Podcast
Questions and Answers
What does an ANCOVA allow researchers to do that an ANOVA does not?
What does an ANCOVA allow researchers to do that an ANOVA does not?
- Apply broadly across different types of data
- Determine if groups differ on average
- Control for the effect of certain variables (correct)
- Assess the relationship between dependent and independent variables
In ANCOVA, what is the purpose of adjusting group means?
In ANCOVA, what is the purpose of adjusting group means?
- To account for the influence of a covariate (correct)
- To remove any significant findings
- To simplify the interpretation of effect sizes
- To increase the overall variance in the data
What does a correlation coefficient measure?
What does a correlation coefficient measure?
- The cause-and-effect relationship between variables
- The difference between group means
- The extent to which two variables are related (correct)
- The statistical significance of a result
In correlational research, the term 'direction' refers to what?
In correlational research, the term 'direction' refers to what?
What is a covariate in the context of ANCOVA?
What is a covariate in the context of ANCOVA?
Which of these values represents a strong, negative correlation?
Which of these values represents a strong, negative correlation?
What is the primary goal when using ANCOVA?
What is the primary goal when using ANCOVA?
Which statistical method is conceptually the same as ANCOVA, but differs in its application?
Which statistical method is conceptually the same as ANCOVA, but differs in its application?
What does a 'zero correlation' mean?
What does a 'zero correlation' mean?
When interpreting an ANCOVA output, what should researchers still examine after accounting for the covariate?
When interpreting an ANCOVA output, what should researchers still examine after accounting for the covariate?
In the context of correlation, what does 'strength' refer to?
In the context of correlation, what does 'strength' refer to?
What is the range of possible values for Pearson's correlation coefficient?
What is the range of possible values for Pearson's correlation coefficient?
Which of the following is TRUE of variance explained in ANCOVA?
Which of the following is TRUE of variance explained in ANCOVA?
When is it useful to compare people with continuous variables?
When is it useful to compare people with continuous variables?
Which is an example of a question that can be answered with correlations?
Which is an example of a question that can be answered with correlations?
If the p-value when testing the significance of a correlation coefficient is greater than .05, what decision do we make?
If the p-value when testing the significance of a correlation coefficient is greater than .05, what decision do we make?
Which word applies to 'numerical value to represent everything'?
Which word applies to 'numerical value to represent everything'?
Which of these is an interpretation of $r = 0.8$?
Which of these is an interpretation of $r = 0.8$?
Expressing covariance to remove the measurement scale is called what?
Expressing covariance to remove the measurement scale is called what?
If variable A increases and variable B decreases, what type of correlation is it?
If variable A increases and variable B decreases, what type of correlation is it?
What does the F-statistic represent in ANOVA?
What does the F-statistic represent in ANOVA?
What is the null hypothesis ($H_0$) when performing an ANOVA?
What is the null hypothesis ($H_0$) when performing an ANOVA?
What is the purpose of Post Hoc tests?
What is the purpose of Post Hoc tests?
What is one pitfall of running many t-tests?
What is one pitfall of running many t-tests?
What does Effect Size indicate?
What does Effect Size indicate?
What is the range of possible values for Eta Squared (n²)?
What is the range of possible values for Eta Squared (n²)?
What is Experimental Control?
What is Experimental Control?
What is examined along with the main effects with an ANCOVA?
What is examined along with the main effects with an ANCOVA?
What does ANCOVA adjust group means to account for
What does ANCOVA adjust group means to account for
Conceptually, a t-Test is the same as what?
Conceptually, a t-Test is the same as what?
What should linearly be related to dependent variable?
What should linearly be related to dependent variable?
What is the 'Student's t-test' related to?
What is the 'Student's t-test' related to?
If a data isn't following a normal distribution, what is a limitation?
If a data isn't following a normal distribution, what is a limitation?
After dividing the SD of variables, what step do you take to fix the measurement scale?
