PSY 350 Unit 2: Comparing Groups & Testing Effects

A set of vocabulary flashcards covering one-sample, paired, and independent-samples t-tests, one-way ANOVA, Levene's test, post hoc tests, effect sizes, and factorial ANOVA designs from the PSY 350 Unit 2 study guide.

One-Sample t-Test

A statistical test used to compare a sample mean with a specified or hypothesized population mean ($\mu_0$), used when testing whether the mean of one sample differs from a specified value.

Population Standard Deviation Estimation (t-Test)

The method of using the sample standard deviation ($s$) to estimate the unknown population standard deviation, distinguishing a t-test from a z-test.

Degrees of Freedom ($df$)

The number of independent pieces of information free to vary after accounting for estimated quantities; calculated as $df = n - 1$ for a one-sample t-test.

Cohen’s d ($\approx 0.20$)

A conventional representation of a small standardized effect size, serving as a rule of thumb rather than a universal threshold for practical importance.

Statistical Significance ($p < \alpha$)

A decision rule leading to the rejection of $H_0$, indicating that the result is statistically significant at the chosen $\alpha$ level.

p-value

The probability of obtaining a test statistic at least as extreme as the observed statistic, assuming $H_0$ and model assumptions are true; it is not the probability that $H_0$ is true.

Type I Error

The error committed by rejecting a true null hypothesis ($H_0$).

Type II Error

The error committed by failing to reject a false null hypothesis ($H_0$).

Paired-Samples t-Test

A test appropriate for related observations, such as before-and-after scores from the same participants or matched pairs (e.g., a parent and their child).

Sample Size ($n$) in Paired-Samples t-Test

The number of pairs in the analysis, rather than the total number of individual scores.

Independent-Samples t-Test

A statistical test appropriate when comparing a continuous dependent variable between two unrelated groups defined by a categorical grouping variable.

Homogeneity of Variance

The assumption that the populations represented by independent groups have equal variances (similar variability).

One-Way ANOVA

A statistical test appropriate for comparing a continuous outcome across three or more independent groups defined by one categorical factor.

Null Hypothesis of a One-Way ANOVA

The proposition that all population group means are equal, formalized as $H_0: \mu_1 = \mu_2 = \dots = \mu_k$.

ANOVA F-Statistic

A ratio comparing between-group variability relative to within-group variability, calculated as $F = \frac{MS_{\text{between}}}{MS_{\text{within}}}$.

Omnibus F-Test

An overall test that, when statistically significant, establishes that at least two population group means differ, without identifying which specific groups differ.

Post Hoc Test

A follow-up test used to determine which specific group pairs differ while accounting for multiple comparisons, generally not pursued if the omnibus test fails to reject $H_0$.

Levene’s Test

An inferential test assessing the null hypothesis that group variances are equal ($H_0$: equal group variances); a result of $p < .05$ rejects the equal-variances assumption.

Welch’s ANOVA

A suitable omnibus comparison approach used when ANOVA group variances are unequal.

Games–Howell Test

A pairwise comparison procedure recommended when ANOVA group variances are unequal.

Tukey HSD

A pairwise comparison procedure typically preferred when the equal-variance assumption across groups is reasonable.

Eta Squared ($\eta^2$)

An effect-size measure for a one-way ANOVA that ranges from $0$ to $1$, indicating the proportion of total variation in the outcome accounted for by group membership.

Factor

An independent variable included in a factorial ANOVA design.

Level

One specific category or condition belonging to a factor in an ANOVA.

Cell

One unique combination of factor levels within a factorial design (e.g., a $3 \times 2$ factorial design contains $6$ cells).

Main Effect

The average association or effect of one factor on the dependent variable, averaging across levels of the other factor.

Interaction Effect

An effect occurring when the effect of one factor on the dependent variable differs depending on the level of another factor.