PSYC 200 Vocab Exam 1

Sampling Error

The difference between a sample statistic and the corresponding population parameter. For a sample mean, sampling error is calculated as M − μ. It occurs naturally because a sample usually does not perfectly represent the population.

Sampling Distribution

The distribution of statistics obtained from all possible random samples of a specific size selected from a population.

Distribution of Sample Means

The sampling distribution created by calculating the mean for every possible sample of a specific size from a population. It shows how sample means vary from sample to sample.

Central Limit Theorem (CLT)

The principle stating that the distribution of sample means becomes approximately normal as the sample size increases, even when the original population is not normally distributed. The mean of the sample means equals the population mean, and the standard error decreases as sample size increases.

Expected Value of M

The mean of the distribution of sample means. The expected value of the sample mean is equal to the population mean

Standard Error of M

The standard deviation of the distribution of sample means. It measures how much sample means typically vary from the population mean. The formula is σM = σ/√n.

Law of Large Numbers

The principle stating that as sample size increases, the sample mean tends to get closer to the population mean. Larger samples generally produce smaller sampling errors.

Hypothesis testing

Theprocess of using sample data to evaluate a claim about a population and decide whether there is enough evidence to reject the null hypothesis.

Null hypothesis (H₀)

The statement that there is no effect, no difference, or no relationship in the population; it is the hypothesis tested statistically.

Level of significance

The criterion used to determine whether a result is statistically significant; it represents the maximum probability of making a Type I error.

Alpha level (α)

The probability of rejecting a true null hypothesis. Common alpha levels are .05 and .01.

Critical region

The range of test-statistic values that leads to rejection of the null hypothesis. It is determined by the alpha level and the type of test.

Test statistic

A value calculated from sample data that is used to determine whether the null hypothesis should be rejected.

Type I error

Rejecting the null hypothesis when it is actually true; a false positive.

Type II error

Failing to reject the null hypothesis when it is actually false; a false negative.

Beta (β)

The probability of making a Type II error.

Significant

A result is statistically significant when it is sufficiently unlikely under the null hypothesis to justify rejecting the null hypothesis, based on the chosen alpha level.

Directional test

A hypothesis test that predicts the specific direction of an effect or difference, such as greater than or less than.

One-tailed test

A hypothesis test in which the critical region is located entirely in one tail of the sampling distribution because the alternative hypothesis is directional.

Effect size

A numerical measure of the magnitude or size of a difference, relationship, or treatment effect, independent of whether it is statistically significant.

Cohen’s d

A standardized measure of effect size for the difference between two means, calculated as the mean difference divided by the standard deviation.

Power

The probability that a statistical test will correctly reject a false null hypothesis; power equals 1 − β.

Population

The complete set of individuals or scores in which a researcher is interested.

Rectangular distribution

A distribution with no peaks and valleys—all conditions are equally as likely to occur.

Sample

A set of individuals selected from a population.

Variable

A characteristic or condition that has different values for different individuals.

Data

The measurements or observations obtained from a research study.

Data set

A complete collection of measurements or observations.

Datum

A single measurement or observation.

Raw score

The original, unaltered value obtained for an individual.

Parameter

A numerical value that describes a population.

Statistic

A numerical value that describes a sample.

Descriptive statistics

Statistical procedures used to organize, summarize, and describe a set of data.

Inferential statistics

Statistical procedures used to use sample data to make conclusions about a population.

Sampling error

The difference between a statistic obtained from a sample and the corresponding parameter for the population.

Correlational method

A research method used to examine the relationship between two variables without manipulating either variable.

Experimental method

A research method in which one variable is manipulated while another variable is measured.

Independent variable

The variable manipulated by the researcher in an experiment.

Dependent variable

The variable observed and measured to determine the effect of the independent variable.

Control condition

The condition that does not receive the experimental treatment and serves as a comparison.

Experimental condition

The condition that receives the treatment or manipulation of the independent variable.

Nonequivalent groups study

A study that compares groups that already exist and were not formed through random assignment.

Pre-post study

A study in which the dependent variable is measured before and after a treatment or intervention.

Quasi-independent study

A variable used to divide participants into groups when the researcher does not manipulate the variable or randomly assign participants.

Construct

A hypothetical concept or characteristic that cannot be observed directly, such as intelligence, anxiety, or motivation.

Operational definition

A definition that identifies the specific procedures used to measure or manipulate a variable.

