Podcast
Questions and Answers
What is a key difference between ANOVA and ANCOVA?
What is a key difference between ANOVA and ANCOVA?
- ANCOVA is simple and broadly applied, while ANOVA is not.
- ANOVA requires a deep understanding of the variables and their relationships, while ANCOVA does not.
- ANCOVA can control for the effects of certain variables, while ANOVA cannot. (correct)
- ANOVA can control for the effects of certain variables, while ANCOVA cannot.
What does ANCOVA adjust to provide a better understanding of the relationship between the dependent variable and the independent variable?
What does ANCOVA adjust to provide a better understanding of the relationship between the dependent variable and the independent variable?
- The independent variable
- The F-statistic
- The dependent variable (correct)
- The degrees of freedom
What is a covariate in the context of ANCOVA?
What is a covariate in the context of ANCOVA?
- The primary variable of interest in the study.
- The independent variable being manipulated.
- A statistical test used to analyze variance.
- A variable that could affect the dependent variable but isn't the main focus of the study. (correct)
In the dog therapy example, what would be the covariate?
In the dog therapy example, what would be the covariate?
What is the purpose of using a covariate in the dog therapy example?
What is the purpose of using a covariate in the dog therapy example?
If the effect of the covariate is removed, what does 'Dose' reflect?
If the effect of the covariate is removed, what does 'Dose' reflect?
Eta-squared in ANCOVA is interpreted as:
Eta-squared in ANCOVA is interpreted as:
What does a 'significant' group difference mean?
What does a 'significant' group difference mean?
What does the formula Covariance(x, y) = Σ(xi – x)(yi – y) / N-1 calculate?
What does the formula Covariance(x, y) = Σ(xi – x)(yi – y) / N-1 calculate?
What is the purpose of standardizing covariance?
What is the purpose of standardizing covariance?
What does the Pearson correlation coefficient measure?
What does the Pearson correlation coefficient measure?
If two variables have a positive correlation, what does this mean?
If two variables have a positive correlation, what does this mean?
What range of values can a Pearson correlation coefficient take?
What range of values can a Pearson correlation coefficient take?
If the variables are opposing, then the value will display what type of number?
If the variables are opposing, then the value will display what type of number?
How can you tell how closely data points align around on a pattern?
How can you tell how closely data points align around on a pattern?
What does a correlation of 0 indicate?
What does a correlation of 0 indicate?
What does this test measure?
What does this test measure?
What does it mean to say, 'Correlation does not equal Causation'?
What does it mean to say, 'Correlation does not equal Causation'?
What is an assumption to calculating an ANOVA?
What is an assumption to calculating an ANOVA?
In ANOVA, what does a significant F-test suggest?
In ANOVA, what does a significant F-test suggest?
After finding a significant F-test in ANOVA, what is a common next step?
After finding a significant F-test in ANOVA, what is a common next step?
What is the purpose of post-hoc tests?
What is the purpose of post-hoc tests?
What does a covariate measure?
What does a covariate measure?
What is the relationship between variance and error?
What is the relationship between variance and error?
What does ANOVA control?
What does ANOVA control?
What does 'homogeneity of regression slopes' mean?
What does 'homogeneity of regression slopes' mean?
Why doesn't correlation equal causation?
Why doesn't correlation equal causation?
What is the range of correlations?
What is the range of correlations?
What makes the tests useful?
What makes the tests useful?
What is something not necessary in statistical analysis?
What is something not necessary in statistical analysis?
What are types of 'variance explained' sizes?
What are types of 'variance explained' sizes?
What are some assumptions for Z-Scores?
What are some assumptions for Z-Scores?
A student finds a correlation r = 0.8 after accounting for the outlier. What does this show?
A student finds a correlation r = 0.8 after accounting for the outlier. What does this show?
What does a t-statistic describe?
What does a t-statistic describe?
If group samples are same...
If group samples are same...
What can we not check often?
What can we not check often?
What is the use for a T test?
What is the use for a T test?
What type of variable(s) do you analyze with ANOVA?
What type of variable(s) do you analyze with ANOVA?
What results will make a significant outcome?
