Research Methods quiz 3

Comprehensive practice fill-in-the-blank flashcards covering sampling methodology, probability and hypothesis testing, descriptive and inferential statistics, t-tests, ANOVA, multiple comparisons, nonparametric methods, chi-square, correlation, and regression models.

What is the primary purpose of an independent samples t-test?

To compare the means of two independent, unrelated groups to determine whether an observed difference between them is statistically significant or likely due to chance.

What are the core parametric assumptions of an independent samples t-test?

1. Independence of observations (different participants in each group)

2. Scale of measurement (continuous dependent variable on interval or ratio scale)

3. Normality (dependent variable is approximately normally distributed in each group)

4. Homogeneity of variance (variances across the two comparison groups are equal)

How is Levene's test for equality of variances interpreted when conducting an independent t-test?

A non-significant result ($p \ge .05$) indicates that variances are equal, satisfying the assumption of homogeneity of variance. A significant result ($p < .05$) indicates unequal variances, requiring the use of the adjusted 'Equal variances not assumed' output.

How are the p-value and the 95% confidence interval of the mean difference used to interpret an independent t-test?

A $p$-value less than $\alpha$ ($p < .05$) and a 95% confidence interval that excludes $0$ indicate that the difference between group means is statistically significant, warranting rejection of the null hypothesis.

What is the primary purpose of a paired samples t-test?

To compare means between two related or correlated conditions (such as pretest versus posttest scores within the same subjects or matched pairs) to determine if the mean difference is statistically significant.

What are the core assumptions required for a paired samples t-test?

1. Paired observations (same subjects measured twice or matched pairs)
2. Scale of measurement (continuous dependent variable on interval or ratio scale)
3. Normality (distribution of the difference scores is approximately normal) Note: Homogeneity of variance is not tested because only one sample of subjects is involved.

Why does a paired t-test typically provide greater statistical power than an independent t-test?

Because each participant acts as their own control, extraneous individual differences between subjects are controlled, which decreases error variance and makes true treatment effects easier to detect.

What is the primary purpose of a one-way analysis of variance (ANOVA)?

To compare the means of three or more independent groups defined by a single independent variable (factor) to test whether at least one group mean differs significantly from the others.

What are the primary assumptions of a one-way ANOVA?

1. Independence of observations across all groups
2. Continuous data (interval or ratio level)
3. Normality of the dependent variable within each group
4. Homogeneity of variance across all comparison groups (tested via Levene's test)

How is a significant omnibus F-test in a one-way ANOVA interpreted, and what subsequent step is required?

A significant omnibus $F$-test ($p < .05$) indicates that a significant difference exists somewhere among the group means, but does not identify which specific groups differ; post hoc multiple comparison tests must be conducted to locate specific pairwise differences.

What is the primary purpose of a two-way factorial ANOVA?

To simultaneously examine the main effects of two independent variables as well as their combined interaction effect on a single continuous dependent variable.

How should researchers interpret main effects when a two-way ANOVA demonstrates a significant interaction effect?

Main effects are generally ignored or interpreted with caution because a significant interaction indicates that the effect of one independent variable differs across the levels of the second independent variable; researchers evaluate simple effects instead.

What is the purpose of conducting a simple effects analysis after a significant interaction in a two-way ANOVA?

To examine the differential effects of one independent variable within separate individual levels of the other independent variable, breaking the factorial design down into smaller single-factor analyses.

What is the primary purpose of a repeated measures ANOVA?

To evaluate differences in mean scores when the same group of participants is tested across three or more treatment conditions or over three or more time intervals.

What is the sphericity assumption in a repeated measures ANOVA, and how is it evaluated?

Sphericity assumes that the variances of the difference scores between all possible pairs of repeated conditions are roughly equal and correlated; it is tested using Mauchly's Test of Sphericity, where $p \ge .05$ indicates the assumption is satisfied.

How are repeated measures ANOVA results interpreted and adjusted when Mauchly's test indicates that sphericity is violated ($p < .05$)?

Degrees of freedom are multiplied downward by an epsilon correction factor (Greenhouse-Geisser or Huynh-Feldt), raising the critical $F$ threshold to compensate for the liberal bias toward Type I error.

What is the purpose and structure of a mixed (split-plot) ANOVA?

To analyze experiments combining at least one between-subjects independent variable (e.g., intervention versus control) and at least one within-subjects repeated measure (e.g., baseline, posttest, follow-up), testing whether groups demonstrate different trajectories over time.

What is the purpose of post hoc multiple comparison procedures following an ANOVA?

To explore all pairwise differences between group means following a significant omnibus $F$-test while controlling the familywise error rate ($\alpha_{FW}$) against Type I error inflation.

