ANCOVAs and Correlations Explained

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Questions and Answers

Which of the following is adjusted in ANCOVA?

  • Extraneous variable
  • Independent variable
  • Covariate
  • Dependent variable (correct)

What does ANCOVA adjust group means for?

  • The treatment effect
  • The number of groups
  • The influence of a covariate (correct)
  • The sample size

What does a covariate do?

  • Reduce variance (correct)
  • Increase variance
  • Randomize variance
  • Have no effect

An ANCOVA is similar to what other test?

<p>ANOVA (A)</p> Signup and view all the answers

If an ANOVA F-test is significant, what is a typical next step?

<p>Post-hoc tests (B)</p> Signup and view all the answers

If a result has a p-value of 0.25, what can be determined?

<p>There are no group differences. (B)</p> Signup and view all the answers

In psychological research, what is correlation useful for understanding?

<p>Relationships between two variables (B)</p> Signup and view all the answers

What is a key characteristic of correlation?

<p>Measuring the extent to which two variables are related (B)</p> Signup and view all the answers

What is an example of something a correlational study can do?

<p>Illustrate relationships between different variables (A)</p> Signup and view all the answers

What is crucial in psychological research that helps gain insights into human behavior and cognition?

<p>Correlations (C)</p> Signup and view all the answers

What does a correlation coefficient of -1 indicate?

<p>A perfect negative correlation (C)</p> Signup and view all the answers

A correlation of 0 indicates...

<p>No linear correlation (A)</p> Signup and view all the answers

What is indicated by a correlation coefficient of +1?

<p>A perfect positive correlation (D)</p> Signup and view all the answers

What is typically considered a 'small' or weak correlation?

<p>0.1 to 0.3 (B)</p> Signup and view all the answers

What is the key difference between correlation and causation?

<p>Correlation does not necessarily imply causation. (D)</p> Signup and view all the answers

What does 'covariance' measure?

<p>The amount two variables vary together (D)</p> Signup and view all the answers

What represents the cross-product deviations in covariance?

<p>Numerator (D)</p> Signup and view all the answers

What does the Pearson correlation coefficient standardize?

<p>Covariance (B)</p> Signup and view all the answers

What does the null hypothesis test with correlation?

<p>That the correlation is not significantly different from 0 (A)</p> Signup and view all the answers

Which of the following could create a third variable problem?

<p>There may be other variables confounding (A)</p> Signup and view all the answers

Which variable in the data is measured on a scale from 1-10?

<p>Happiness (C)</p> Signup and view all the answers

In the sample provided, what is the total sum of squares denoted as?

<p>SST (C)</p> Signup and view all the answers

What does effect size measure?

<p>The strength of a relationship. (A)</p> Signup and view all the answers

What is the effect size for ANOVA?

<p>Eta Squared (n²) (D)</p> Signup and view all the answers

What does the 'F- statistic' show?

<p>It looks to see if group membership has some effect above and beyond individual differences. (A)</p> Signup and view all the answers

What does rejecting the null value tell you?

<p>At least 1 group mean is different (B)</p> Signup and view all the answers

Why should you avoid running multiple t-tests?

<p>Inflates the Type 1 error rate (D)</p> Signup and view all the answers

What term can be described as 'examining mean differences between 3 or more groups'?

<p>ANOVA (B)</p> Signup and view all the answers

What graph can be used to analyze if data normality needs to be adjusted?

<p>P-P Plot (B)</p> Signup and view all the answers

If one uses the conventional 95% Cl with an a = .05, what is the next course of action?

<p>Then we only need to find the t-value for one side of distribution. (B)</p> Signup and view all the answers

What describes a sample mean compared to some known population mean?

<p>One Sample (A)</p> Signup and view all the answers

What are experimental designs compared to?

<p>Treatment Group (D)</p> Signup and view all the answers

What describes Comparing differences within individuals over time?