What results will make a significant outcome?
What can affect if the test is significant?
What can affect if the test is significant?
What is the measure of effects equal too?
What is the measure of effects equal too?
What should be checked frequently?
What should be checked frequently?
In relation to outliers, what happens if you estimate SD & CI?
In relation to outliers, what happens if you estimate SD & CI?
What does ANCOVA adjust group means for?
What does ANCOVA adjust group means for?
In the dog therapy example, what does adjusting for the 'love of dogs' allow us to better understand?
In the dog therapy example, what does adjusting for the 'love of dogs' allow us to better understand?
What is a key consideration when using ANCOVA?
What is a key consideration when using ANCOVA?
In the ANCOVA output F(1, 26) = 4.96, p = .035 for 'dog_love', what does the p-value indicate?
In the ANCOVA output F(1, 26) = 4.96, p = .035 for 'dog_love', what does the p-value indicate?
What does the term 'Adjusting Means' refer to?
What does the term 'Adjusting Means' refer to?
What does the magnitude of Eta squared represent?
What does the magnitude of Eta squared represent?
What does a partial eta-squared in ANCOVA tell us?
What does a partial eta-squared in ANCOVA tell us?
When is a variable considered to have a strong effect size, in behavioral sciences?
When is a variable considered to have a strong effect size, in behavioral sciences?
What does it mean for the 'Independence of Covariate and Treatment'?
What does it mean for the 'Independence of Covariate and Treatment'?
What does it mean for 'homogeneity of regression slopes'?
What does it mean for 'homogeneity of regression slopes'?
What is the overarching idea of ANCOVA?
What is the overarching idea of ANCOVA?
Which test is useful at deciphering groups differing on average and if they come from the same population?
Which test is useful at deciphering groups differing on average and if they come from the same population?
Which test is useful at removing influence of confounding variables and providing understanding between IV and DV?
Which test is useful at removing influence of confounding variables and providing understanding between IV and DV?
If you want to analyze relationships using a categorical variable, what do you use?
If you want to analyze relationships using a categorical variable, what do you use?
What determines a correlation?
What determines a correlation?
What are the key aspects measured by Correlation?
What are the key aspects measured by Correlation?
How can you describe the 'Direction' of correlations?
How can you describe the 'Direction' of correlations?
What is the range of correlation coefficients?
What is the range of correlation coefficients?
What coefficient describes no correlation or little linear relationship?
What coefficient describes no correlation or little linear relationship?
What does the correlation measure?
What does the correlation measure?
What is the purpose of calculating covariance?
What is the purpose of calculating covariance?
The numerator of the covariance formula represents
The numerator of the covariance formula represents
What does it mean when variables are described as positive covariances?
What does it mean when variables are described as positive covariances?
Why is it important to standardize covariance?
Why is it important to standardize covariance?
What type of correlation is essentially a standardized version of covariance?
What type of correlation is essentially a standardized version of covariance?
If a test concludes with the statement, 'Correlation is not significantly different from 0', what does this mean?
If a test concludes with the statement, 'Correlation is not significantly different from 0', what does this mean?
What may happen to a null hypothesis that is falsely rejected?
What may happen to a null hypothesis that is falsely rejected?
What kind of coefficient describes the range across correlation?
What kind of coefficient describes the range across correlation?
If the test concludes the statement of significant result, what may be next?
If the test concludes the statement of significant result, what may be next?
If the variables are opposing, then that will show what type of coefficient?
If the variables are opposing, then that will show what type of coefficient?
What can change a correlation in terms of outliers.
What can change a correlation in terms of outliers.
The t-statistic is characterized by...
The t-statistic is characterized by...
In relation to a true mean of 0, what happens and why?
In relation to a true mean of 0, what happens and why?
The 'Explained' vs 'Unexplained' values represents what?
The 'Explained' vs 'Unexplained' values represents what?
What does a test measuring a t-test?
What does a test measuring a t-test?
If the samples collected on the pre/post test differ, what can it be calculated?
If the samples collected on the pre/post test differ, what can it be calculated?
What does the Independent Samples show?
What does the Independent Samples show?