How do Tukey's HSD, Student-Newman-Keuls (SNK), and Scheffé's method compare regarding Type I and Type II error control?

1. Tukey's HSD: Balanced approach using a single familywise critical threshold for all pairwise contrasts.
2. SNK: More liberal and powerful by varying critical values based on range of means, but carries higher Type I error risk.
3. Scheffé: The most conservative and rigorous post hoc method; provides maximal protection against Type I error across all simple and complex contrasts at the cost of statistical power.

What is the purpose of the Mann-Whitney U test, and when should it be chosen over an independent t-test?

To compare the rank-sum distributions of two independent groups; it is chosen when the dependent variable is ordinal, sample sizes are very small, or parametric assumptions of normality and equal variances are violated.

How is statistical significance interpreted in the Mann-Whitney U test?

The null hypothesis of identical distributions is rejected when the calculated $U$ statistic is equal to or less than the tabled critical value (or when the associated $p < .05$), indicating a significant difference in ranks between groups.

What is the purpose of the Wilcoxon signed-ranks test, and when is it indicated?

To compare two related conditions or paired observations (such as pretest and posttest) using ranks; it is indicated when working with ordinal data or non-normally distributed continuous difference scores.

Why is the Wilcoxon signed-ranks test generally preferred over the sign test for paired comparisons?

The sign test only assesses the direction of differences (+ versus -) and discards ties, whereas the Wilcoxon signed-ranks test evaluates both the direction and the relative magnitude of differences by ranking absolute difference scores, providing greater statistical power.

What is the purpose of the Kruskal-Wallis test, and what is its parametric counterpart?

To compare the rank-sum distributions of three or more independent groups; it serves as the nonparametric analog to the one-way ANOVA when parametric assumptions are violated.

How are results from a Kruskal-Wallis test interpreted and followed up?

A significant test statistic ($H$ with $p < .05$) indicates that at least one group distribution differs, but does not identify which specific groups differ; post hoc multiple comparison tests (such as Dunn's test or Mann-Whitney tests with Bonferroni correction) are required.

What is the purpose of the Friedman test, and what is its parametric counterpart?

To test for differences across three or more related conditions or repeated measures using ranks assigned within each subject; it serves as the nonparametric analog to the one-way repeated measures ANOVA.

What is the primary purpose of a chi-square goodness of fit test?

To determine whether observed frequency counts of a single categorical variable differ significantly from expected frequencies derived from a theoretical (uniform) or known population distribution.

What are the core assumptions and sample size criteria for a chi-square goodness of fit test?

1. Data represent actual individual counts (not percentages or ranks)
2. Categories are exhaustive and mutually exclusive
3. Observations are independent
4. Expected cell frequencies should be at least $5.0$ per category

How are standardized residuals used to interpret a significant chi-square test?

Standardized residuals quantify the relative discrepancy between observed and expected frequencies for each cell; absolute values close to or exceeding $1.96$ indicate the specific categories that contribute significantly to the overall chi-square finding.

What is the primary purpose of a chi-square test of independence?

To determine whether two categorical classification variables arranged in a contingency table are independent of one another or whether a statistically significant association exists between them.

What sample size assumptions apply to a chi-square test of independence, and how can violations be managed?

No more than $20\%$ of cells should have expected counts less than $5$, and no cell should have an expected count less than $1$; if violated, categories may be combined (collapsed) or Fisher's exact test should be used.

What is the primary purpose and indication for Fisher's exact test?

To evaluate the association between two categorical variables in a $2 \times 2$ contingency table when expected cell frequencies are too small (expected count $< 1$ or $> 20\%$ of cells with expected counts $\le 5$) for the standard chi-square approximation.

What is the purpose of the McNemar test, and for what study design is it indicated?

To evaluate changes or differences in proportions in a $2 \times 2$ table involving paired or correlated samples, particularly useful in pretest-posttest designs with a dichotomous outcome variable.

How does the McNemar test interpret discordant versus concordant pairs in a 2x2 contingency table?

The test analyzes only discordant pairs (subjects who changed status from before to after) to determine if change occurs equally in both directions; concordant pairs (subjects who showed no change) provide no information and are omitted.

What is the primary purpose of the Pearson product-moment correlation coefficient (r)?

To quantitatively describe the strength and direction of a linear bivariate relationship between two continuous variables.

What are the core statistical assumptions required for a valid Pearson correlation?

1. Continuous variables measured on interval or ratio scales
2. Bivariate normal distribution in the underlying population
3. A linear relationship between the two variables (assessed via scatterplot)
4. Independent pairs of observations (neither variable is a mathematical component of the other)

How should a researcher interpret a statistically significant Pearson correlation that has a low magnitude (e.g., r = .25)?

