Repeated Measures & ANOVA Concepts
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Questions and Answers

What is the primary limitation of statistics in determining causal relationships?

  • Statistics can only show correlations. (correct)
  • Statistics depend solely on mathematical models.
  • Statistics do not account for variance.
  • Statistics require random assignment to show causation.

    • What characterizes an experimental design in studies?

  • Participants are randomly assigned to treatment groups. (correct)
  • Only one treatment is tested at a time.
  • Participants are assigned to groups based on their characteristics.
  • No random assignment to treatments is utilized.

    • Which of the following best describes a main effect in a two-way ANOVA?

  • The average effect of one factor ignoring other factors. (correct)
  • The total variance contributed by all subjects.
  • The interaction between two factors.
  • The combined influence of all factors considered together.

    • What is the purpose of using blocking in factorial designs?

    <p>To draw conclusions about each block and reduce error.</p> Signup and view all the answers

    How does a regression approach help in analyzing unequal cells in factorial designs?

    <p>By adjusting each effect for all other effects.</p> Signup and view all the answers

    What is a factorial-block design primarily characterized by?

    <p>Inclusion of blocking factors intrinsic to subjects.</p> Signup and view all the answers

    What should be the preferred condition regarding subjects per cell in a factorial ANOVA?

    <p>Equal numbers of subjects per cell are preferred.</p> Signup and view all the answers

    What does the term 'orthogonal' refer to in the context of effects in ANOVA?

    <p>The effects are completely unrelated and independent.</p> Signup and view all the answers

    What does a significant interaction effect in ANCOVA indicate?

    <p>Unequal slopes are present.</p> Signup and view all the answers

    In randomized ANCOVA designs, what is the primary effect achieved?

    <p>Elimination of systematic differences.</p> Signup and view all the answers

    Why might MANOVA be preferred over multiple univariate tests?

    <p>It reduces the overall Type 1 error rate.</p> Signup and view all the answers

    What could potentially invalidate the interpretation of ANCOVA in a non-randomized design?

    <p>Systematic bias existing between groups.</p> Signup and view all the answers

    What is a potential drawback of using a total score in statistical analysis?

    <p>It might obscure significant effects due to canceling out.</p> Signup and view all the answers

    Which of the following best describes homogeneous regression slopes in ANCOVA?

    <p>They suggest the covariate does not interact with the treatment effects.</p> Signup and view all the answers

    What does the null hypothesis (H0) state in a MANOVA test?

    <p>All groups are equivalent in all dependent variables.</p> Signup and view all the answers

    What statistical issue can arise from conducting separate analyses on multiple dependent variables?

    <p>Inflated Type 1 error rate.</p> Signup and view all the answers

    What is the primary objective of forming homogeneous blocks in randomized-blocks design?

    <p>To minimize within-group variability</p> Signup and view all the answers

    What is a potential downside of post-hoc blocking in experimental designs?

    <p>It can lead to unequal sample sizes and data fishing</p> Signup and view all the answers

    Which of the following is NOT a method to improve statistical power?

    <p>Decrease the level of significance</p> Signup and view all the answers

    What type of error occurs when the null hypothesis is rejected when it should not be?

    <p>Type 1 error</p> Signup and view all the answers

    What is ANCOVA primarily used for in experimental design?

    <p>To eliminate confounding and minimize variability</p> Signup and view all the answers

    In which situation is a retrospective power analysis typically used?

    <p>After analyzing the results to understand power levels</p> Signup and view all the answers

    Which design involves measuring the same subjects under different treatment levels?

    <p>Repeated-measures design</p> Signup and view all the answers

    What does increasing the error variance do to the statistical power of a test?

    <p>Decreases the power</p> Signup and view all the answers

    What does the null hypothesis state in a one-way ANOVA?

    <p>All group means are equal.</p> Signup and view all the answers

    What method is used to confirm the assumption of equal variances in ANOVA?

    <p>Levene's test</p> Signup and view all the answers

    Which of the following statements about effect size in ANOVA is true?

    <p>Effect size measures the strength of the relationship or difference between group means.</p> Signup and view all the answers

    Which characteristic is NOT necessary for an experimental design in ANOVA?

    <p>Use of multiple independent variables.</p> Signup and view all the answers

    What is the primary point of conducting an ANOVA test?

