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Questions and Answers
What does a bivariate table specifically compare?
What does a bivariate table specifically compare?
What range of values can the correlation coefficient take?
What range of values can the correlation coefficient take?
Which of the following correlation types is particularly useful for measuring relationships involving dichotomous variables?
Which of the following correlation types is particularly useful for measuring relationships involving dichotomous variables?
What does a Pearson r correlation coefficient of +0.8 indicate?
What does a Pearson r correlation coefficient of +0.8 indicate?
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In cross tabulation, which of the following best describes the 'Row Total'?
In cross tabulation, which of the following best describes the 'Row Total'?
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What does a correlation coefficient close to 0 indicate?
What does a correlation coefficient close to 0 indicate?
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When is it appropriate to use Pearson r correlation?
When is it appropriate to use Pearson r correlation?
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Which type of distribution is most appropriate for summarizing data in a cross tabulation?
Which type of distribution is most appropriate for summarizing data in a cross tabulation?
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What does the Pearson r correlation coefficient primarily measure?
What does the Pearson r correlation coefficient primarily measure?
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What conditions must be met for the Pearson r correlation to be valid?
What conditions must be met for the Pearson r correlation to be valid?
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In evaluating the strength of a Pearson correlation, a coefficient of 0.72 would be interpreted as what size of effect?
In evaluating the strength of a Pearson correlation, a coefficient of 0.72 would be interpreted as what size of effect?
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What type of data is required for a Pearson correlation analysis?
What type of data is required for a Pearson correlation analysis?
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Which assumption pertains to the distribution of residuals in Pearson correlation?
Which assumption pertains to the distribution of residuals in Pearson correlation?
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Kendall rank correlation differs from Pearson correlation in that it is:
Kendall rank correlation differs from Pearson correlation in that it is:
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In the context of correlation, what does an effect size of .20 suggest about the relationship?
In the context of correlation, what does an effect size of .20 suggest about the relationship?
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What is represented by $∑xy$ in the Pearson r formula?
What is represented by $∑xy$ in the Pearson r formula?
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What is the primary purpose of the Spearman rank correlation?
What is the primary purpose of the Spearman rank correlation?
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Which of the following correctly describes 'concordant' pairs in Kendall rank correlation?
Which of the following correctly describes 'concordant' pairs in Kendall rank correlation?
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In the context of Spearman rank correlation, what do the assumptions regarding ordinal data imply?
In the context of Spearman rank correlation, what do the assumptions regarding ordinal data imply?
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Which coefficient range indicates a medium association in Spearman rank correlation?
Which coefficient range indicates a medium association in Spearman rank correlation?
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What distinguishes Kendall rank correlation from Spearman rank correlation?
What distinguishes Kendall rank correlation from Spearman rank correlation?
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What is the requirement for the variables being analyzed in Spearman rank correlation?
What is the requirement for the variables being analyzed in Spearman rank correlation?
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What does the term 'effect size' refer to in statistical analysis?
What does the term 'effect size' refer to in statistical analysis?
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In Kendall's correlation, what do the terms 'Nc' and 'Nd' represent?
In Kendall's correlation, what do the terms 'Nc' and 'Nd' represent?
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Study Notes
Pearson R Correlation
- Measures the strength and direction of a linear relationship between two continuous variables.
- Uses the following formula:
- r=∑xy−(∑x)(∑y)N√[∑x2−(∑x)2N]√[∑y2−(∑y)2N]r = \frac{∑xy - \frac{(∑x)(∑y)}{N}}{√[∑x^2 - \frac{(∑x)^2}{N}]√[∑y^2 - \frac{(∑y)^2}{N}]}r=√[∑x2−N(∑x)2]√[∑y2−N(∑y)2]∑xy−N(∑x)(∑y)
- Assumptions:
- Both variables are normally distributed.
- Linearity: A straight line relationship exists between the variables.
- Homoscedasticity: Data points are equally spread around the regression line.
- Effect Size: Cohen's standard is used to evaluate the strength of the relationship.
- Small association: .10 to .29
- Medium association: .30 to .49
- Large association: .50 and above
- Example research questions:
- Is there a relationship between age and height?
- Is there a relationship between temperature and ice cream sales?
- Is there a relationship between job satisfaction and income?
Kendall Rank Correlation
- A non-parametric test that measures the strength of dependence between two variables.
- Used when variables are not normally distributed or when data is ordinal.
- Formula:
- τ=Nc−Ndn(n−1)2τ = \frac{Nc - Nd}{\frac{n(n-1)}{2}}τ=2n(n−1)Nc−Nd
- Nc=number of concordant pairsNc = number \ of \ concordant \ pairsNc=number of concordant pairs
- Nd=number of discordant pairsNd = number \ of \ discordant \ pairsNd=number of discordant pairs
- Key Terms:
- Concordant: Ordered in the same way.
- Discordant: Ordered differently.
Spearman Rank Correlation
- A non-parametric test that measures the strength of association between two variables.
- Suitable for ordinal variables or variables with a monotonic relationship.
- Formula:
- ρ=1−6∑di2n(n2−1)ρ = 1 - \frac{6∑d_i^2}{n(n^2-1)}ρ=1−n(n2−1)6∑di2
- di=difference between ranks of corresponding values Xi and Yid_i = difference \ between \ ranks \ of \ corresponding \ values \ X_i \ and \ Y_idi=difference between ranks of corresponding values Xi and Yi
- n=number of values in each data setn = number \ of \ values \ in \ each \ data \ setn=number of values in each data set
- Assumptions:
- Data must be at least ordinal.
- Scores on one variable must be monotonically related to the other variable.
- Effect Size: Cohen's standard is used to evaluate the strength of the relationship.
- Small association: .10 to .29
- Medium association: .30 to .49
- Large association: .50 and above
- Example research questions:
- Is there a relationship between participants' responses to two Likert scale questions?
- Is there a relationship between how horses rank in a race and their ages?
Cross Tabulation
- A table that displays the frequency distribution of two or more categorical variables.
- Also known as "crosstab" or "contingency table."
- Format: Matrix of rows and columns.
- Used to examine the relationship between two variables.
- Example: Secondary School Participants who attended the 1st UCNHS Research Conference.
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Description
This quiz covers the concepts of Pearson R and Kendall Rank Correlation, including how to measure the strength and direction of relationships between continuous variables. It explores essential assumptions, effect sizes, and provides examples of research questions relevant to these correlations. Test your understanding of these statistical tools!