<p>Paired sample (A)</p> Signup and view all the answers

What is an advantage of planned contrasts/comparisons?

<p>It increases power (D)</p> Signup and view all the answers

What are considered parametric tests?

<p>Tests using estimation population (C)</p> Signup and view all the answers

What do Violations of assumptions effect?

<p>Effect cis and p-values (A)</p> Signup and view all the answers

What is an advantage of using Cohen's d?

<p>It measures effect sizes. (C)</p> Signup and view all the answers

What graph can determine if you should adjust data set parameters based on a model?

<p>Residuals vs Predicted Plot (A)</p> Signup and view all the answers

What is an omnibus F-test?

<p>There are differences between means (B)</p> Signup and view all the answers

What test allows you to compare people with continuous variables?

<p>ANCOVA (C)</p> Signup and view all the answers

What values can Cohen's d be expressed as?

<p>Small, Medium, Large (C)</p> Signup and view all the answers

What does ANOVA stand for?

<p>Analysis of Variance (D)</p> Signup and view all the answers

What is the primary purpose of ANCOVA?

<p>To control for the effect of certain variables (C)</p> Signup and view all the answers

In the dog therapy example, what is the independent variable?

<p>Dose of dog therapy (C)</p> Signup and view all the answers

In the dog therapy example, what would be the covariate?

<p>The student's love of dogs (B)</p> Signup and view all the answers

What does it mean to adjust the group means?

<p>To remove the covariate influence (D)</p> Signup and view all the answers

What does the F statistic indicate?

<p>The ratio of explained variance to unexplained variance (B)</p> Signup and view all the answers

What is the acceptable range for eta squared values?

<p>Values between 0 and 1 (C)</p> Signup and view all the answers

What does a 'small' eta squared value indicate?

<p>A small, but detectable difference (B)</p> Signup and view all the answers

In analysis of variance, if the F-test is significant, this means...

<p>at least one group mean is different (A)</p> Signup and view all the answers

After obtaining a statistically significant F-test in ANOVA, what should be done next?

<p>a post-hoc test (B)</p> Signup and view all the answers

According to the material, which of the following is NOT a possible problem with NSH?

<p>Statistical power (B)</p> Signup and view all the answers

Why can it be a problem to interpret p-values too holistically

<p>It does not take affect size into account (A)</p> Signup and view all the answers

Which of the following is used to reduce variance?

<p>Experimental Control (D)</p> Signup and view all the answers

What is being indicated by a arrow/line going from 300 downward to 0?

<p>Heteroscedasticity (B)</p> Signup and view all the answers

Spearman's rho correlations are the same as doing what?

<p>Pearson's correlations but on ranked data (A)</p> Signup and view all the answers

What is the use case for Kendall's Tau?

<p>If you rank the data and have outliers (A)</p> Signup and view all the answers

One major component used in ANOVA is calculating what of each component?

<p>Mean squares (A)</p> Signup and view all the answers

What is the goal of an ANOVA?

<p>To examine mean differences between 3 or more groups (A)</p> Signup and view all the answers

ANOVA's are extensions of what test?

<p>T-test (C)</p> Signup and view all the answers

Who is accredited with creating or experimenting with t-tests?

<p>Student (A)</p> Signup and view all the answers

Variance that is not explained is caused by what?

<p>Standard Error (B)</p> Signup and view all the answers

If the true mean difference is 0 standard errors away from the hypothesized mean difference the value is what?

<p>0 (D)</p> Signup and view all the answers

What must remain constant when doing correlations?

<p>Variance (C)</p> Signup and view all the answers

What kind of distribution is needed for most tests to work?

<p>Normal Distribution (A)</p> Signup and view all the answers

Where is homoscedasticity derived?

<p>NHST (D)</p> Signup and view all the answers

What statistical tests would involve additivity and linearity?

<p>General Linear Model (A)</p> Signup and view all the answers

What is examined with the mean of the data in a ANOVA?

