2 Correlation + Pearson's r Flashcards
Q: What is correlation?
A: Correlation refers to the relationship between two variables. When variables are correlated, changes in one variable tend to be associated with predictable changes in the other variable.
Q: How is covariance related to correlation?
A: Covariance measures the extent to which changes in one variable are associated with predictable changes in another variable. It serves as the foundation for understanding correlation between variables.
Q: Can causality be inferred from correlation?
A: No, causality cannot be inferred from correlation alone. Correlation indicates a relationship between variables but does not imply causation. Other factors and research designs are necessary to establish causality.
Q: Why can’t Pearson’s correlation coefficient (r) be used if the relationship between variables is not linear?
A: Pearson’s correlation coefficient assumes a linear relationship between variables. If the relationship is not linear, Pearson’s r may not accurately represent the degree and direction of association between variables.
Q: What is covariance?
A: Covariance measures the extent to which changes in one variable are associated with predictable changes in another variable. A high covariance indicates that when the score for one variable changes, the scores for the other variable also change in a predictable manner.
Q: How is covariance calculated?
A: To calculate covariance, you first subtract the mean of each variable from its respective values to center the data around zero. Then, you multiply these centered values for each pair of observations and sum them up. The result is the covariance between the two variables.
Q: What does positive covariance indicate?
A: Positive covariance indicates that higher-than-average values of one variable tend to be paired with higher-than-average values of the other variable.
Q: What does negative covariance indicate?
A: Negative covariance indicates that higher-than-average values of one variable tend to be paired with lower-than-average values of the other variable.
Q: How is sample covariance different from sample variance?
A: Sample covariance describes the extent to which two variables co-vary, while sample variance measures the spread of individual variables around their mean. However, sample variance can be considered a special case of sample covariance where the variables are the same (covariance between a variable and itself).
Q: What is Pearson’s
𝑟?
A: Pearson’s
𝑟
r is a correlation coefficient that provides a scale-free measure of covariance, allowing the assessment of the strength and direction of the relationship between two variables without being influenced by the units of measurement.
Q: How is Pearson’s
𝑟
r calculated?
A: Pearson’s
𝑟
r is calculated by dividing the covariance between two variables by the product of their standard deviations. Alternatively, it can be calculated as the square root of the ratio of the covariance of each variable with itself (variance) multiplied together.
Q: What does the value of Pearson’s
𝑟
r indicate?
A: Pearson’s
𝑟
r varies between -1 and +1. A value close to +1 indicates a strong positive correlation, while a value close to -1 indicates a strong negative correlation. A value of 0 indicates no linear correlation between the variables.
Q: How is Pearson’s
𝑟
r used in hypothesis testing?
A: In hypothesis testing using Pearson’s
𝑟
r, the null hypothesis assumes that there is no correlation between the variables. The
𝑝
p-value is calculated from the sample Pearson’s
𝑟
r statistic, indicating the probability of obtaining the observed correlation coefficient if the null hypothesis is true. If the
𝑝
p-value is less than the chosen significance level (often 0.05), the null hypothesis is rejected.
Q: What limitation does the
𝑝
p-value have in interpreting correlation strength?
A: The
𝑝
p-value indicates the probability of observing the correlation coefficient given the null hypothesis, but it does not provide information about the strength of the correlation itself. Therefore, a significant
𝑝
p-value does not necessarily imply a strong correlation, and vice versa.
