Psychological Statistics Comprehensive Review Flashcards

F-test

A targeted test used to compare two population variances by assessing the ratio of their sample values to verify homogeneity of variance.

F-statistic calculation

Mathematically, the larger sample variance ($s_1^2$) is placed in the numerator to ensure the computed value is always greater than or equal to $1.00$.

Degrees of freedom for the numerator (d.f.N.)

The sample size of the group with the larger variance minus one ($n_{num} - 1$).

F distribution

An inherently positively skewed distribution that peaks near $1.00$ and has no fixed upper limit, with values that can never be negative because it is a ratio of variances.

Welch's t-test

A parametric test that modifies standard error and degrees of freedom using the Welch–Satterthwaite equation when variances are unequal but normality holds.

Conservative d.f. rule

A manual calculation strategy for independent t-tests with unequal variances that uses the smaller of $n_1 - 1$ or $n_2 - 1$ to prevent underestimating Type I error risk.

Analysis of Variance (ANOVA) assumptions

Core requirements including a continuous level of measurement, normality of distributions, and homogeneity of population variances across all evaluated groups.

Quantile-Quantile (Q-Q) plot

A visual tool that graphs observed values against an ideal normal distribution; linear alignment along the diagonal axis validates the normality assumption.

Independent samples

A condition where selecting a participant for one group has zero statistical impact or structural influence on who is placed into another group.

Pearson correlation coefficient ($r$)

A parametric statistic designed strictly to measure the strength and direction of linear (straight-line) relationships between two continuous variables.

Mann-Whitney U test

The distribution-free nonparametric alternative to the independent samples t-test that compares sorted ranked data instead of raw means.

Levene's test

A robust test used to evaluate the null hypothesis that all comparative population variances are identical, often used before running an ANOVA.

Central Limit Theorem (CLT)

A principle stating that as sample sizes grow to $n \text{ } ≥ 30$, the sampling distribution of the means approaches a normal profile regardless of the raw sample shape.

Homoscedasticity

The regression assumption requiring that the spread of errors (residuals) stays consistent across all tracking levels of the independent predictor variable.

Spearman rank correlation (̑)

A nonparametric test used to measure the strength and direction of a monotonic relationship between two ordinal variables or skewed continuous variables.

Kruskal-Wallis test

The nonparametric alternative to a one-way ANOVA used to compare three or more independent groups when data is ordinal or normality is violated.

Wilcoxon signed-rank test

The nonparametric alternative to a paired t-test used for ordinal, within-subjects designs comparing the same individuals across two time periods.

Nominal level of measurement

The lowest level of measurement, used purely to label or categorize data into mutually exclusive groups without inherent ranking.

Ordinal level of measurement

A scale that categorizes data with a clear sequential order, such as product ratings, but lacks consistent, equal spacing between points.

Interval level of measurement

A scale with equal spacing between metric units, such as Celsius temperature, but lacking a true, absolute zero point.

Ratio level of measurement

A scale with equal intervals and an absolute zero point (e.g., annual salary), where ratios between values are mathematically meaningful.

Continuous variables

Variables that can assume an infinite number of fractional values between any two points and are typically obtained by measuring.

Discrete variables

Variables that can assume only specific, distinct whole values with no fractional steps, typically obtained through counting.

Independent variable

The factor in an experiment that is deliberately manipulated or controlled by the researcher to determine its effect.

Dependent variable

The observed outcome or response that changes in response to the manipulation of an independent variable.

Mean

The arithmetic balance point of a dataset, calculated as the sum of all observed values divided by the total number of observations ($∑ X / n$).

Median

The value falling exactly in the physical middle of an ordered dataset, splitting it so $50$ of observations are above and $50$ are below.

Mode

The value that appears with the highest frequency in a dataset.

Platykurtic

A description of a distribution curve that is relatively flat and spread out along the base.

Range

A measure of total dispersion calculated by finding the difference between the highest and lowest values ($X_{max} - X_{min}$).

Z-score

A standardized value indicating how many standard deviation units a raw score falls above or below the mean, calculated as z = \frac{X - ̑}{̓}.

Standard normal distribution

A specific normal curve with a mean of $0$ and a standard deviation of $1$, where the total area under the curve equals $1.00$.

Empirical Rule

A