After dividing the SD of variables, what step do you take to fix the measurement scale?
What is being adjusted in 'adjusted means'?
What is being adjusted in 'adjusted means'?
What are statistical Models useful to?
What are statistical Models useful to?
If a sample mean is said to be "0 standard errors away", what does this mean?
If a sample mean is said to be "0 standard errors away", what does this mean?
A statistical result showed it was significant at the .05 level, but what is something else that must be questioned as well?
A statistical result showed it was significant at the .05 level, but what is something else that must be questioned as well?
Name an example of assessing the 'linear assumption'.
Name an example of assessing the 'linear assumption'.
When should 'Student's t-test' should be used?
When should 'Student's t-test' should be used?
What is the point of checking for statistical assumptions?
What is the point of checking for statistical assumptions?
After finding a linear relationship, we want to find if it is consistent but how in relation to error-rate?
After finding a linear relationship, we want to find if it is consistent but how in relation to error-rate?
What is the primary purpose of conducting an ANCOVA?
What is the primary purpose of conducting an ANCOVA?
What does the term 'Covariance' refer to?
What does the term 'Covariance' refer to?
What does a 'Positive correlation' mean?
What does a 'Positive correlation' mean?
What is the range of possible values for a correlation coefficient?
What is the range of possible values for a correlation coefficient?
In the context of ANCOVA, what is a 'covariate'?
In the context of ANCOVA, what is a 'covariate'?
What is the purpose of calculating 'adjusted means' in ANCOVA?
What is the purpose of calculating 'adjusted means' in ANCOVA?
According to the material, what does ANCOVA help remove the influence of?
According to the material, what does ANCOVA help remove the influence of?
What does the 'Numerator' refer to when considering Covariance?
What does the 'Numerator' refer to when considering Covariance?
What is the purpose of partial eta-squared $(η_p^2)$ in ANCOVA?
What is the purpose of partial eta-squared $(η_p^2)$ in ANCOVA?
How is the effect size interpreted when using partial eta-squared ($η_p^2$)?
How is the effect size interpreted when using partial eta-squared ($η_p^2$)?
According to the content, what variables are linearly related?
According to the content, what variables are linearly related?
If the data points do not align around a pattern, what does this say of 'Strength'?
If the data points do not align around a pattern, what does this say of 'Strength'?
If variables are 'inconsistent' what is a result of that?
If variables are 'inconsistent' what is a result of that?
If Covariances are scale-dependent, what can one do?
If Covariances are scale-dependent, what can one do?
What relationship do the 'Mean Square for model & error' demonstrate?
What relationship do the 'Mean Square for model & error' demonstrate?
The shape of the t-distribution is related to what?
The shape of the t-distribution is related to what?
What does it mean if a sample mean is said to be '0 standard errors away' from the hypothesized mean?
What does it mean if a sample mean is said to be '0 standard errors away' from the hypothesized mean?
When is ANCOVA most suitable to use?
When is ANCOVA most suitable to use?
What values can Eta Squared ($n^2$) range from?
What values can Eta Squared ($n^2$) range from?
What do statistical models help to do?
What do statistical models help to do?
Expressed as a coefficient, what range of correlations can it be?
Expressed as a coefficient, what range of correlations can it be?
According to text, if data aren't normally distributed, what is a limitation?
According to text, if data aren't normally distributed, what is a limitation?
Why is 'experimental control' important?
Why is 'experimental control' important?
If results were collected from people, what's a type we compare them with?
If results were collected from people, what's a type we compare them with?
How are correlations expressed?
How are correlations expressed?
What is a limitation of the T-test?
What is a limitation of the T-test?
If a study reports a 'zero correlation' what does this mean?
If a study reports a 'zero correlation' what does this mean?
In relation to the F-statistic, what can explain variances?
In relation to the F-statistic, what can explain variances?
What does an ANOVA test tell you about group means?
What does an ANOVA test tell you about group means?