    <p>To determine whether differences in means are due to chance or are significant.</p> Signup and view all the answers

    Which of the following is an example of a post hoc comparison?

    <p>Conducting multiple comparisons with no specific hypothesis in mind.</p> Signup and view all the answers

    What is the significance of the p-value in the context of ANOVA?

    <p>It indicates the likelihood that any observed differences are due to chance.</p> Signup and view all the answers

    What condition must be satisfied for the assumption of independent observations in ANOVA?

    <p>Random assignment must be used to allocate subjects to treatments.</p> Signup and view all the answers

    What does the null hypothesis (H0) state regarding interaction effects?

    <p>There is no interaction effect.</p> Signup and view all the answers

    What is an implication of missing data pertaining to effective sample size?

    <p>It always results in a smaller effective sample size.</p> Signup and view all the answers

    Which type of missing data is considered the least severe?

    <p>Missing completely at random (MCAR)</p> Signup and view all the answers

    How does missing data related to participant nonresponse differ from data lost due to technical failures?

    <p>Nonresponse data leads to increased bias.</p> Signup and view all the answers

    What can be a consequence of data being not missing at random (NMAR)?

    <p>Smaller effective sample size with introduced bias.</p> Signup and view all the answers

    What is an example of missing at random (MAR)?

    <p>Dropouts occur equally across different treatment groups.</p> Signup and view all the answers

    What is the impact of computer failure on missing data?

    <p>It decreases effective sample size but does not introduce bias.</p> Signup and view all the answers

    What characterizes the 'missing completely at random' (MCAR) classification?

    <p>The missing data is not related to any study variable.</p> Signup and view all the answers

    Study Notes

    Repeated Measures & ANOVA

    • Between-factor one-way ANOVA compares means between groups (independent populations).
    • The null hypothesis states that all group means are equal.
    • The alternative hypothesis states that at least one group mean is different.
    • ANOVA with two groups is equivalent to a t-test.
    • ANOVA analyzes a fixed number of groups with a variable number of possible outcomes.
    • P-value indicates the significance of a factor by showing the probability of obtaining the observed differences if the population means were equal.
    • Effect size indicates the magnitude of the effect, specifically the difference between group means in the population.
    • Eta-squared (N2) represents the proportion of variance explained by the effect.
    • Partial eta-squared represents the proportion of variance explained by the effect after considering other factors.
    • Multiple comparisons are used to further examine group differences when the null hypothesis is rejected.
      • Planned comparisons (contrasts) are pre-specified based on hypotheses.
      • Post-hoc comparisons are unplanned and data-driven.
    • Assumptions of ANOVA
      • Independent observations
      • Normally distributed scores within each group
      • Equal variances across groups

    Experimental Designs

    • Three characteristics of experiment designs
      • Manipulation of treatment levels: Creating groups based on different treatment conditions.
      • Random assignment of subjects: Randomly assigning subjects to treatment levels.
      • Control of extraneous variables: Controlling the effect of factors other than the independent variable through methods like:
        • Holding constant: Maintaining the variable at a specific level to eliminate its influence.
        • Randomization: Randomly assigning subjects to treatments to balance out the effects of potentially confounding variables.
        • Counterbalancing: Ensuring each condition in the experiment appears in the same position on the list, but in a different order for different subjects.
        • Turning extraneous variables into additional factors: Including potentially confounding factors as independent variables in the analysis.

    Between-Subjects Designs

    • Between-subjects designs test treatment differences between groups of subjects with different individuals in each treatment level.
      • Experimental designs: Randomly assign subjects to treatment conditions.
      • Nonexperimental designs: Do not involve random assignment.

    Factorial Designs

    • Factorial designs involve more than one factor and are often used for studying the main effects of each factor and their interactions.
    • Two-way ANOVA is a common analysis for factorial designs with two independent variables.
    • Sources of variance in factorial designs:
      • Each factor is a source of variance.
      • Combinations of factors create interactions, which are also sources of variance.
      • The error term represents variability due to individual differences.

    Main Effects in Two-way ANOVA

    • Main effects are the average effect of a factor over the levels of the other factor(s).
    • They can be interpreted most accurately when there is no interaction effect.
      • Unequal sample sizes can complicate the interpretation of main effects.

