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Questions and Answers
What is the primary purpose of a scatter plot in analyzing bivariate data?
What is the primary purpose of a scatter plot in analyzing bivariate data?
- To calculate the mean of the two variables
- To determine the correlation coefficient between the two variables
- To visually represent the relationship between the two variables (correct)
- To test the normality of the data
Which of the following is a requirement for using the Pearson product-moment correlation?
Which of the following is a requirement for using the Pearson product-moment correlation?
- Both variables must be normally distributed (correct)
- Both variables must have the same unit of measurement
- Both variables must be linearly related
- Both variables must have the same range of values
What does a straight diagonal line in a Q-Q probability plot indicate?
What does a straight diagonal line in a Q-Q probability plot indicate?
- The data is correlated
- The data is linearly related
- The data is not normally distributed
- The data is normally distributed (correct)
What is the term used to describe the degree of the relationship between linearly related variables?
What is the term used to describe the degree of the relationship between linearly related variables?
Which of the following methods can be used to determine if the data is following a normal distribution?
Which of the following methods can be used to determine if the data is following a normal distribution?
What is the purpose of testing the normality of the data in correlation analysis?
What is the purpose of testing the normality of the data in correlation analysis?
What can be concluded from the Q-Q plots of age and height?
What can be concluded from the Q-Q plots of age and height?
What is the Pearson correlation coefficient (r) between the toddler's age in months and their height?
What is the Pearson correlation coefficient (r) between the toddler's age in months and their height?
What is the interpretation of the correlation coefficient (r = 0.75)?
What is the interpretation of the correlation coefficient (r = 0.75)?
What statistical test is used to test if there is a significant relationship between two sets of scores?
What statistical test is used to test if there is a significant relationship between two sets of scores?
What is the purpose of normality testing in this context?
What is the purpose of normality testing in this context?
What can be concluded from the p-values (0.749 and 0.231) in the normality testing?
What can be concluded from the p-values (0.749 and 0.231) in the normality testing?
What does a P-value greater than the alpha indicate in a normality test?
What does a P-value greater than the alpha indicate in a normality test?
What is the interpretation of a correlation coefficient of ±0.75?
What is the interpretation of a correlation coefficient of ±0.75?
What is the purpose of the Shapiro-Wilk Test?
What is the purpose of the Shapiro-Wilk Test?
What does a correlation coefficient of ±0.25 indicate?
What does a correlation coefficient of ±0.25 indicate?
What is the null hypothesis in a normality test?
What is the null hypothesis in a normality test?
What is the purpose of the Pearson Product-Moment Correlation?
What is the purpose of the Pearson Product-Moment Correlation?
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Study Notes
Normality Tests
- The Q-Q plot can be used to determine if data is normally distributed, where points lying on a diagonal line indicate normality.
- The Shapiro-Wilk test is a numerical method for testing normality, where a p-value greater than 0.05 indicates normality and a p-value less than 0.05 indicates non-normality.
Correlation Analysis
- The Pearson Product-Moment Correlation coefficient (r) measures the degree of linear relationship between two variables.
- The correlation coefficient (r) can be interpreted as:
- 0.00: no correlation
- ±0.01 to ±0.20: very low correlation
- ±0.21 to ±0.40: slight correlation
- ±0.41 to ±0.70: moderate correlation
- ±0.71 to ±0.90: high correlation
- ±0.91 to ±0.99: very high correlation
- ±1.00: perfect correlation
- A scatter plot is a visual representation of the relationship between two variables, showing direction and strength of the relationship.
Hypothesis Testing
- Null hypothesis (Ho): the data does not follow a normal distribution
- Alternative hypothesis (Ha): the data follows a normal distribution
- Alpha (α) is the level of significance, typically set at 0.05
Example Problem
- Determine if there is a significant relationship between toddlers' age and height
- Use the Pearson Product-Moment Correlation formula to calculate the correlation coefficient (r)
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