Week 2 - ANOVA theory Flashcards
Anovo is short for what?
Analysis of variance
ANOVA Analysis is identical for ____ and non____ designs
experimental
why use ANOVA?
compare several means, can be used when you have manipulated two or more IVs
why not use multiple t-tests instead of ANOVA?
-Inflates the type 1 error rate (essentially the more tests we run, the more likely we are to get a false positive)
-can try controlling for it (bonferroni correction) but lose power.
- Tests for an overall difference between groups.
-Tells us that the group means are different but, doesn’t tell us exactly which means differ.
ANOVA
What does ANOVA stand for?
Analysis of Variance.
A statistical technique used to determine if there are any statistically significant differences between the means of three or more independent groups.
One-Way ANOVA
Who developed the basic technique of ANOVA?
Sir Ronald Fisher.
What is the primary focus of one-way ANOVA?
Investigating differences in means among multiple groups.
The hypothesis that states that there are no differences among the group means, implying that any observed differences are due to sampling error.
Null Hypothesis (H0)
The hypothesis that states at least one group mean is different from the others, suggesting significant effects among groups.
Alternative Hypothesis (H1)
What are the key assumptions of one-way ANOVA?
Normality, homogeneity of variance, and independence of observations.
The variation accounted for by the differences between the group means in an ANOVA.
Between-Group Variability
The variation accounted for by the differences within each group in an ANOVA.
Within-Group Variability
How is the F-ratio calculated in ANOVA?
The F-ratio is calculated by dividing the mean square between groups by the mean square within groups.
An estimate of variance calculated by dividing the sum of squares by the corresponding degrees of freedom.
Mean Square (MS)
What does a significant F-value indicate in ANOVA?
It suggests that there are significant differences among the group means, leading to the rejection of the null hypothesis.
A measure of the strength of the relationship between the independent variable and the dependent variable in ANOVA, commonly reported as eta squared (η²).
Effect Size
What is the purpose of post hoc tests in ANOVA?
To determine which specific group means are significantly different after finding a significant overall F-value.
A statistical adjustment method used to reduce the chances of Type I error when multiple comparisons are being made.
Bonferroni Correction
What is the role of the Levene’s test in ANOVA?
To check for homogeneity of variance across groups before proceeding with ANOVA.
A statistical test used to assess the normality of residuals in ANOVA.
Shapiro-Wilk Test
What is a repeated measures ANOVA?
An analysis that evaluates differences among means when the same subjects are used for each treatment.
The condition where variances of the differences between all combinations of related groups are equal, necessary for repeated measures ANOVA.
Sphericity
What is a primary limitation of ANOVA?
ANOVA does not indicate where differences lie among means, necessitating post hoc tests for further analysis.
A non-parametric alternative to one-way ANOVA, used when the assumption of normality is violated.
Kruskal-Wallis Test
What does the p-value represent in the context of an ANOVA test?
The probability of obtaining the observed results or more extreme results if the null hypothesis is true.
A measure of effect size that indicates the proportion of variance in the dependent variable that can be attributed to the independent variable.
Eta Squared (η²)
How can you check the assumptions of ANOVA visually?
By using QQ plots to assess normality and box plots to evaluate homogeneity of variances.
The differences between observed values and the values predicted by the ANOVA model, used to assess model fit and check assumptions.
Residuals
What are the main types of ANOVA
Between subjects, Repeated measures, Factorial, ANCOVA.
A design where different levels of the independent variable (IV) are experienced by different entities, also known as “Independent ANOVA”.
Between-groups ANOVA
What is ANCOVA?
ANCOVA stands for Analysis of Co-variance, and it can transform any of the three ANOVA types by adding covariates.
An ANOVA design that includes at least one within-groups independent variable and one between groups independent variable, requiring at least two IVs.
Mixed ANOVA
How does a one-way ANOVA differ from a factorial ANOVA?
A one-way ANOVA involves one independent variable, while a factorial ANOVA involves two or more independent variables.
A design where different levels of the independent variable are experienced by the same entities over time, allowing for repeated measures.
Repeated measures ANOVA
A type of ANOVA where different levels of the independent variable are experienced by different entities, also referred to as “Independent” ANOVA.
Between-subjects ANOVA
What is a One-way ANOVA?
A One-way ANOVA examines the effect of one independent variable with different levels on a dependent variable.
Repeated measures ANOVA
A design where different levels of the independent variable are experienced by the same entities, often utilized in studies with pre and post-intervention measurements.
What constitutes a Factorial ANOVA?
A Factorial ANOVA involves two or more independent variables, with each participant experiencing one level of each independent variable.
