Statistics: Partitioning Variance in ANOVA

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What is the purpose of partitioning variability in ANOVA?

To identify the experimental manipulation

To separate variability into different components (correct)

To calculate the grand mean

To calculate the mean square model

What type of variability is calculated by summing up the variability of each subject around their own mean?

Error variability

Between-subjects variability

Treatment variability

Within-subjects variability (correct)

What is the purpose of experimental manipulation in ANOVA?

To calculate the mean square residual

To identify the grand mean

To separate treatment and error variability

To introduce a treatment effect (correct)

What is the difference between treatment variability and error variability?

Treatment variability is due to the experimental manipulation, while error variability is due to random fluctuations (C) Signup and view all the answers

What is the purpose of the repeated-measures ANOVA?

To partition variability into treatment and error components (C) Signup and view all the answers

What are SSmodel and SSresidual adjusted by in the repeated-measures ANOVA?

The degrees of freedom (A) Signup and view all the answers

What is the primary goal of partitioning variability in ANOVA?

To separate the variability into within-group and between-group components (C) Signup and view all the answers

What type of variability is accounted for in the error term in repeated-measures ANOVA?

Within-subjects variability (A) Signup and view all the answers

What is the primary source of variability in the experimental manipulation?

Treatment effects (B) Signup and view all the answers

What is the main difference between within-subjects variability and between-subjects variability?

One is used for repeated-measures ANOVA and the other is used for between-subjects ANOVA (B) Signup and view all the answers

Why is it important to separate the variability into within-group and between-group components in ANOVA?

To identify the sources of variability and estimate the treatment effects (D) Signup and view all the answers

What is the main advantage of using repeated-measures ANOVA?

It can control for individual differences in performance (C) Signup and view all the answers

What is the main purpose of using a repeated-measures design in an experiment?

To reduce the impact of individual differences on the results (C) Signup and view all the answers

What is the primary source of variability that is 'cancelled out' in a repeated-measures design?

Variance created by individual differences (D) Signup and view all the answers

What is the benefit of using a repeated-measures design in terms of error variance?

It reduces the error variance (C) Signup and view all the answers

What is the main disadvantage of using a repeated-measures design?

It is prone to fatigue and learning effects (B) Signup and view all the answers

What is the research question being addressed in the example experiment?

What is the effect of weather on problem solving? (A) Signup and view all the answers

What is the statistical test used to analyze the data in the example experiment?

One-way repeated-measures ANOVA (D) Signup and view all the answers

What is the primary purpose of the Bonferroni correction in post-hoc tests?

To reduce the familywise error rate (B) Signup and view all the answers

What is the main difference between the Holm's and Hochberg's tests in sequential post-hoc analysis?

The order of testing significance (D) Signup and view all the answers

What is the Friedman test used for in non-parametric ANOVA alternatives?

Comparing multiple groups with repeated measures (C) Signup and view all the answers

What is the main disadvantage of non-parametric tests, such as the Kruskal-Wallis test?

They are developed for a limited range of situations (C) Signup and view all the answers

What is the purpose of calculating ranks in the Friedman test?

To calculate the mean ranks per treatment (B) Signup and view all the answers

What is the primary purpose of bootstrapping in non-parametric ANOVA alternatives?

To estimate the confidence intervals (C) Signup and view all the answers

What is the main drawback of using non-parametric tests, such as the Kruskal-Wallis test, compared to their parametric counterparts?

They are less powerful and may lose information about the magnitude of differences. (B) Signup and view all the answers

What is the purpose of ranking the data in the Kruskal-Wallis test?

To allow for the calculation of the H statistic. (C) Signup and view all the answers

Which of the following is a non-parametric alternative to the one-way repeated-measures ANOVA?

Friedman test. (C) Signup and view all the answers

Why are direct tests of normality, such as the Shapiro-Wilk test, not recommended?

They have a high false positive rate for larger samples and low power for smaller samples. (A) Signup and view all the answers

What is the advantage of using the Kruskal-Wallis test instead of the one-way ANOVA when the data is not normally distributed?

It is more robust to outliers and non-normality. (C) Signup and view all the answers

What is the purpose of the H statistic in the Kruskal-Wallis test?

To compare the sums of ranks between groups. (C) Signup and view all the answers

What is the primary advantage of using the Kruskal-Wallis test over traditional ANOVA?

It is more robust to deviations from normality (A) Signup and view all the answers

What is the main difference between the Kruskal-Wallis test and the Friedman test?

The Kruskal-Wallis test is used for between-subjects designs, while the Friedman test is used for within-subjects designs (B) Signup and view all the answers

What is the primary purpose of using rank-based statistical analysis?

To accommodate non-normal data (C) Signup and view all the answers

What is the purpose of using post-hoc tests with Bonferroni correction?

To reduce the Type I error rate (D) Signup and view all the answers

What is the primary limitation of non-parametric ANOVA alternatives?

They are less powerful than parametric tests (D) Signup and view all the answers

What is the primary advantage of using resampling methods?

They are more robust to deviations from normality (C) Signup and view all the answers

What is the primary limitation of direct tests of normality, such as the Kolmogorov-Smirnov test?

High false positive rate for larger samples and low power for smaller samples. (A) Signup and view all the answers

What is the purpose of calculating skewness and kurtosis in statistical analysis?

To test for normality of the data. (B) Signup and view all the answers

What is the advantage of using the Kruskal-Wallis test over traditional ANOVA when the data is not normally distributed?

It is less sensitive to deviations from normality. (B) Signup and view all the answers

What is the purpose of interpreting the standard error in statistical analysis?

To determine the significance of the results. (B) Signup and view all the answers

What is the primary advantage of using non-parametric tests, such as the Kruskal-Wallis test?

