Podcast
Questions and Answers
What is the primary limitation of statistics in determining causal relationships?
What is the primary limitation of statistics in determining causal relationships?
What characterizes an experimental design in studies?
What characterizes an experimental design in studies?
Which of the following best describes a main effect in a two-way ANOVA?
Which of the following best describes a main effect in a two-way ANOVA?
What is the purpose of using blocking in factorial designs?
What is the purpose of using blocking in factorial designs?
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How does a regression approach help in analyzing unequal cells in factorial designs?
How does a regression approach help in analyzing unequal cells in factorial designs?
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What is a factorial-block design primarily characterized by?
What is a factorial-block design primarily characterized by?
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What should be the preferred condition regarding subjects per cell in a factorial ANOVA?
What should be the preferred condition regarding subjects per cell in a factorial ANOVA?
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What does the term 'orthogonal' refer to in the context of effects in ANOVA?
What does the term 'orthogonal' refer to in the context of effects in ANOVA?
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What does a significant interaction effect in ANCOVA indicate?
What does a significant interaction effect in ANCOVA indicate?
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In randomized ANCOVA designs, what is the primary effect achieved?
In randomized ANCOVA designs, what is the primary effect achieved?
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Why might MANOVA be preferred over multiple univariate tests?
Why might MANOVA be preferred over multiple univariate tests?
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What could potentially invalidate the interpretation of ANCOVA in a non-randomized design?
What could potentially invalidate the interpretation of ANCOVA in a non-randomized design?
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What is a potential drawback of using a total score in statistical analysis?
What is a potential drawback of using a total score in statistical analysis?
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Which of the following best describes homogeneous regression slopes in ANCOVA?
Which of the following best describes homogeneous regression slopes in ANCOVA?
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What does the null hypothesis (H0) state in a MANOVA test?
What does the null hypothesis (H0) state in a MANOVA test?
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What statistical issue can arise from conducting separate analyses on multiple dependent variables?
What statistical issue can arise from conducting separate analyses on multiple dependent variables?
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What is the primary objective of forming homogeneous blocks in randomized-blocks design?
What is the primary objective of forming homogeneous blocks in randomized-blocks design?
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What is a potential downside of post-hoc blocking in experimental designs?
What is a potential downside of post-hoc blocking in experimental designs?
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Which of the following is NOT a method to improve statistical power?
Which of the following is NOT a method to improve statistical power?
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What type of error occurs when the null hypothesis is rejected when it should not be?
What type of error occurs when the null hypothesis is rejected when it should not be?
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What is ANCOVA primarily used for in experimental design?
What is ANCOVA primarily used for in experimental design?
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In which situation is a retrospective power analysis typically used?
In which situation is a retrospective power analysis typically used?
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Which design involves measuring the same subjects under different treatment levels?
Which design involves measuring the same subjects under different treatment levels?
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What does increasing the error variance do to the statistical power of a test?
What does increasing the error variance do to the statistical power of a test?
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What does the null hypothesis state in a one-way ANOVA?
What does the null hypothesis state in a one-way ANOVA?
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What method is used to confirm the assumption of equal variances in ANOVA?
What method is used to confirm the assumption of equal variances in ANOVA?
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Which of the following statements about effect size in ANOVA is true?
Which of the following statements about effect size in ANOVA is true?
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Which characteristic is NOT necessary for an experimental design in ANOVA?
Which characteristic is NOT necessary for an experimental design in ANOVA?
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What is the primary point of conducting an ANOVA test?
What is the primary point of conducting an ANOVA test?
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Which of the following is an example of a post hoc comparison?
Which of the following is an example of a post hoc comparison?
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What is the significance of the p-value in the context of ANOVA?
What is the significance of the p-value in the context of ANOVA?
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What condition must be satisfied for the assumption of independent observations in ANOVA?
What condition must be satisfied for the assumption of independent observations in ANOVA?
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What does the null hypothesis (H0) state regarding interaction effects?
What does the null hypothesis (H0) state regarding interaction effects?
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What is an implication of missing data pertaining to effective sample size?
What is an implication of missing data pertaining to effective sample size?
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Which type of missing data is considered the least severe?
Which type of missing data is considered the least severe?
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How does missing data related to participant nonresponse differ from data lost due to technical failures?
How does missing data related to participant nonresponse differ from data lost due to technical failures?
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What can be a consequence of data being not missing at random (NMAR)?
What can be a consequence of data being not missing at random (NMAR)?
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What is an example of missing at random (MAR)?
What is an example of missing at random (MAR)?
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What is the impact of computer failure on missing data?
What is the impact of computer failure on missing data?
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What characterizes the 'missing completely at random' (MCAR) classification?
What characterizes the 'missing completely at random' (MCAR) classification?
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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.
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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.
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Assumptions of ANOVA
- Independent observations
- Normally distributed scores within each group
- Equal variances across groups
Experimental Designs
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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.
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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
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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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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.
