Guide for Assumptions Checks in Hypothesis Testing

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Questions and Answers

Which test is recommended for checking equal variances in t-test and ANOVA?

Kolmogorov-Smirnov Test

Levene’s Test (correct)

Q-Q Plot

Shapiro-Wilk Test

What does a boxplot indicate when no dots are present?

There are no outliers present. (correct)

The data follows a uniform distribution.

There are significant outliers present.

The data is normally distributed.

What characterizes heteroscedasticity in correlation data?

The data points 'fan out' across the graph. (correct)

The data points are all clustered closely together.

The data points show a consistent spread.

The data points maintain a linear relationship.

Which method is primarily used to visually check for outliers in correlation data?

Scatterplot Signup and view all the answers

When using the Shapiro-Wilk Test, what does a p-value less than .05 imply?

The data is non-normal. Signup and view all the answers

In the context of the Kolmogorov-Smirnov Test, what does a sample size of n ≥ 50 indicate?

This test is suitable for assessing normality. Signup and view all the answers

What is an indication of no significant outliers in the context of a scatterplot?

The points are densely packed around the line of best fit. Signup and view all the answers

Which plot helps to visually assess if a dataset follows a normal distribution in large samples?

Histogram Signup and view all the answers

Which assumption must be checked before using One-Way ANOVA?

Normal distribution in both categorical groups Signup and view all the answers

What should be used if the assumptions of the t-Test for Independent Samples are violated?

Mann-Whitney U Test Signup and view all the answers

What is a requirement for using Tukey’s HSD test?

Equal sample sizes Signup and view all the answers

Which test is appropriate when there is a significant variability in group variances?

Welch’s ANOVA Signup and view all the answers

When using the Kruskal-Wallis H Test for nonparametric data, what should follow if significant differences are found?

Bonferroni Procedure Signup and view all the answers

What is NOT an assumption for the t-Test for Independent Samples?

Normal distribution among all groups Signup and view all the answers

If the assumptions of One-Way ANOVA are met except for homogeneity of variance, which approach is recommended?

Games-Howell test Signup and view all the answers

Which test is the nonparametric counterpart of the paired t-Test?

Wilcoxon-Signed Rank Test Signup and view all the answers

Which test is more robust when the assumptions of correlation are violated?

Kendall’s tau-B correlation Signup and view all the answers

What is a prerequisite for conducting the Chi-Square Test for Goodness of Fit?

One categorical variable Signup and view all the answers

Which of the following assumptions must be met when conducting a Pearson’s r correlation?

There must be no univariate outliers Signup and view all the answers

Which of the following is NOT an assumption of the Chi-Square Test for Independence?

Bivariate normal distribution Signup and view all the answers

What does the term 'homoscedasticity' refer to in correlation analysis?

Variance of the dependent variable is constant across levels of the independent variable. Signup and view all the answers

What is the primary focus of a Two-Way ANOVA?

Examining the influence of two factors Signup and view all the answers

In the context of ANOVA, what does ANCOVA control for?

External variables that might affect the study Signup and view all the answers

What must be ensured when using multiple dependent variables in MANCOVA?

Homogeneity of variance and similar assumptions as ANCOVA must hold Signup and view all the answers

Study Notes

Assumptions Checks Overview

Assumptions checks determine the appropriateness of hypothesis-testing procedures for data.
Conduct various methods to assess assumptions and identify violations.

Normality Assumption

Shapiro-Wilk Test: Ideal for n < 50; assesses normality.
- p-value < .05 indicates non-normality.
- p-value ≥ .05 indicates normality.
Kolmogorov-Smirnov Test: Suitable for n ≥ 50; similar decision criteria as Shapiro-Wilk.
Histogram: Use for large sample sizes (e.g., n = 300); visually assess normality.
Q-Q Plot: Complement histogram for large samples; normal distribution indicated if dots align along the straight line.

No Significant Outliers Assumption

Boxplot: Identifies outliers.
- Absence of dots indicates no outliers.
- Presence of dots indicates outliers.
Scatterplot: For correlation, visually check for data points deviating from the pattern indicating significant outliers.

Equal Variances Assumption

Homogeneity of Variance: Critical for t-tests and ANOVA.
- Levene’s Test: p < .05 indicates unequal variance; p ≥ .05 indicates equal variance.
Homoscedasticity: Assessed with scatterplot for correlation; data should “fan out” evenly.

Tests for Differences

Wilcoxon-Signed Rank Test: Nonparametric alternative to Paired t-Test when assumptions are violated.
t-Test for Independent Samples: Compares two datasets from different groups.
- Assumptions include continuous dependent variable, two categorical groups, independent observations, normal distribution, no outliers, and homogeneity of variance.
- Mann-Whitney U Test: Nonparametric alternative if assumptions are violated.

One-Way ANOVA

Used for comparing three or more groups.
- Assumptions involve continuous dependent variables, independent categorical groups, independent observations, no significant outliers, normal distribution across groups, and homogeneity of variances.
- If assumptions are met, use Student’s ANOVA.
- Post hoc comparisons for significant ANOVA results:
  - Tukey’s HSD for equal sample sizes.
  - Tukey-Kramer for unequal sample sizes.
  - Scheffé test for unequal sample sizes.
To address violation of homogeneity of variance, use Welch’s ANOVA and Games-Howell post hoc test.
Kruskal-Wallis H Test: Used when assumptions are violated, followed by Dunn’s test or Bonferroni Procedure for post hoc testing.

Variations of ANOVA

Repeated-Measures ANOVA: Analyzes three or more scores from the same respondents.
Two-Way ANOVA: Assesses effects of two factors (e.g., coffee and music on memory).
ANCOVA: ANOVA controlling for other influencing variables.
MANOVA: Simultaneous ANOVA for multiple dependent variables.
MANCOVA: Like ANCOVA but for multiple dependent variables.

Pearson’s r Correlation

Examines the relationship between two continuous variables.
- Assumptions include both variables being continuous, paired observations, independence, linear relationship, bivariate normal distribution, no outliers, and homoscedasticity.
If assumptions are violated, use Kendall’s tau-B or Spearman’s rho for correlation analysis.

Chi-Square Tests

Chi-Square Test for Goodness of Fit: Determines if actual proportions align with expected proportions (e.g., gender representation in crime statistics).
- Assumptions include one categorical variable, independence of observations, mutually exclusive groups, and at least 5 expected frequencies per group.
Chi-Square Test for Independence: Assesses whether categories are related (e.g., color preference and personality traits).

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Description

This quiz focuses on the various assumptions checks necessary for evaluating hypothesis-testing procedures. It discusses methods like the Shapiro-Wilk Test for normality assumption and provides guidance on when to use these techniques. Perfect for those studying statistics or preparing for data analysis.