They are less sensitive to deviations from normality. (A) Signup and view all the answers

What is the primary limitation of non-parametric tests, such as the Kruskal-Wallis test, compared to their parametric counterparts?

They are less powerful than parametric tests. (D) Signup and view all the answers

What is the underlying assumption that is being addressed by using a Bonferroni correction in pairwise comparison?

Homogeneity of variance (A) Signup and view all the answers

What is the primary advantage of using the Friedman test over the Kruskal-Wallis test?

It is suitable for repeated-measures designs (C) Signup and view all the answers

What is the consequence of violating the assumption of homogeneity of variance in ANOVA?

Increased risk of Type I errors (A) Signup and view all the answers

What is the purpose of bootstrapping in non-parametric ANOVA alternatives?

To generate confidence intervals for the treatment effect (D) Signup and view all the answers

Why are non-parametric tests, such as the Kruskal-Wallis test, preferred over traditional ANOVA when the data is not normally distributed?

They are more robust to non-normality (C) Signup and view all the answers

What is the primary limitation of using sequential methods, such as Holm's and Hochberg's tests, in post-hoc analysis?

They are too conservative and result in low power (C) Signup and view all the answers

What is the consequence of having unequal sample sizes in between-subjects ANOVA?

F-ratio becomes more conservative (D) Signup and view all the answers

What is the rule of thumb for sample size in normality testing?

≥ 30 (C) Signup and view all the answers

What is the purpose of checking for skewness and kurtosis in normality testing?

To determine if the data is normally distributed (B) Signup and view all the answers

What is the consequence of violating the assumption of homogeneity of variance in ANOVA?

F-ratio becomes more liberal (B) Signup and view all the answers

What is the purpose of Levine's test in ANOVA?

To check for homogeneity of variance (A) Signup and view all the answers

What is the central limit theorem related to in normality testing?

Sampling distribution of the parameter (B) Signup and view all the answers

Statistics: Partitioning Variance in ANOVA

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Questions and Answers

What is the purpose of partitioning variability in ANOVA?

What type of variability is calculated by summing up the variability of each subject around their own mean?

What is the purpose of experimental manipulation in ANOVA?

What is the difference between treatment variability and error variability?

What is the purpose of the repeated-measures ANOVA?

What are SSmodel and SSresidual adjusted by in the repeated-measures ANOVA?

What is the primary goal of partitioning variability in ANOVA?

What type of variability is accounted for in the error term in repeated-measures ANOVA?

What is the primary source of variability in the experimental manipulation?

What is the main difference between within-subjects variability and between-subjects variability?

Why is it important to separate the variability into within-group and between-group components in ANOVA?

What is the main advantage of using repeated-measures ANOVA?

What is the main purpose of using a repeated-measures design in an experiment?

What is the primary source of variability that is 'cancelled out' in a repeated-measures design?

What is the benefit of using a repeated-measures design in terms of error variance?

What is the main disadvantage of using a repeated-measures design?

What is the research question being addressed in the example experiment?

What is the statistical test used to analyze the data in the example experiment?

What is the primary purpose of the Bonferroni correction in post-hoc tests?

What is the main difference between the Holm's and Hochberg's tests in sequential post-hoc analysis?

What is the Friedman test used for in non-parametric ANOVA alternatives?

What is the main disadvantage of non-parametric tests, such as the Kruskal-Wallis test?

What is the purpose of calculating ranks in the Friedman test?

What is the primary purpose of bootstrapping in non-parametric ANOVA alternatives?

What is the main drawback of using non-parametric tests, such as the Kruskal-Wallis test, compared to their parametric counterparts?

What is the purpose of ranking the data in the Kruskal-Wallis test?

Which of the following is a non-parametric alternative to the one-way repeated-measures ANOVA?

Why are direct tests of normality, such as the Shapiro-Wilk test, not recommended?

What is the advantage of using the Kruskal-Wallis test instead of the one-way ANOVA when the data is not normally distributed?

What is the purpose of the H statistic in the Kruskal-Wallis test?

What is the primary advantage of using the Kruskal-Wallis test over traditional ANOVA?

What is the main difference between the Kruskal-Wallis test and the Friedman test?

What is the primary purpose of using rank-based statistical analysis?

What is the purpose of using post-hoc tests with Bonferroni correction?

What is the primary limitation of non-parametric ANOVA alternatives?

What is the primary advantage of using resampling methods?

What is the primary limitation of direct tests of normality, such as the Kolmogorov-Smirnov test?

What is the purpose of calculating skewness and kurtosis in statistical analysis?

What is the advantage of using the Kruskal-Wallis test over traditional ANOVA when the data is not normally distributed?

What is the purpose of interpreting the standard error in statistical analysis?

What is the primary advantage of using non-parametric tests, such as the Kruskal-Wallis test?

What is the primary limitation of non-parametric tests, such as the Kruskal-Wallis test, compared to their parametric counterparts?

What is the underlying assumption that is being addressed by using a Bonferroni correction in pairwise comparison?

What is the primary advantage of using the Friedman test over the Kruskal-Wallis test?

What is the consequence of violating the assumption of homogeneity of variance in ANOVA?

What is the purpose of bootstrapping in non-parametric ANOVA alternatives?

Why are non-parametric tests, such as the Kruskal-Wallis test, preferred over traditional ANOVA when the data is not normally distributed?

What is the primary limitation of using sequential methods, such as Holm's and Hochberg's tests, in post-hoc analysis?

What is the consequence of having unequal sample sizes in between-subjects ANOVA?

What is the rule of thumb for sample size in normality testing?

What is the purpose of checking for skewness and kurtosis in normality testing?

What is the consequence of violating the assumption of homogeneity of variance in ANOVA?

What is the purpose of Levine's test in ANOVA?

What is the central limit theorem related to in normality testing?

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