Statistics & Research Methods – Core Vocabulary

A curated set of vocabulary flashcards covering fundamental terms, tests, and concepts in statistics and research methods, suitable for exam preparation.

Descriptive Statistics

Methods that summarize and present data without drawing conclusions beyond the sample (e.g., frequency tables, histograms).

Inferential Statistics

Techniques that use sample data to make conclusions or predictions about a population (e.g., t-tests, ANOVA).

Central Tendency

Measures that indicate a typical score in a distribution: mean, median, and mode.

Variability

Statistics that describe the spread of scores: range, variance, standard deviation, interquartile range.

Mean

Arithmetic average of a dataset; sum of scores divided by N.

Median

Middle score when data are ordered; splits the distribution in half.

Mode

Most frequently occurring score in a dataset.

Range

Difference between the highest and lowest values in a dataset.

Variance

Average of squared deviations from the mean; symbol s² for samples.

Standard Deviation (SD)

Square root of variance; expresses average distance of scores from the mean in original units.

Interquartile Range (IQR)

Spread of the middle 50 % of scores; Q3 − Q1.

Parametric Test

Statistical test that assumes interval/ratio data, normality, and (often) equal variances; generally more powerful if assumptions hold.

Nonparametric Test

Test that makes few distributional assumptions; used for ordinal or non-normal data (e.g., Mann–Whitney U).

One-Sample t-Test

Parametric test comparing a sample mean to a known or hypothesized population mean.

Paired t-Test

Parametric test that compares means of two related measurements from the same participants.

Independent t-Test

Parametric test comparing means of two separate groups; assumes equal variances unless Welch’s version is used.

Degrees of Freedom (df)

Number of independent pieces of information in a statistic; determines the critical value of a test.

Sign Test

Nonparametric test for paired data that counts the direction of differences only.

Wilcoxon Signed-Rank Test

Nonparametric paired test that analyzes ranks of difference scores.

Mann–Whitney U Test

Nonparametric alternative to the independent t-test; compares rank distributions of two groups.

One-Way ANOVA

Parametric test that compares means of three or more independent groups using the F-statistic.

Repeated-Measures ANOVA

ANOVA in which the same participants appear in all conditions; requires the sphericity assumption.

F-Statistic

Ratio of mean square between groups to mean square within groups (MSbetween / MSwithin).

Sphericity

Assumption that variances of pairwise differences are equal in repeated-measures designs.

Greenhouse–Geisser Correction

Adjustment to df and p-values when sphericity is violated; makes the test more conservative.

Huynh–Feldt Correction

Alternative df adjustment for sphericity violations; usually less conservative than Greenhouse–Geisser.

Within-Subjects Design

Experimental design in which each participant experiences every condition (repeated measures).

Between-Subjects Design

Design in which different participants are assigned to each condition.

Counterbalancing

Technique that varies the order of conditions across participants to control order effects.

Independent Variable (IV)

Variable manipulated by the researcher to observe its effect on the DV.

Dependent Variable (DV)

Outcome variable measured to assess the impact of the IV.

Population Parameter

Numerical characteristic of an entire population (e.g., μ, σ).

Sample Statistic

Numerical summary of a sample used to estimate a population parameter (e.g., x̄, s).

Nominal Data

Categorical data with no intrinsic order (e.g., eye color).

Ordinal Data

Categorical data with a meaningful order but unequal intervals (e.g., race rankings).

Interval Data

Numeric data with equal intervals but no true zero (e.g., °C temperature).

Ratio Data

Numeric data with equal intervals and a true zero, allowing ratio statements (e.g., reaction time).

Normal Distribution

Symmetrical, bell-shaped distribution where mean = median = mode.

Standard Normal Distribution

Normal distribution with a mean of 0 and SD of 1; basis for z-scores.

Z-Score

Standardized value indicating how many SDs a score lies from the mean.

Null Hypothesis (H₀)

Statement that no effect or difference exists; tested for possible rejection.

Alternative Hypothesis (H₁)

Statement that an effect or difference exists; accepted if H₀ is rejected.

Directional Hypothesis

Alternative hypothesis that specifies the direction of an expected effect.

Non-Directional Hypothesis

Alternative hypothesis that predicts an effect but not its direction.

Type I Error

Incorrectly rejecting a true null hypothesis (false positive).

Type II Error

Failing to reject a false null hypothesis (false negative).

p-Value

Probability of observing data as extreme as the sample, assuming H₀ is true.

Significance Level (α)

Threshold probability (commonly 0.05) for deciding whether to reject H₀.

Test Statistic

Calculated value (e.g., t, F, z) used to decide whether to reject H₀.

Homogeneity of Variance

Assumption that population variances are equal across groups in between-subjects tests.