In 'Test of significance of correlation', what's it simply testing whether it's just test by what?
In 'Test of significance of correlation', what's it simply testing whether it's just test by what?
What's an accurate description for 'Causation'?
What's an accurate description for 'Causation'?
If there a relationship between 2 quant variables, Pearson Correlation is commonly done but what if there isn't numerical data, what then?
If there a relationship between 2 quant variables, Pearson Correlation is commonly done but what if there isn't numerical data, what then?
Why is important to check assumptions?
Why is important to check assumptions?
With the violation of Homoscedasticity, what's an accurate answer?
With the violation of Homoscedasticity, what's an accurate answer?
What is 'Eta Squared'?
What is 'Eta Squared'?
According to the PowerPoint, what is the value to represent everything on a numerical standard?
According to the PowerPoint, what is the value to represent everything on a numerical standard?
What does 'adjusting group means' refer to in ANCOVA?
What does 'adjusting group means' refer to in ANCOVA?
In the dog therapy example, what was the independent variable?
In the dog therapy example, what was the independent variable?
What does the effect size measure?
What does the effect size measure?
What values can a partial eta-squared range from?
What values can a partial eta-squared range from?
In correlational research, what is meant by the 'form' of the relationship?
In correlational research, what is meant by the 'form' of the relationship?
What does 'quantification' refer to in the context of correlation?
What does 'quantification' refer to in the context of correlation?
What is the range of a correlation coefficient?
What is the range of a correlation coefficient?
What is indicated by a 'positive correlation'?
What is indicated by a 'positive correlation'?
If the data's Mean is '4' and a Covariance '14.00', what's the Cov(x,y)?
If the data's Mean is '4' and a Covariance '14.00', what's the Cov(x,y)?
We can remove which measurement scale by dividing by the SD of the variables?
We can remove which measurement scale by dividing by the SD of the variables?
What is the first step to take, when conducting ANOVAs?
What is the first step to take, when conducting ANOVAs?
Where would one check for normality during ANOVAs?
Where would one check for normality during ANOVAs?
During ANOVAs, what tests show equal variance?
During ANOVAs, what tests show equal variance?
If not aligning with planned test, what comes after?
If not aligning with planned test, what comes after?
What is the goal of Analysis of Variance (ANOVA)?
What is the goal of Analysis of Variance (ANOVA)?
What is examined/compared in the formula for the t-test?
What is examined/compared in the formula for the t-test?
In Student's t-test, 'A t = 0' means what?
In Student's t-test, 'A t = 0' means what?
When analyzing 2 samples, what's something to be aware of when doing the T-Test?
When analyzing 2 samples, what's something to be aware of when doing the T-Test?
Flashcards
ANOVA (Analysis of Variance)
ANOVA (Analysis of Variance)
A statistical test used to examine mean differences between 3 or more groups. It extends the t-test.
F-statistic
F-statistic
Represents the ratio of explained variance to unexplained variance.
ANCOVA
ANCOVA
Adjusts the Dependent Variable (DV) to remove the influence of additional variables, offering a clearer understanding of the relationship between the DV and Independent Variable (IV).
