EXAM 2

Representative sample

A sample from which researchers can draw accurate, unbiased estimates of the characteristics of the population.

Probability sample

A sample in which every individual has a known probability of being selected.

Nonprobability sample

A sample in which the probability of selection is unknown.

When are probability samples necessary?

When researchers want to accurately estimate characteristics of a population.

Why are probability samples usually unnecessary in behavioral research?

Most behavioral research tests relationships between variables rather than estimating population characteristics.

Sampling error

The natural difference between a sample and the population.

Error of estimation (margin of error)

The amount sample results are expected to differ from the population.

A smaller error of estimation means...

The sample more accurately represents the population.

Three factors affecting error of estimation

Sample size, population size, and variance.

How does sample size affect error of estimation?

Larger samples decrease the error of estimation.

How does variance affect error of estimation

Greater variance increases the error of estimation.

Simple random sample

Every possible sample of the desired size has an equal chance of being selected.

Sampling frame

A complete list of the population from which the sample is selected.

Systematic sampling

Selecting every nth person from a sampling frame.

Stratified random sampling

Dividing the population into groups, then randomly sampling from each group.

Main advantage of stratified random sampling

Ensures adequate representation of important subgroups.

Cluster sampling

Dividing the population into clusters (often geographic) and randomly selecting clusters.

Main advantage of cluster sampling

Participants are geographically closer together and no sampling frame is required.

Convenience sample

A sample consisting of participants who are easiest to obtain.

Quota sample

A convenience sample that ensures certain groups are represented in specific proportions.

Purposive sample

A sample in which participants are intentionally selected because they are typical or informative.

Nonresponse

The failure to obtain responses from selected participants.

Why is nonresponse a problem?

It destroys the advantages of probability sampling by making the sample less representative.

Misgeneralization

Generalizing findings to a population different from the one actually sampled.

Economic sample

A sample that balances accuracy with reasonable cost and effort.

Power

The ability of a study to detect a true effect if one exists.

What increases power?

Larger sample sizes.

Effect size

The strength of a relationship or difference between variables.

Relationship between effect size and power

Smaller effects require greater power (usually larger samples) to detect.

Why are many behavioral studies underpowered?

Their sample sizes are too small.

Purpose of descriptive research

To systematically and accurately describe characteristics or behaviors of a population.

Three major types of descriptive research

Survey, demographic, and epidemiological research.

Survey research

A descriptive design using questionnaires, interviews, or observations to describe attitudes or behaviors.

Cross-sectional survey

A single sample is surveyed once.

Successive independent samples survey

Different samples answer the same questions at different times.

Panel (longitudinal) survey

The same participants are surveyed more than once.

Advantage of a panel survey

It allows researchers to study change within the same individuals.

Demographic research

Studies life events such as birth, marriage, divorce, migration, employment, and death.

Epidemiological research

Studies patterns of disease and death in populations.

Prevalence

The proportion of a population with a disorder at a particular time.

Incidence

The rate of new cases of a disorder over a specified period.

Three characteristics of good descriptive data

Accuracy, conciseness, and understandability.

Frequency distribution

A summary showing how often each score occurs.

Relative frequency

Frequency divided by the total number of observations.

If 15 of 60 participants are in one category, what is the relative frequency?

.25

Mean

The arithmetic average.

Median

The middle score after scores are ordered.

Mode

The most frequently occurring score.

Which is NOT a measure of central tendency?

Standard deviation.

Range

The highest score minus the lowest score.

Variance

The average squared deviation from the mean.

Standard deviation

The square root of the variance.

Small standard deviation means...

Scores are clustered close to the mean.

Large standard deviation means...

Scores are spread farther from the mean.

Confidence interval

A range likely to contain the true population value.

A narrow confidence interval indicates...

A more precise estimate.

Correct interpretation of a 95% confidence interval

If the study were repeated many times, about 95% of the confidence intervals would contain the true population mean.

z-score

The number of standard deviations a score is above or below the mean.

Formula for a z-score

z = (X − M) / SD

Positive z-score

The score is above the mean.

Negative z-score

The score is below the mean.

z-score of 0

The score is exactly equal to the mean.

Purpose of z-scores

To compare scores from different distributions using the same scale.

In a normal distribution, about what percentage of scores fall between the mean and +1 SD?

34%

Correlational research

A research method used to determine whether two or more variables are related.

Correlation coefficient (r)

A statistic that indicates the strength and direction of a linear relationship between two variables.

Possible values of r

-1.00 to +1.00.

Positive correlation

As one variable increases, the other also increases.

Negative correlation

As one variable increases, the other decreases.

Correlation of 0.00

No linear relationship exists between the variables.

The sign of a correlation tells...

The direction of the relationship.

The magnitude of a correlation tells...

The strength of the relationship.

Which correlation is strongest: -.60, +.55, -.45, or .00?

-.60

Scatterplot

A graph used to display the relationship between two variables.

What does a correlation of .00 look like on a scatterplot?

A random array of points.

What does a perfect positive correlation look like?

A straight line sloping upward to the right.

What does a perfect negative correlation look like?

A straight line sloping downward to the right.

Curvilinear relationship

A relationship that is not linear; Pearson's r may be near zero even when variables are related.

Why should researchers examine scatterplots?

To check for curvilinear relationships and outliers before interpreting r.

Coefficient of determination (r²)

The proportion of variance in one variable explained by the other.

Formula for coefficient of determination

r² = r × r.

If r = .60, what is r²?

.36 (36% of the variance explained).

If r = .30, what is r²?

.09 (9% of the variance explained).

Can a correlation of .80 be considered twice as strong as .40?

No. Correlations must be squared before comparing explained variance.

Statistically significant correlation

A correlation that is very unlikely to be zero in the population.

Three factors that distort correlations

Restricted range, unreliable measurements, and outliers.

Restricted range

Reduces the size of a correlation by limiting variability.

Unreliable measurements

Reduce the magnitude of a correlation.

Outliers

Can artificially increase or decrease a correlation.

Why can't correlation establish causation?

It cannot determine direction of causality or rule out third variables.

Spurious correlation

A correlation produced by a third variable.

Partial correlation

The relationship between two variables after controlling for another variable.

When is a partial correlation useful?

When determining whether a third variable explains a relationship.

Regression analysis

A statistical method used to predict one variable from one or more predictor variables.

Purpose of regression analysis

To describe relationships and predict outcomes.

Regression equation

y = β₀ + β₁x

Criterion (dependent) variable

The outcome variable being predicted (y).

Predictor (independent) variable

The variable used to predict the outcome (x).

Regression constant (β₀)

The y-intercept of the regression line.

Regression coefficient (β₁)

The slope of the regression line.