Omnibus Test

Statistical test (e.g., ANOVA) that determines whether any group differences exist without identifying specific pairs.

Post-Hoc Test

Follow-up comparison after a significant omnibus test to locate specific group differences.

Tukey’s HSD

Common post-hoc test that controls Type I error rate when comparing all pairs of means.

Bonferroni Correction

Adjustment of significance threshold (α/k) to control Type I error across multiple comparisons.

Power

Probability of correctly rejecting a false null hypothesis; higher when effect size is large and variability is low.

Descriptive Statistics

Methods that summarize and present data without drawing conclusions beyond the sample (e.g., frequency tables, histograms).

Inferential Statistics

Techniques that use sample data to make conclusions or predictions about a population (e.g., t-tests, ANOVA).

Central Tendency

Measures that indicate a typical score in a distribution: mean, median, and mode.

Variability

Statistics that describe the spread of scores: range, variance, standard deviation, interquartile range.

Mean

Arithmetic average of a dataset; sum of scores divided by N.

Median

Middle score when data are ordered; splits the distribution in half.

Mode

Most frequently occurring score in a dataset.

Range

Difference between the highest and lowest values in a dataset.

Variance

Average of squared deviations from the mean; symbol s^2 for samples.

Standard Deviation (SD)

Square root of variance; expresses average distance of scores from the mean in original units.

Interquartile Range (IQR)

Spread of the middle 50\% of scores; Q3 - Q1.

Parametric Test

Statistical test that assumes interval/ratio data, normality, and (often) equal variances; generally more powerful if assumptions hold.

Nonparametric Test

Test that makes few distributional assumptions; used for ordinal or non-normal data (e.g., Mann–Whitney U).

One-Sample t-Test

Parametric test comparing a sample mean to a known or hypothesized population mean.

Paired t-Test

Parametric test that compares means of two related measurements from the same participants.

Independent t-Test

Parametric test comparing means of two separate groups; assumes equal variances unless Welch’s version is used.

Degrees of Freedom (df)

Number of independent pieces of information in a statistic; determines the critical value of a test.

Sign Test

Nonparametric test for paired data that counts the direction of differences only.

Wilcoxon Signed-Rank Test

Nonparametric paired test that analyzes ranks of difference scores.

Mann–Whitney U Test

Nonparametric alternative to the independent t-test; compares rank distributions of two groups.

One-Way ANOVA

Parametric test that compares means of three or more independent groups using the F-statistic.

Repeated-Measures ANOVA

ANOVA in which the same participants appear in all conditions; requires the sphericity assumption.

F-Statistic

Ratio of mean square between groups to mean square within groups (MS{between} / MS{within}).

Sphericity

Assumption that variances of pairwise differences are equal in repeated-measures designs.

Greenhouse–Geisser Correction

Adjustment to df and p-values when sphericity is violated; makes the test more conservative.

Huynh–Feldt Correction

Alternative df adjustment for sphericity violations; usually less conservative than Greenhouse–Geisser.

Within-Subjects Design

Experimental design in which each participant experiences every condition (repeated measures).

Between-Subjects Design

Design in which different participants are assigned to each condition.

Counterbalancing

Technique that varies the order of conditions across participants to control order effects.

Independent Variable (IV)

Variable manipulated by the researcher to observe its effect on the DV.

Dependent Variable (DV)

Outcome variable measured to assess the impact of the IV.

Population Parameter

Numerical characteristic of an entire population (e.g., \mu, \sigma).

Sample Statistic

Numerical summary of a sample used to estimate a population parameter (e.g., \bar{x}, s).

Nominal Data

Categorical data with no intrinsic order (e.g., eye color).

Ordinal Data

Categorical data with a meaningful order but unequal intervals (e.g., race rankings).

Interval Data

Numeric data with equal intervals but no true zero (e.g., °C temperature).

Ratio Data

Numeric data with equal intervals and a true zero, allowing ratio statements (e.g., reaction time).

Normal Distribution

Symmetrical, bell-shaped distribution where mean = median = mode.

Standard Normal Distribution

Normal distribution with a mean of 0 and SD of 1; basis for z-scores.

Z-Score

Standardized value indicating how many SDs a score lies from the mean.

Null Hypothesis (H_0)

Statement that no effect or difference exists; tested for possible rejection.

Alternative Hypothesis (H_1)

Statement that an effect or difference exists; accepted if H_0 is rejected.

Directional Hypothesis

Alternative hypothesis that specifies the direction of an expected effect.

Non-Directional Hypothesis

Alternative hypothesis that predicts an effect but not its direction.

Type I Error

Incorrectly rejecting a true null hypothesis (false positive).