    Factorial-Blocks Designs

    • Factorial-blocks designs use a blocking factor that's intrinsic to the subjects and related to the dependent variable.
    • The purpose of blocking is to reduce error variance and draw conclusions about specific blocks.
    • Two types of factors:
      • Experimental factors: Manipulated variables of interest.
      • Blocking factors: Variables used to control for extraneous variation.

    Specific Factorial-Blocks Designs

    • Randomized blocks design: Subjects are pre-grouped into homogeneous blocks to reduce within-group variability and improve power for the experimental factor.
    • Post-hoc blocks design: Blocking is done after data collection and was not initially planned. This can lead to unequal sample sizes and data fishing.

    Within-Subjects Designs

    • Within-subjects (repeated-measures) designs involve the same subjects participating in multiple treatment levels.
    • Differences in scores are tested within the same set of subjects.

    Power Analysis

    • A priori power analysis: Computes the sample size needed to achieve a desired power level, significance level, and effect size.
    • Retrospective power analysis: Computes the power of a statistical test after data collection based on the obtained sample size, significance level, and effect size.

    ANCOVA

    • ANCOVA is a statistical technique that controls for the effects of continuous covariates to reduce within-group variance and increase power.
    • The covariate is measured without error and is included as a predictor in the model, even if it's not the primary focus of the research.
    • Important considerations regarding ANCOVA:
      • Homogeneous regression slopes: The relationship between the covariate and the dependent variable should be the same across all treatment groups.
      • Randomized designs: ANCOVA is most appropriate when subjects are randomly assigned to groups, preventing systematic differences in covariates.
      • Natural/intact groups: If groups are based on pre-existing classifications, ANCOVA should be used cautiously as systematic differences between groups might be reflected in the covariate.
    • Non-randomized designs: ANCOVA is not appropriate when systematic bias exists between groups, as it may be difficult to interpret its results, especially in situations where the covariate might be confounding.

    MANOVA

    • MANOVA (Multivariate Analysis of Variance) is used when there are multiple dependent variables.
    • It models the association between dependent variables and analyzes the joint effects of factors on these variables.
    • Reasons for using MANOVA:
      • A treatment might affect subjects in multiple ways.
      • Examining multiple dependent variables provides a more comprehensive understanding of the phenomenon under investigation.
    • Null hypothesis for MANOVA: The combination of means for all outcome variables in one group is equal to the combination in another group.
    • Statistical reasons for MANOVA:
      • Multiple univariate tests increase the overall Type 1 error rate (false positives).
      • Univariate tests ignore the correlation between dependent variables.
      • MANOVA can be more powerful than individual tests, especially when variables have a joint effect.

    Reasons for Not Using MANOVA

    • Within-subjects designs: When there's an interaction effect between the factor and time, MANOVA might not be the appropriate choice.

    Missing Data

    • Missing data occurs when a score is not obtained when it was intended to be measured.
    • Reasons for missing data:
      • Participant refusing or not participating.
      • Participant unable or unwilling to provide a score.
      • Loss of data due to technical issues or other reasons.
    • Consequences of missing data:
      • Reduced effective sample size: This leads to lower power and larger standard errors.
      • Possible bias: If the missing data is related to the research, the results might not represent the population of interest.
    • Missingness mechanism categories (least to most severe):
      • Missing completely at random (MCAR): Data is missing randomly and unrelated to the study.
      • Missing at random (MAR): Missingness is related to the observed variables but not the dependent variable.
      • Not missing at random (NMAR): Missingness is related to the unobserved values of the dependent variable.

    Dealing with Missing Data

    • Diagnosing the type of missing data: It's not always possible, but it's crucial for determining the best approach for addressing missingness.
    • Imputation: Replacing missing values with estimates based on the available data, using methods like mean imputation or more sophisticated techniques.
    • Model-based approaches: Incorporating missing data patterns into the statistical model.

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    Repeated Measures ANOVA Lecture PDF

    Description

    Dive into the essential concepts of repeated measures and ANOVA. This quiz covers topics such as null and alternative hypotheses, effect size, p-values, and multiple comparisons. Test your knowledge on how to analyze group differences and understand the implications of variance in your data.

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