Covariate
Covariate
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Correlation
Correlation
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Range of Correlation
Range of Correlation
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Covariance
Covariance
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Pearson's Correlation Coefficient
Pearson's Correlation Coefficient
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Pearson Correlation Coefficient Value
Pearson Correlation Coefficient Value
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Categorical Variable Relationships
Categorical Variable Relationships
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Relationships with Categorical Variables
Relationships with Categorical Variables
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Eta Squared (η²)
Eta Squared (η²)
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Variance
Variance
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Study Notes
ANCOVAs & Correlations
- ANCOVAs and Correlations are Introductory Experimental Psychology topics
Today’s Agenda: ANCOVA
- Adjusting Group Means involves modifying group averages to account for the influence of a covariate
- Interpreting Output involves examining the results of the ANCOVA analysis
- Effect Sizes determine the magnitude of the impact
Today’s Agenda: Measuring Relationships
- Covariance measures how two variables change together
- Correlation Coefficient quantifies the strength and direction of a linear relationship between two variables
Dog Therapy Example
- Dependent variable in the dog therapy example is student Happiness
- Independent variable is the Dose of dog therapy, including control, 15-minute, and 30-minute sessions
- A student's love for dogs acts as a covariate, measured on a scale of 0-7
- Using love of dogs as the covariate allows for the group means to adjust, also accounting for its influence on happiness
- The dog therapy is reflected with its adjusted results
Interpreting Output - Main Analysis
- "dog_love" covariate; F(1, 26) = 4.96, p = .035; indicating students' happiness is influenced by their love of dogs
- "Dose", an IV has the effect of a covariate removed
- F(2, 26) = 4.14, p=.027; indicating it is also significant
- It’s important to examine the mean differences between the groups to complete the story
Estimated Marginal Mean; AKA Adjusting Means
- Estimates are the means that have been adjusted based on the covariate
- Adjusted mean comparisons are between all levels of all groups and are outputted via ANOVA
Effect Size For ANCOVAs
- ANCOVAs use a partial eta-squared (𝜼2p)
- It Interprets the proportion of variance that a variable explains that isn't explained by other variables in the analysis
- IV: 𝜼2p = .24
- Covariate = .160
Independence of Covariate & Treatment
- Total variance in DV, showing unexplained variance is separate from variance explained by the covariate
- Violation of Assumption shows unexplained and explained variance overlapping
Homogeneity of Regression Slopes
- Illustrates Homogeneity of Regression Slopes and Heterogeneity of Regression slopes via graphs
Wrapping Up ANOVA & ANCOVA
- Conceptually, ANOVA & ANCOVA are the same, differing only in their application
- ANCOVA is used to control for the effect of certain variables unlike ANOVA
- ANOVA helps decipher differences between group averages and same origin population
- ANCOVA adjusts the DV to remove the influence of confounding variables for better understanding
- ANOVA is broadly applied and simple
- ANCOVA requires extensive knowledge of variable relationships
The Remainder of the Course
- Exploring relationships often involves a categorical variable, like dividing people into Group A and Group B
- Common group divisions include: -people(between-subjects design) -treatment and control groups (experimental design) -individuals (pre/post test design)
- Psychology wants to compare people with continuous variables like the relationship between motivation and engagement
Understanding Correlation
- Correlation measures a way to indicate how much two variables are related
- Correlations measure the pattern of responses across variables
- Variable A ↑, Variable B ↑
- Variable A ↑, Variable B ↓
- Variable A ↑, Variable B stays the same
- Helps gain insights into human behavior and cognition/crucial in psych
- Pearson’s Correlation deals with the Relationship between two quant variables
Correlations Tell Us
- Form refers to the type of relationship the variables have
- Strength refers to how closely data points align to a pattern
- Direction analyzes if the variables move in opposing or the same direction
- Quantification uses a number to represent everything(r)
Correlation Types & Use in Psych
- Correlations are Expressed as a coefficient
- Correlation Ranges from -1 to +1
- Positive Correlations mean Variable A ↑, Variable B ↑
- Negative Correlations mean Variable A ↑, Variable B↓