A researcher wants to minimize data error and better understand relationships between groups using a continuous variable. Which test is appropriate?
A researcher wants to minimize data error and better understand relationships between groups using a continuous variable. Which test is appropriate?
In a correlation study, what refers to the process adjusting a Pearson correlation to focus in between two variables?
In a correlation study, what refers to the process adjusting a Pearson correlation to focus in between two variables?
A test must do what?
A test must do what?
What type of variable is commonly used to explore relationships?
What type of variable is commonly used to explore relationships?
In correlation analysis, what refers to the alignment of data points?
In correlation analysis, what refers to the alignment of data points?
What describes the direction in correlation?
What describes the direction in correlation?
When the correlation expresses the numerical value it represents what?
When the correlation expresses the numerical value it represents what?
What range can correlation coefficients be in?
What range can correlation coefficients be in?
When there is 'no correlation or linear relationship' among the variables, this symbolizes what?
When there is 'no correlation or linear relationship' among the variables, this symbolizes what?
What process does covariance represent?
What process does covariance represent?
What is 'the average amount that data vary from the mean of that variable'?
What is 'the average amount that data vary from the mean of that variable'?
What is useful in determining the measurement scale?
What is useful in determining the measurement scale?
What does the asterisk represent in a test?
What does the asterisk represent in a test?
What are ANCOVA's used in?
What are ANCOVA's used in?
Which test is used to adjust the group means to account for differences explained by covariates?
Which test is used to adjust the group means to account for differences explained by covariates?
What does ANCOVA help do?
What does ANCOVA help do?
Conceptually, ANOVA & ANCOVA are different by what?
Conceptually, ANOVA & ANCOVA are different by what?
In an ANCOVA analysis, what are Covariates?
In an ANCOVA analysis, what are Covariates?
The 'Dog Therapy Example' used in this study has what as the independent variable?
The 'Dog Therapy Example' used in this study has what as the independent variable?
What is 'Student Happiness' measuring?
What is 'Student Happiness' measuring?
In relation to 'love of dogs' in the dog therapy example what does that show?
In relation to 'love of dogs' in the dog therapy example what does that show?
Flashcards
What is ANCOVA?
What is ANCOVA?
A statistical test similar to ANOVA but includes a covariate to control for extraneous variables, it helps reduce error variance.
What are Covariates?
What are Covariates?
Variables that could affect the dependent variable but are not the main focus of the study, it could be love of dogs in our example.
ANCOVA's Purpose
ANCOVA's Purpose
ANCOVA adjusts group means to account for differences explained by the covariate.
Partial Eta-Squared (η²)
Partial Eta-Squared (η²)
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What is Correlation?
What is Correlation?
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Form (Correlation)
Form (Correlation)
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Strength (Correlation)
Strength (Correlation)
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Direction (Correlation)
Direction (Correlation)
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Quantification (Correlation)
Quantification (Correlation)
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Range of Correlations
Range of Correlations
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Positive Correlation
Positive Correlation
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Negative Correlation
Negative Correlation
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Zero Correlation
Zero Correlation
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Variance
Variance
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Covariance
Covariance
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Standardizing Covariance Purpose
Standardizing Covariance Purpose
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Pearson Correlation
Pearson Correlation
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Correlation Significance
Correlation Significance
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Correlation Null Hypothesis
Correlation Null Hypothesis
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Pearson Correlation Coefficient Value
Pearson Correlation Coefficient Value
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Interpreting Pearson Correlation Coefficent
Interpreting Pearson Correlation Coefficent
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Correlation means what?
Correlation means what?
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Causation with Correlation?
Causation with Correlation?
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Correlation Types
Correlation Types
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Analysis of Variance(ANOVA)
Analysis of Variance(ANOVA)
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Post Hoc Test
Post Hoc Test
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Planned Constrasts / Comparison
Planned Constrasts / Comparison
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Assumptions
Assumptions
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Study Notes
ANCOVAs & Correlations
- This lecture covers Analysis of Covariance (ANCOVA) and correlations.
- The intent is to review adjusting group means, interpreting output, effect sizes, covariance, and correlation coefficients.
