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Questions and Answers
What is a correlation?
What is a correlation?
What type of correlation is present when an increase in one variable leads to an increase in another?
What type of correlation is present when an increase in one variable leads to an increase in another?
Which correlation coefficient is calculated using the 'Analyze -> Correlate -> Bivariate' option in SPSS?
Which correlation coefficient is calculated using the 'Analyze -> Correlate -> Bivariate' option in SPSS?
What is the range of values for Pearson's r?
What is the range of values for Pearson's r?
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What is the difference between a one-tailed and a two-tailed hypothesis?
What is the difference between a one-tailed and a two-tailed hypothesis?
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What does a negative t-value indicate in the context of this analysis?
What does a negative t-value indicate in the context of this analysis?
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In the output of the independent samples t-test, which row should be interpreted when the Levene's test results are non-significant?
In the output of the independent samples t-test, which row should be interpreted when the Levene's test results are non-significant?
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What statistical test is used to determine if there is a significant difference between the means of two groups?
What statistical test is used to determine if there is a significant difference between the means of two groups?
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What does 't(11) = -2.47, p = .031' indicate in the context of this analysis?
What does 't(11) = -2.47, p = .031' indicate in the context of this analysis?
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What is the purpose of defining the groups in SPSS for the independent samples t-test?
What is the purpose of defining the groups in SPSS for the independent samples t-test?
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What is the name of the SPSS procedure used to perform a dependent t-test?
What is the name of the SPSS procedure used to perform a dependent t-test?
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In the output of a dependent t-test, what does the 'Paired Samples Statistics' table display?
In the output of a dependent t-test, what does the 'Paired Samples Statistics' table display?
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Why is correlation not a significant concern in a dependent t-test?
Why is correlation not a significant concern in a dependent t-test?
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The output of a dependent t-test also includes a 'Paired Samples Correlations' table. What information does this table provide?
The output of a dependent t-test also includes a 'Paired Samples Correlations' table. What information does this table provide?
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What does the 'Paired Samples T-Test' table in the output tell us?
What does the 'Paired Samples T-Test' table in the output tell us?
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What is the primary difference between a dependent t-test and an independent t-test?
What is the primary difference between a dependent t-test and an independent t-test?
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What does the assumption of homogeneity of variance refer to in the context of independent t-tests?
What does the assumption of homogeneity of variance refer to in the context of independent t-tests?
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Which assumption is relevant for both independent and dependent t-tests?
Which assumption is relevant for both independent and dependent t-tests?
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What is the major purpose of a t-test?
What is the major purpose of a t-test?
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What does it mean when a t-test result is considered "statistically significant"?
What does it mean when a t-test result is considered "statistically significant"?
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Why is the assumption of independence of scores crucial for t-tests?
Why is the assumption of independence of scores crucial for t-tests?
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Which of the following is NOT an assumption of t-tests?
Which of the following is NOT an assumption of t-tests?
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Study Notes
Data Analysis Lecture 5: Correlation
- Correlation measures the relationship between two variables.
- Positive correlation: one variable increases as the other increases.
- Negative correlation: one variable increases as the other decreases.
- Correlation coefficients range from -1 (perfect negative) to +1 (perfect positive), with 0 indicating no relationship.
- Types of correlations include Pearson's r, Spearman's rho, Kendall's tau, point-biserial, and partial correlations.
- Different correlation types are used depending on the data characteristics.
Types of Correlation Coefficients
- Pearson's r: Used with interval/ratio data and assumes a linear relationship.
- Spearman's rho: Used with ordinal data, ranks variables, and is not sensitive to outliers.
- Kendall's tau: Another correlation measure for ordinal data; less sensitive to outliers than Spearman's rho.
Correlation and SPSS
- SPSS is used to evaluate whether the relationship between variables is significant .
- Analyze -> Correlate -> Bivariate.
- Datasets such as Exam Anxiety can be used to analyze correlations.
Pearson's r
- Values between -1 and +1.
- p value less than .05, or .01, or .001 indicates statistical significance.
- SPSS outputs correlations, significance values, and sample size (N).
- Exam performance negatively correlates with exam anxiety (r=-.44, p<.01).
- Exam performance positively correlates with time spent revising (r=.40, p<.01).
- Time spent revising negatively correlates with exam anxiety (r=-.71, p<.01).
Assumptions of Pearson's r
- Interval or ratio level data.
- Normally distributed data.
- Parametric test.
Difference between Parametric and Non-parametric Tests
- Parametric tests rely on underlying population parameters.
- Non-parametric tests do not assume anything about the distribution.
Spearman's rho
- Used when data are ordinal, like ranks.
- Data set example is 'The Biggest Liar' competition.
- Creativity level negatively correlates with position (r_s = -.37, p<.01).
Kendall's tau
- Another ordinal correlation measure.
- Creativity negatively correlates with position in 'The Biggest Liar' competition (τ = -.30, p < .01).
- Kendall's τ is often used when there are a lot of tied ranks.
Biserial and Point-Biserial Correlations
- Used when one variable is dichotomous (e.g., gender).
- Dichotomous means there are only two categories (e.g., male/female).
- Biserial correlation assumes an underlying continuum (e.g., prettiness).
- Point-biserial correlation does not assume an underlying continuum (e.g., pregnancy).
Point-biserial correlations
- Example dataset: PBCorr
- Gender of cat is related to time spent away from home (r_pb = .38, p < .01).
Partial Correlations
- Controls for the effect of a third variable on a relationship.
- Used to examine the relationship between two variables when a third variable is influencing either (or both).
- Example: Relationship between exam performance and exam anxiety controlling for time spent revising.
- In the example, the correlation between exam performance and exam anxiety is reduced from -.44 to -.247 when controlling for the revision time variable.
- SPSS output shows the correlation matrix of zero-order correlations first, then a matrix of correlations for the variables controlling for a third.
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Description
This quiz explores the concept of correlation, including its definition and types. Participants will learn about positive and negative correlations, correlation coefficients, and statistical methods like Pearson's r, Spearman's rho, and Kendall's tau. The importance of SPSS in evaluating correlations will also be discussed.