Significance ($p < .05$) only indicates that the correlation is unlikely to be zero in the population, often driven by large sample size; clinical relevance must be evaluated based on the practical magnitude of the association, as a low $r$ reflects poor predictive utility.

What is the purpose and indication for the Spearman rank correlation coefficient (rho)?

To assess the monotonic relationship between two sets of ranked scores; it is indicated when variables are measured on an ordinal scale or when continuous data violate normality assumptions.

What is the purpose of Kendall's tau-b, and when is it preferred over Spearman's rho?

A rank-order correlation coefficient based on concordance that adjusts for tied ranks and serves as an unbiased estimate of a population parameter, preferred when the dataset contains numerous tied ranks.

What is the primary purpose of a partial correlation analysis?

To examine the true linear association between two variables ($X$ and $Y$) while statistically removing the linear confounding influence of a third variable ($Z$).

What is the primary purpose of simple linear regression?

To predict values of a continuous dependent outcome variable ($Y$) based on values of a single continuous independent predictor variable ($X$) by establishing a line of best fit.

What are the core assumptions of simple linear regression, and how are residuals evaluated?

1. Linear relationship between $X$ and $Y$
2. Normal distribution of $Y$ scores at each value of $X$
3. Homoscedasticity (equal variance of residuals across all predicted values) Assumptions are met when a scatterplot of standardized residuals against predicted values forms a random horizontal band centered around zero.

How is the coefficient of determination (R-squared) interpreted in regression analysis?

It indicates the proportion of total variance in the dependent variable that is directly explained by the independent predictor variable(s), ranging from $0.00$ to $1.00$ ($0\%$ to $100\%$).

What is the clinical interpretation of the Standard Error of the Estimate (SEE) in regression?

The SEE represents the standard deviation of the residuals, providing a measure of the average error of prediction in the actual units of the dependent variable.

What is the primary purpose of multiple linear regression?

To predict and explain variance in a continuous dependent variable using a linear combination of two or more independent predictor variables (continuous or dummy-coded categorical).

What is multicollinearity in multiple regression, and how is it detected and interpreted?

Multicollinearity occurs when predictor variables are highly correlated with each other, resulting in redundant information and unstable regression coefficients; it is detected by low Tolerance ($< .20\text{ to } .25$) or high Variance Inflation Factor ($\text{VIF} > 4\text{ to } 10$).

How are standardized beta coefficients (Beta weights) interpreted in multiple regression?

Beta weights represent regression coefficients transformed into standard deviation units, allowing direct comparison of the relative predictive contribution of each independent variable regardless of differences in measurement scales.

What is the purpose of stepwise multiple regression, and what critical caveat applies to excluded variables?

To identify the most parsimonious model by entering or removing predictors sequentially based on statistical criteria ($p \le .05$); however, an excluded variable is not necessarily unimportant clinically, as it may have been omitted purely due to collinearity with an entered predictor.

What is the purpose of dummy variables in multiple linear regression?

To represent categorical independent variables with $k$ groups using $k - 1$ dichotomous indicator variables coded $0$ and $1$, allowing categorical predictors to be entered into regression equations.

What is the primary purpose of binary logistic regression?

To predict the probability or odds of a dichotomous categorical outcome (such as disease present/absent or discharge home/institution) using one or more continuous or categorical predictor variables.

How is the exponentiated regression coefficient [Exp(B)] interpreted in binary logistic regression?

It represents the adjusted odds ratio (aOR); an aOR greater than $1.0$ indicates increased odds of the target outcome per one-unit increase in the predictor, while a 95% confidence interval containing $1.0$ indicates that the predictor is not statistically significant.

What is the purpose of the Hosmer-Lemeshow test in logistic regression, and how is it interpreted?

It evaluates goodness of fit by determining whether observed event rates match expected rates predicted by the model; a non-significant result ($p > .05$) indicates that the model is a good fit for the data.

What is the primary purpose of an Analysis of Covariance (ANCOVA)?

To compare posttest group means on a continuous dependent variable while statistically controlling for and adjusting for the confounding influence of an extraneous baseline continuous variable (covariate).

What is the homogeneity of slopes assumption in ANCOVA, and how is it tested?

It assumes that the regression slopes relating the covariate to the dependent variable are parallel across all comparison groups; it is tested via the interaction between the treatment group and the covariate, where a non-significant interaction ($p > .05$) confirms the assumption is satisfied.

What assumptions must be met regarding the covariate in an ANCOVA?

1. The covariate must be linearly correlated with the dependent variable
2. The covariate must be measured reliably
3. The covariate must be independent of the treatment (measured prior to intervention so treatment cannot influence it)

How are adjusted means interpreted in an ANCOVA?

Adjusted means represent the estimated performance of each comparison group on the dependent variable after mathematically equalizing all groups to the grand mean of the baseline covariate.