Discrete variable

A variable consisting of separate, indivisible values.

Continuous variable

A variable that can take any value within a range and can be divided into smaller units.

Real limits

The boundaries of a measurement interval that indicate the actual limits of the scores in the interval.

Upper real limit

The point halfway between a score and the next higher possible score.

Lower real limit

The point halfway between a score and the next lower possible score.

Nominal scale

A measurement scale that classifies observations into categories identified only by names or labels.

Ordinal scale

A measurement scale that classifies observations into categories that are ordered or ranked.

Interval scale

A measurement scale with equal intervals between values but no meaningful zero point.

Ratio scale

A measurement scale with equal intervals and a meaningful zero point.

Frequency distribution

A table that lists the possible scores or categories and the number of times each occurs.

Range

The distance from the lowest score to the highest score in a distribution.

Grouped frequency distribution

A frequency distribution in which scores are organized into intervals.

Class interval

A group of consecutive score values used as one category in a grouped frequency distribution.

Apparent limits

The lowest and highest values stated for a class interval.

Histogram

A graph used for quantitative data in which the frequencies are represented by adjacent bars that touch.

Polygon

A line graph formed by connecting points representing the frequencies of scores or class intervals.

Bar graph

A graph used to display frequencies for separate categories, with spaces between the bars.

Relative frequency

The proportion of the total frequency represented by a particular score or class interval.

Symmetrical distribution

A distribution in which the two sides are approximately mirror images of one another.

Tails of a distribution

The sections of a distribution that extend beyond the central group of scores.

Positively skewed distribution

A distribution with a tail extending toward the higher scores.

Negatively skewed distribution

A distribution with a tail extending toward the lower scores.

Percentile

A score or location below which a specified percentage of the distribution falls.

Percentile rank

The percentage of individuals in a distribution with scores at or below a specified score.

Cumulative frequency (cf)

The total frequency of scores at or below a particular score or class interval.

Cumulative percentage (c%)

The percentage of scores at or below a particular score or class interval.

Interpolation

The process of estimating a value between two known values.

Stem and leaf display

A method for organizing data by separating each score into a stem and a leaf while retaining the original scores.

Central tendency

A statistical measure that identifies a typical or central score in a distribution.

Population mean (μ)

The arithmetic average of the scores in a population, represented by μ; μ = ΣX/N.

Sample mean (M)

The arithmetic average of the scores in a sample, represented by M; M = ΣX/n.

Weighted mean

A mean in which different scores or group means contribute unequally according to their relative frequency or size.

Median

The score that divides a distribution into two equal portions when the scores are arranged in order.

Mode

The score or category that occurs most frequently in a distribution.

Bimodal

A distribution with two peaks.

Multimodal

A distribution with more than two peaks.

Major mode

The mode with the highest frequency in a distribution containing more than one mode.

Minor mode

A mode with a lower frequency than the major mode.

Line graph

A graph that displays data points connected by lines, often to show changes across an ordered variable.

Variability

A measure of the amount of difference or spread among the scores in a distribution.

Deviation score

The distance between a score and the mean; it is calculated as X − μ for a population or X − M for a sample.

Population variance (σ²)

The average squared deviation from the population mean; σ² = SS/N.

Population standard deviation (σ)

The square root of the population variance and a measure of the typical distance of scores from the population mean.

Sum of squares (SS)

The sum of the squared deviation scores; SS = Σ(X − μ)² for a population or SS = Σ(X − M)² for a sample.

Sample variance (s²)

The average squared deviation in a sample, calculated using n − 1 as the denominator; s² = SS/(n − 1).

Sample standard deviation (s)

The square root of the sample variance and a measure of the typical distance of sample scores from the sample mean.

Degrees of freedom (df)

The number of scores that are free to vary when a statistic is calculated; for sample variance, df = n − 1.

Biased statistic

A statistic that systematically tends to overestimate or underestimate the population parameter.

Unbiased statistic

A statistic that, over many samples, tends to estimate the population parameter accurately.

Z-score

A standardized score that describes a raw score’s position relative to the mean in standard-deviation units.

Z-score transformation

The process of converting raw scores into z-scores by subtracting the mean and dividing by the standard deviation.

Standardized distribution

A distribution formed by transforming raw scores into standardized scores.

Standardized score

A score expressed in a standard unit that indicates its position relative to the mean.

Probability

A mathematical value describing the likelihood that an event will occur.