The Best Measure to Correlate Parents' Income with Children's Happiness
Evaluating the Correlation Between Parents' Income and Children's Happiness
When studying the relationship between parents' income and children's happiness, it is essential to use the appropriate statistical measure to ascertain the correlation accurately. In this scenario, parents' income is categorized simply as "high" or "low," while children's happiness is measured on a scale of 1 to 20. To determine the best measure for this analysis, we need to consider the nature of the variables and the type of correlation we wish to establish.
Pearson's correlation: Pearson's correlation coefficient is typically used to measure the strength and direction of the relationship between two continuous variables. However, in this case, one variable (parents' income) is dichotomous, making Pearson's correlation less suitable for this type of analysis.
Point-biserial correlation: This type of correlation is specifically designed to evaluate the relationship between a continuous variable and a dichotomous variable. Given that parents' income is categorized as "high" or "low" and children's happiness is measured on a continuous scale, the point-biserial correlation may be the most appropriate measure for this study.
Biserial correlation: Biserial correlation is similar to point-biserial correlation but is used when both variables are continuous. Since one variable in our scenario is dichotomous, biserial correlation may not provide the most accurate representation of the correlation between parents' income and children's happiness.
Kendall's tau: Kendall's tau is a non-parametric measure of correlation that does not assume a linear relationship between variables. While it is a valuable measure in certain analyses, it may not be the most suitable choice for correlating parents' income and children's happiness in this case.
None of the above: Given the nature of the variables in question, the best measure to use for correlating parents' income (dichotomous variable) with children's happiness (continuous variable) would likely be the point-biserial correlation.
What would be the BEST measure to use?
a. Pearson's correlation.
b. Point-biserial correlation.
c. Biserial correlation.
d. Kendall's tau.
e. None of the above.
Final answer:
In a situation where one variable is dichotomous (parents' income: high or low) and the other is continuous (children's happiness scale), the best statistical measure to use would be the Point-biserial correlation. This measure provides a correlation coefficient indicating the direction and strength of the correlation.
Explanation:
The best measure to use in this situation would be b. Point-biserial correlation. This type of correlation is utilized when one variable is dichotomous (in this case, parents' income: high or low) and the other variable is continuous (children's happiness: a scale of 1 to 20). The point-biserial correlation measures the relationship between these two distinct types of variables and provides a correlation coefficient, which can range from -1 to 1. This coefficient will indicate to what degree the two factors are correlated. A positive number indicates a positive correlation, a negative number shows a negative correlation, and a zero signifies no correlation at all. For instance, a positive correlation might imply that children with high-income parents tend to score higher in the happiness scale.