Psychological statistics FINAL

Z Test

Compares a sample mean to a known population mean when population SD is known or sample size ≥ 30; Example: Comparing sample IQ to population IQ when σ = 15 is known.

Single-Sample t Test

Compares a sample mean to a population mean when population SD is unknown; Example: Testing if your school’s GPA differs from the national mean.

Paired-Samples t Test

Compares two related scores such as before–after or matched pairs; Example: Blood pressure before and after medication.

Independent-Samples t Test

Compares two independent group means; Example: Flashcard learners vs. practice-test learners.

ANOVA

Tests differences among three or more group means; Example: Comparing anxiety levels across grade levels.

Effect Size

Measures magnitude/strength of an effect; Example: Cohen’s d = 0.80 indicates a large effect.

F Statistic

Ratio of between-group variance to within-group variance; Example: F = 5 means between-group variance is 5× larger than within-group variance.

F Distribution

Distribution used in ANOVA; always right-tailed because F cannot be negative.

Between-Groups Variance

Variance due to differences between groups; Example: Different teaching methods producing different mean scores.

Within-Groups Variance

Variance within each group caused by individual differences; Example: students in the same class vary.

Source Table (ANOVA Table)

Table showing SS, df, MS, and F for between and within groups; used to compute ANOVA.

Homoscedasticity

Equal variances across groups; Example: all class sections have similar score variance.

Heteroscedasticity

Unequal variances across groups; Example: one class has wide score range and another narrow.

Between-Groups ANOVA

Different participants in each group; Example: three separate classrooms.

Within-Groups ANOVA

Same participants measured multiple times; Example: reaction time at three caffeine levels.

Degrees of Freedom in ANOVA

the number of independent values that can vary; dfbetween = k – 1; dfwithin = N – k;

Sum of Squares (SS)

Total variability measure; Example: SS_between measures variance between the group means.

Mean Squares (MS)

Average variability (SS ÷ df); Example: MSbetween = SSbetween / df_between.

Familywise Type I Error

Increased chance of at least one false positive when running multiple tests; Example: 10 t tests increases risk.

Tukey HSD Test

Post-hoc test after ANOVA to compare all group pairs; Example: compares freshmen vs sophomores vs juniors.

Post Hoc Test

Tests done after ANOVA to detect which groups differ; Example: Tukey or Bonferroni tests.

Bonferroni Correction

Adjusts alpha to prevent a Type I error by dividing α by the number of tests; Example: 5 tests → α = .05/5 = .01.

Correlation

Measures relationship strength and direction between two variables; Example: study time ↑ → scores ↑.

Positive Correlation

Both variables increase together; Example: height ↑ → weight ↑.

Negative Correlation

One variable increases while the other decreases; Example: stress ↑ → sleep ↓.

Correlation Coefficient (r)

Value between -1 and +1 showing correlation direction and strength; Example: r = .70 = strong positive.

Spurious Correlation

Meaningless correlation caused by a third variable; Example: ice cream sales and drowning rates (summer heat).

Psychometrics

Study of psychological measurement and test creation; Example: designing personality tests.

Reliability

Consistency of a measurement over time; Example: a test giving similar scores each month.

Validity

Accuracy of a measurement—whether it measures what it claims to; Example: a depression test measuring depression.

Parametric Tests

Assume normal distribution and interval/ratio data; Examples: t tests, ANOVA.

Non-Parametric Tests

Do not require normal distribution; used for ordinal or categorical data; Example: Chi-square, Mann–Whitney U.

Chi-Square Test

Compares observed frequencies to expected frequencies; Example: gender × major independence test.

Observed Variables

Actual measured frequencies; Example: 40 students prefer Pepsi.

Expected Variables

Predicted frequencies if no association exists; Example: expected = 50 if equal preference is assumed.