Stats Test 3

Repeated-Measures Design

A research design where the same group of participants is measured on the same dependent variable at two different time points or under two different conditions.

Difference Score (D)

The score obtained by subtracting one of the paired measurements from the other for each individual participant (D = X₂ - X₁).

Null Hypothesis (H₀)

States that there is no consistent or systematic difference between the two measurement occasions or conditions in the population (µ = 0).

Alternative Hypothesis (H₁)

States that there is a systematic difference between the two measurement occasions or conditions, resulting in a non-zero mean difference.

Estimated Standard Error of M (s_M)

An estimate of the standard deviation of the sampling distribution of mean difference scores, calculated as sample standard deviation of difference scores divided by the square root of the number of participants.

Repeated-Measures t-Statistic

Used to test hypotheses about population mean difference based on sample mean difference and estimated standard error of M.

Degrees of Freedom (df)

Calculated as the number of participants minus one (df = n - 1) for the repeated-measures t-test.

Testing Effects

A disadvantage where exposure to the first condition influences performance in the second condition, such as practice or fatigue.

Floor Effects

Occurs when participants' scores in the first condition are so low that they can only increase in the second condition.

Ceiling Effects

Occurs when participants' scores in the first condition are so high that they can only decrease in the second condition.

Effect Size (Cohen's d)

A measure of the magnitude of the treatment effect, calculated as Cohen’s d = M / s.

Analysis of Variance (ANOVA)

A hypothesis testing procedure used to evaluate mean differences between two or more populations, examining variance within and between groups.

F-ratio

The test statistic for ANOVA, calculated as a ratio of two variance estimates (F = MSbetween / MSwithin).

Degrees of Freedom Between Groups (df_between)

Calculated as the number of levels minus one (df_between = k - 1).

Degrees of Freedom Within Groups (df_within)

Calculated as the total number of participants minus the number of levels (df_within = N - k).

Post Hoc Tests

Statistical tests conducted after a significant ANOVA to determine which specific group means are significantly different from each other.

Two-Factor ANOVA

An ANOVA procedure examining the effects of two independent variables (factors) on a single dependent variable.

Main Effect

The effect of one independent variable on the dependent variable, averaged across the levels of the other independent variable.

Interaction Effect

Occurs when the effect of one independent variable on the dependent variable depends on the level of the other independent variable.

Cell

A specific combination of the levels of the two factors in a two-factor design.

Sum of Squares Total (SS_total)

A measure of the total variability in the entire dataset, calculated as SStotal = SSbetween + SS_within.

Effect Size (η²)

A measure of the proportion of variance in the dependent variable accounted for by the independent variable, calculated as η² = SSbetween / SStotal.