<p>Differences between 3 or more groups (C)</p> Signup and view all the answers

One reason to not complete several t-tests to look at group mean differences is because of the error rate is...

<p>Inflated to a Type 1 error (D)</p> Signup and view all the answers

If there is no evidence to group mean differences what can be said about about the F-Test statistic?

<p>It is not significant (A)</p> Signup and view all the answers

Before determining the value of a ANOVA one must calculate what values first?

<p>Sum of squares (A)</p> Signup and view all the answers

When calculating effect size in ANOVA, effect size indicates what?

<p>Mean different size (A)</p> Signup and view all the answers

Correlation measures the extent to which two variables are related

<p>Extent (A)</p> Signup and view all the answers

One tool that aids in getting insights into human behavior is

<p>Correlation (B)</p> Signup and view all the answers

Direction implies if variables have what interaction?

<p>Same or opposing direction (B)</p> Signup and view all the answers

If variables A increases and B decreases, then this would considered as the following correlation.

<p>Negative correlation (A)</p> Signup and view all the answers

Which study type has the most parameters?

<p>Causation (C)</p> Signup and view all the answers

When calculating statistical significance what must be considered

<p>If it is significantly different than 0 or by testing chance (A)</p> Signup and view all the answers

In the slide titled "Correlation Types & Use in Psych", what are all the correlations categorized as?

<p>Academic (A)</p> Signup and view all the answers

Which can be used to better understand the relationship between the DV and IV?

<p>Deep understanding of the variables (B)</p> Signup and view all the answers

Is it possible to use continuous variable over categorical data?

<p>Categorical over groups (B)</p> Signup and view all the answers

Why may a researcher want to utilize planned contrasts or comparisons?

<p>increases power (B)</p> Signup and view all the answers

If a study finds an overall effect in ANOVA, how many specific groups may differ?

<p>to identify which specific groups (D)</p> Signup and view all the answers

According to the material, there specific comparisons between what is being tested?

<p>specific groups are planned in data collection. (A)</p> Signup and view all the answers

What is covariance used for in measuring relationships?

<p>Quantifying the sum of combined deviations between two variables (B)</p> Signup and view all the answers

What does a 'zero correlation' generally imply?

<p>No linear relationship between two variables (C)</p> Signup and view all the answers

In the context of correlation, what is meant by 'direction'?

<p>Whether variables move in some or opposing fashion (C)</p> Signup and view all the answers

In the dog therapy example, what is the role of 'love of dogs'?

<p>Covariate (C)</p> Signup and view all the answers

In the context of ANCOVA, what is the purpose of adjusting group means?

<p>To account for the influence of a covariate (D)</p> Signup and view all the answers

According to the slides, what is the range of values a correlation coefficient (r) can take?

<p>-1 to +1 (C)</p> Signup and view all the answers

Which of the following statements best describes a 'positive correlation'?

<p>As one variable increases, the other variable increases. (A)</p> Signup and view all the answers

What is the definition of ANCOVA?

<p>Similar to ANOVA but with a third variable (A)</p> Signup and view all the answers

Based on slide 7/82, how would happiness be measured for the dog therapy example?

<p>Measured on a scale from 1-10 (B)</p> Signup and view all the answers

What is the purpose of tests like Bonferroni correction or Tukey HSD?

<p>Adjusting the level of significance to control for Type 1 error (C)</p> Signup and view all the answers

What does the F-statistic represent?

<p>The ratio of explained variance to unexplained variance (A)</p> Signup and view all the answers

In analysis of variance, what does a 'significant F-test' mean?

<p>At least one group mean is different from the others (C)</p> Signup and view all the answers

What are Post Hoc tests?

<p>Pairwise comparisons of means (A)</p> Signup and view all the answers

What should one consider when calculating statistical significance?

<p>Effect size and practical significance (B)</p> Signup and view all the answers

When conducting an ANOVA, which values must be calculated to determine its value?

