the difference between a single-blind and a double-blind experiment?

In a single-blind experiment, participants do not know which treatment they have been assigned. In a double-blind experiment, neither the participant nor the researcher taking measurements knows who received which treatment.

Which experimental design is depicted in this flow diagram?

Completely Randomized Design

Which experimental design is depicted in this flow diagram?

Matched Pairs design

Which experimental design is depicted in this flow diagram?

Block Design

How is a conditional proportion calculated in a contingency table?

First condition upon a category to establish the denominator, then divide the specific cell frequency by that denominator.

Which measures of center and spread are resistant to outliers and skewness?

The median and quartiles (or Interquartile Range) are resistant to outliers and skewness, whereas the mean and standard deviation are not resistant.

What equation is used to calculate a $Z$-score?

$$Z = \frac{X - \mu}{\sigma}$$

According to the provided guide, what ranges of $r$ define a moderate correlation?

A moderate positive correlation is $0.3 < r < 0.7$, and a moderate negative correlation is $-0.7 < r < -0.3$.

How does moving standard deviations in $x$ affect standard deviations in $y$ along a regression line?

Moving any number of standard deviations in $x$ moves $r$ times that number of standard deviations in $y$.

How is $R^2$ defined in terms of predictive power, and how is $r$ calculated from $R^2$?

$R^2$ is the percentage of variability in $Y$ that is explained by the regression line. To find $r$ from $R^2$, write $R^2$ as a proportion, take the square root, and check the sign of the slope to determine the sign of $r$.

How is a residual defined, and what do positive and negative residual values mean?

$\text{Residual} = \text{observed } y - \text{predicted } y$. A negative residual means the prediction is too high, while a positive residual means the prediction is too low.

What does a pattern such as fanning or curvature in a residual plot indicate?

It indicates that the regression line is not a good fit for the data.

What is extrapolation, and why is it cautioned against in regression analysis?

Extrapolation is making predictions outside of the range of data collected; it should be avoided because the linear pattern may not hold outside that range.