- Zero Correlation means there is no correlation or linear relationship
- Correlation Applications:
- Academic Performance & Sleep
- Social Media & Well-Being
- Stress & Health Outcomes
- Parenting Styles & Child Behavior
- Exercise & Mental Health
- Technology Use & Attention Span
- Income & Happiness
Measuring Relationships
- Single Variable Variance is average amount that data vary from the mean of that variable
- Two Variable Covariance is the sum of combined deviations measure of variance in 2 variables
More About Measuring Relationships
- Positive Covariances mean variables are moving in + way
- Negative Covariances mean variables are moving in-way
- Inconsistency in covariances = No Linear Relationship
- Cov depends on the scale of measurement
- Can't compare in an objective way unless you convert this to standard set of units
Standardizing the Covariance
- Standardizing the Covariance lets you fix how we can standardize the units. -You can remove the measurement scale by dividing by the SD of the variables. -The SD measures average deviation from the mean
- With 2 variables & 2 SDs you just take the product of both SDS: SxSy = 14.390 -So divide 𝑪𝑪𝑪𝑪𝑪𝑪XY (14.00 ) by (SxSy)14.390 and it =.973 ≈.97
- Pearson's correlation coefficient is essentially a standardized version of covariance
Pearson Correlation Coefficient
- Denoted by r it will range from -1 to 1
- Interpreted significance in context -r = 0 means No linear correlation -0.1 to 0.3 or (-0.1 to -0.3) means Small/Weak Correlation -0.3 to 0.5 or (-0.3 to -0.5) means Moderate/Medium Correlation -0.5 to 0.7 or (-0.5 to -0.7) means Large/Strong Correlation -0.7 to 0.9 or (-0.7 to -0.9) means Very Large/Very Strong Correlation +1/(-1) = Perfect Positive/Negative Correlation
- When Testing significance the Correlation has to be different than 0
- Null Hypothesis: Correlation is not significantly different from 0
Correlation & Causality
- Correlation doesn't equal causation cause: ◦Correlation is just a statistical indicator of relationship ◦Causation is instead change in one variable brings about changes in the other/cause and affect
- Reasons this is ◦Third variable problem: other confounding ◦Direction of causality ◦Coincidence
Conducting a Correlation Analysis
- Correlation between Anxiety and Exam Performance
- With 103 Participants
- Analyzed with Correlate > Bivariate
- Time spent revising (hours) exam
- Score on exam
- Anxious take on exam
Other Types of Correlations
- Nonparametrics happen when Quantitative variables don't have relationship or don't have a normal distribution.
- Spearman's rho ◦Same as Pearson's correlation with ranked data
- Kendall's Tau ◦More robust than rho and good with outliers
- You can conduct these similar tests in SPSS and just uncheck Pearson and check either Spearman or Kendall
- Partial Correlations ◦Measure the relationship between two variables, adjusting for the effect that a third can get from them
Check your understanding
- Researchers finding correlation between hours for undergraduate students and exam scores means: ◦To tell direction and determine relationship to hours, tell strength, also can't tell results imply by increasing social media will increase GPA it doesn't explain
ANOVA Recap
- In ANOVA it can check the normality but needs multiple comparison with bonferroni so that way you can correct with appropriate results and
- report p values as they become significant
Analysis of Covariance ANCOVA
- What is in ANCOVA analysis is that reduce variance so experiment works and ANCOVA is adjusting and then that also explained
ANCOVAs in practice
-In order analyze ANCOVA follow these steps
- Find total Variablity
- Calculate variability explained 3.Figure out how much can't be explained
- calculate mean squares
- Calculare ratio that the F statistic
Interpreating for F statistics
- F Statistic gives an idea if overall means
- P values should show as group to the others to have stat diff.
How Do We Know What's Different?
- Planned Contrasts/Comparisons for RQ's to Hypotheses and also test on group with plan ahead
- With Hoc its use for find sigs when that data has tested across all test to stay with different variances
Common Pitfalls of ANOVAs
- Avoid Misinterpreting results and the Violating Assumptions to better interpret with result
Effect Size in ANOVAs
- Effect indicates the means or variance and explains
- Values range with results but still need have be detectable that means
Test for ANOVA
- A researcher wants compare from 10 that will used or to give multiple test
One Way One ANOVA
- One way is to follow a group of 3 people on scales and on how they interpret
Independent Samples t test
- If a certain that is not accurate find different sample or pooled variant
Internet Resources
- Some webs to help in find value in P and D to test on one t table
Rationale for t test
- See if population is equal of spread between variables.
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