ANCOVA
- Adjusts group means to account for covariates influencing the dependent variable.
- Requires interpreting output and understanding effect sizes.
Dog Therapy Example
- This example illustrates ANCOVA where the dependent variable is student happiness.
- The independent variable was the dose of dog therapy, with groups receiving control, 15-minute, and 30-minute sessions.
- A student's love of dogs (measured on a scale of 0-7) is used as a covariate.
- Adjust the group means to account for how the love of dogs can affect the student's happiness to reflect dog therapy's influence beyond that which is simply loving dogs.
- Raw data collected, the total participant happiness was 4.37 (1.96)
- The total dog love rating was 2.73 (1.86).
Interpreting ANCOVA Output
- Use the "dog_love" covariate F(1, 26) = 4.96, p = .035, establishing that student happiness is influenced by their love of dogs.
- The "Dose" independent variable with the covariate's effect removed is also significant: F(2, 26) = 4.14, p = .027. This suggests that dog therapy has an effect.
- In addition to the above still examine mean differences among groups.
Estimated Marginal Mean
- Estimated marginal means compare adjusted means across levels, similar to ANOVA output.
- These means are adjusted based on the covariate.
Effect Size in ANCOVAs
- ANCOVAs use partial eta-squared (𝜼²p), indicating the portion of variance that a variable explains that other variables in the analysis do not account for.
- In the dog therapy example, the Independent Variable has an effect size of .24.
Formulas
- Formula: 𝜼²p= (SS Effect) / (SS Effect + SS Residual ) where SS stands for Sum of Squares
- For the independent variable: .24 = 25.185 / (25.185 + 79.047)
- For the covariate: .160 =15.076 / (15.076 + 79.047)
Independence of Covariate and Treatment
- Independence between the covariate and the treatment needs to be established.
Homogeneity of Regression Slopes
- Homogeneity of regression slopes is an assumption of ANCOVA.
ANOVA vs ANCOVA
- ANOVA and ANCOVA are conceptually the same, but differ in application.
- ANCOVA controls for the effect of certain variables, whereas ANOVA cannot.
- ANOVA deciphers whether groups differ on average and come from the same population.
- ANCOVA adjusts the DV to remove the influence of additional/confounding variables, better understanding the DV and IV relationship.
- ANCOVA requires a deep understanding of the variables and their relationships while ANOVA is simple and broadly applied.
Remainder of Course
- Further exploration into relationships using categorical variables
- These relationships including between groups, treatment/control groups, and within individuals.
- Psychology will focus to comparing people with continuous variables with examples including motivation and engagement.
What is Correlation
- Correlation measures the extent to which two variable are related
- Correlation measures the patterns of responses across variables. For example Variable A increases, Variable B increases, or Variable B stays the same
- Correlation is crucial in psychology as it helps gain insights into human behavior and cognition.
- Pearson's Correlation is about the relationship between 2 quantitative variables,
Aspects of Correlation
- Form: What kind of relationship the variables have
- Strength: How closely data points align around a pattern
- Direction: Do the variables move more in the same or opposing direction?
- Quantification: A numerical value representing everything (r)
Correlation Types and Uses in Psych
- Expressed as a coefficient, with a range of -1 to +1.
- Positive Correlation: As one variable increases, the other increases
- Negative Correlation: As one variable increases, the other decreases
- Zero Correlation: No correlation or linear relationship
- Used to evaluate academic performance and sleep, Social Media use and well being, stress and health outcomes, parenting styles and child behaviour, income and happiness, technology use and attention span
Measuring Relationships
- Single Variable: Variance is the average amount that data vary from the mean of that variable.
- Two Variables: Covariance is the sum of combined deviations. Σ(xi – x)(yi – y) / N-1
- Numerator: cross-product deviations
Covariances
- Positive Covariances: Variables move in a + way, and you generally get positive numbers
- Negative Covariances: variables move in a - way, and you generally get negative numbers
- Inconsistency in Covariances means No Linear Relationship
- Covariance depends on scale of measurement so cannot be measured on conversion to standard set of units
Standardizing Covariance
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