Statistics: Partitioning Variance in ANOVA
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Questions and Answers

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?

    <p>Treatment variability is due to the experimental manipulation, while error variability is due to random fluctuations</p> Signup and view all the answers

    What is the purpose of the repeated-measures ANOVA?

    <p>To partition variability into treatment and error components</p> Signup and view all the answers

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

    <p>The degrees of freedom</p> Signup and view all the answers

    What is the primary goal of partitioning variability in ANOVA?

    <p>To separate the variability into within-group and between-group components</p> Signup and view all the answers

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

    <p>Within-subjects variability</p> Signup and view all the answers

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

    <p>Treatment effects</p> Signup and view all the answers

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

    <p>One is used for repeated-measures ANOVA and the other is used for between-subjects ANOVA</p> Signup and view all the answers

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

    <p>To identify the sources of variability and estimate the treatment effects</p> Signup and view all the answers

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

    <p>It can control for individual differences in performance</p> Signup and view all the answers

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

    <p>To reduce the impact of individual differences on the results</p> Signup and view all the answers

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

    <p>Variance created by individual differences</p> Signup and view all the answers

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

    <p>It reduces the error variance</p> Signup and view all the answers

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

    <p>It is prone to fatigue and learning effects</p> Signup and view all the answers

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

    <p>What is the effect of weather on problem solving?</p> Signup and view all the answers

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

    <p>One-way repeated-measures ANOVA</p> Signup and view all the answers

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

    <p>To reduce the familywise error rate</p> Signup and view all the answers

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

    <p>The order of testing significance</p> Signup and view all the answers

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

    <p>Comparing multiple groups with repeated measures</p> Signup and view all the answers

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

    <p>They are developed for a limited range of situations</p> Signup and view all the answers

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

    <p>To calculate the mean ranks per treatment</p> Signup and view all the answers

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

    <p>To estimate the confidence intervals</p> 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?

    <p>They are less powerful and may lose information about the magnitude of differences.</p> Signup and view all the answers

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

    <p>To allow for the calculation of the H statistic.</p> Signup and view all the answers

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

    <p>Friedman test.</p> Signup and view all the answers

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

    <p>They have a high false positive rate for larger samples and low power for smaller samples.</p> 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?

    <p>It is more robust to outliers and non-normality.</p> Signup and view all the answers

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

    <p>To compare the sums of ranks between groups.</p> Signup and view all the answers

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

    <p>It is more robust to deviations from normality</p> Signup and view all the answers

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

    <p>The Kruskal-Wallis test is used for between-subjects designs, while the Friedman test is used for within-subjects designs</p> Signup and view all the answers

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

    <p>To accommodate non-normal data</p> Signup and view all the answers

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

    <p>To reduce the Type I error rate</p> Signup and view all the answers

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

    <p>They are less powerful than parametric tests</p> Signup and view all the answers

    What is the primary advantage of using resampling methods?

    <p>They are more robust to deviations from normality</p> Signup and view all the answers

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

    <p>High false positive rate for larger samples and low power for smaller samples.</p> Signup and view all the answers

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

    <p>To test for normality of the data.</p> 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?

    <p>It is less sensitive to deviations from normality.</p> Signup and view all the answers

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

    <p>To determine the significance of the results.</p> Signup and view all the answers

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

    <p>They are less sensitive to deviations from normality.</p> 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?

    <p>They are less powerful than parametric tests.</p> Signup and view all the answers

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

    <p>Homogeneity of variance</p> Signup and view all the answers

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

    <p>It is suitable for repeated-measures designs</p> Signup and view all the answers

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

    <p>Increased risk of Type I errors</p> Signup and view all the answers

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

    <p>To generate confidence intervals for the treatment effect</p> 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?

    <p>They are more robust to non-normality</p> 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?

    <p>They are too conservative and result in low power</p> Signup and view all the answers

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

    <p>F-ratio becomes more conservative</p> Signup and view all the answers

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

    <p>≥ 30</p> Signup and view all the answers

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

    <p>To determine if the data is normally distributed</p> Signup and view all the answers

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

    <p>F-ratio becomes more liberal</p> Signup and view all the answers

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

    <p>To check for homogeneity of variance</p> Signup and view all the answers

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

    <p>Sampling distribution of the parameter</p> Signup and view all the answers

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