<p>F statistic (D)</p> Signup and view all the answers

What would be an example of examining people with continuous variables?

<p>Motivation with engagement (B)</p> Signup and view all the answers

The goal of ANOVA can be described as which option?

<p>Seeing if groups differ on average and come from the same population (B)</p> Signup and view all the answers

Conceptually, what can be said of ANOVA & ANCOVA tests?

<p>They are the same, but differ in their application (D)</p> Signup and view all the answers

What kind of variable should be used with categorical data?

<p>Independent variable (D)</p> Signup and view all the answers

Why should ANOVA's be performed over multiple t-tests?

<p>to lower Type 1 error rate (C)</p> Signup and view all the answers

Flashcards

What is ANOVA?

A statistical test that assesses the difference in means between three or more groups.

What is Eta Squared?

Indicates the proportion of total variance in a dependent variable that is explained by an independent variable or variables.

What is ANCOVA?

A statistical test similar to ANOVA but includes one or more covariates to control for.

What is a Covariate?

A variable that is not the main focus of the study but could affect the dependent variable.

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What is a Correlation?

A way of measuring the extent to which two variables are related.

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What is Covariance?

A measure of how two variables change together.

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What is the range of r?

Correlation will always get a value that can range from -1 to 1.

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What does r = 0 mean?

No linear correlation.

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What is Correlation?

Statistical indicator of relationship.

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What is Causation?

Change in one variable brings about changes in the other.

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What is Spearman's rho?

A nonparametric test used when the relationship isn't linear nor follows a normal distribution.

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What is Standardizing the Covariance?

To fix that we can standardize the units

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What is Analysis of Variance (ANOVA)?

An Analysis of Variance that is an Extension of t-test that is used to examine mean differences between 3 or more groups

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What are Degrees of Freedom?

Generally, df are one less than the number of values used to calculate the sum of squares

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When are we dealing with statistical test?

To test hypothesis are about a sample from the population. When are we dealing when these are unknown?

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What are Tests covered in 3090 follow General Linear Modeling?

Statistical tests have specific assumptions we must meet. Which should we be following?

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Study Notes

ANCOVAs and Correlations

  • ANCOVA adjusts group means to account for a covariate's influence on happiness and uses a partial eta-squared (ηp²) to interpret the variance proportion a variable explains beyond other variables.
  • The independent variable's effect size is .24 after accounting for the covariate impact, while the covariate effect size is .160.
  • ANOVA and ANCOVA are conceptually similar but differ in application as ANCOVA controls for certain variable effects that ANOVA cannot.
  • ANCOVA adjusts the dependent variable related to additional potentially compounding variables, offering a deep relationship understanding between the dependent and independent variables,

Correlation Analysis

  • Correlation measures a variable's to which two variables are related across patterns in the response across variables using a coefficient to describe the relationship
  • A numerical value represents everything in quantification (r).

Statistical Information

  • Raw means include data points for SPSS which is 29.4, Online at 25.1, Group 17.9, Lecture is 9.8
  • Adjusted means include data points with SPSS at 27.1, Online at 22.5, Group is 18.5, Lecture is 14.1
  • "Dog_love" the covariate shows F (1, 26) = 4.96, p = .035 as students' happiness is influenced by love of dogs
  • "Dose" the IV has the covariate effect removed where F(2, 26) = 4.14, p= .027 and is significant.

ANOVA Information

  • ANOVA helps decipher if groups differ on average and come from the same population.
  • An F-statistic's Procedure tests a null hypothesis.
  • The null: group means are the same.
  • The alternative states: at least 1 group differs from another.
  • 𝜼² = 36.6% test score variation arises from study hours

The T-Test

  • A T-test examines mean differences between groups.
  • The T-test's Primary use is to compare means of two populations
  • The test's hypothesis state null (X₁ = X₂) and alternative ( X₁ ≠ X₂).
  • Apply the t-statistic to the t-distribution to gain probability of the observed mean difference

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