What is the purpose of a Mixed ANOVA design?
A Mixed ANOVA design includes both within-groups (repeated measures) and between-groups independent variables.
A type of ANOVA where each subject experiences all levels of the independent variable, commonly referred to as “repeated measures” ANOVA.
Within-groups ANOVA
How can any ANOVA type become an ANCOVA?
By adding one or more covariates to control for nuisance variables that may affect the dependent variable.
A type of ANOVA that assesses the impact of a single independent variable on a dependent variable.
One-way ANOVA
What is a factorial design in ANOVA?
A factorial design in ANOVA involves multiple independent variables and examines their combined effects on a dependent variable.
An ANOVA design that includes at least one within-groups and one between-groups independent variable, used for more complex analyses
Mixed Factorial ANOVA
Give an example of a Between-groups ANOVA scenario.
An example is studying how different dietary conditions impact weight loss by using separate groups of participants for each diet.
A variable that is not the primary interest in a study but is controlled for in an analysis to reduce potential confounding.
Covariate
What effect does adding covariates have in ANCOVA?
Adding covariates in ANCOVA helps control for variability and increase the precision of the results for the primary independent variables.
A variable that may obscure or confound the results of an analysis if not controlled or accounted for.
Nuisance variable
What does a Repeated measures ANOVA allow researchers to assess?
A Repeated measures ANOVA allows researchers to assess the impact of different interventions on the same subjects over time.
The variable that is manipulated in an experiment to observe its effect on the dependent variable.
Independent Variable (IV)
Why is classifying ANOVA types important in research?
Classifying ANOVA types is essential for clearly communicating the analysis strategy in research reports and ensuring appropriate statistical methods are used.
The outcome variable that is measured to assess the effect of changes in the independent variable.
Dependent Variable (DV)
What does “pre/post intervention” mean in the context of ANOVA?
“Pre/post intervention” refers to measurements taken before and after an intervention to observe changes attributable to the treatment.
A document that presents and discusses the findings of a research study, including details about methodology, analysis, and conclusions.
Research Report
What is the significance of the design in ANCOVA?
The design in ANCOVA significantly impacts how covariates are included and analyzed, which affects the interpretation of the results.
The overarching plan or structure for conducting research that outlines how data will be collected and analyzed.
Experimental Design
How does a Factorial ANOVA differ from a One-way ANOVA?
A Factorial ANOVA involves two or more independent variables, while a One-way ANOVA examines only one independent variable.
What is the primary purpose of using within-groups (repeated measures) designs?
To measure each participant on the dependent variable (DV) at least twice to track changes over time or levels of the independent variable (IV).
The assumption that the variances of the differences between all combinations of related groups (levels of the independent variable) are roughly equal.
Sphericity
What are the advantages of using within-groups designs in research?
Each participant serves as their own control, which reduces the effect of individual differences and requires fewer participants for the same statistical power.
What are two examples of when within-groups designs might be used?
Measuring aggression before and after treatment, or assessing weight at pre-diet, post-diet, and follow-up stages.
A statistical test used to evaluate the assumption of sphericity in within-groups designs; if p < .05, the assumption is considered violated.
Mauchly’s Test
What is one disadvantage of within-groups designs?
They are not possible for existing groups; for example, you cannot change dogs into cats for a study.
An adjusted estimate used in statistical analysis when the sphericity assumption is violated, typically used when the estimate of sphericity is less than .75.
Greenhouse-Geisser Estimate
How is sphericity tested in within-groups designs?
By assessing if the correlation between treatment levels is the same and using Mauchly’s test to verify if the assumption is violated.
A more liberal adjustment used in statistical analysis when the sphericity assumption is violated, typically used when the sphericity estimate is greater than .75.
Huynh-Feldt Estimate
What does a violation of the sphericity assumption indicate?
It suggests that the variances in the differences between conditions are not equal, affecting the validity of the statistical results.
A test that assesses the homogeneity of variances between groups; used for between-groups designs rather than within-groups.
Levene’s Test
Why is the assumption of sphericity often violated in large samples?
Because larger samples have more power to detect even small differences, making violations more likely.
What is a practical implication of each participant being their own control in within-groups designs?
It minimizes variability due to individual differences, which can enhance the sensitivity of detecting effects.
The phenomenon where participants’ performance improves on a measure over time due to repeated exposure, potentially confounding results in within-groups designs.
Practice Effects
What types of studies might face issues with carry-over effects?
studies where the same participants undergo multiple treatment levels, such as repeated measurements of behaviors or cognitive tasks.
