46. A nonprofit organization is determining which existing donors will donate again for a current campaign. The organization decides to look at its donor database for all donors who have donated two or more × over the past five years. Which measure should be used to determine the probability of receiving a donation from an existing donor over time?
Answer: D
Z-score
The Z-score is the appropriate measure for determining the probability of receiving a donation from an existing donor over time. It helps to standardize the donor's donation history, allowing the organization to assess how many standard deviations a donor's past donations are from the mean donation amount, thereby indicating the likelihood of future donations.
A) R-squared
R-squared is a statistical measure that indicates the proportion of variance for a dependent variable that's explained by an independent variable in a regression model. While it can provide insights into the effectiveness of a predictive model, it does not directly assess the probability of future donations based on historical data.
B) F-statistic
The F-statistic is used in the context of ANOVA or regression analysis to determine if there are significant differences between group means. Although it plays a role in hypothesis testing, it is not suitable for evaluating the likelihood of future donations from existing donors, as it does not directly measure individual donor behavior.
C) Median
The median is a measure of central tendency that indicates the middle value in a dataset. While it provides a useful summary of donation amounts, it does not capture the variability or probability of future donations based on individual donor behavior, making it inadequate for this specific assessment.
D) Z-score
The Z-score effectively quantifies how far a donor's past donations are from the average, allowing the organization to assess the probability of future donations. By standardizing the donation amounts, it provides a clear framework for understanding donor behavior over time.
Conclusion
The Z-score stands out as the most effective measure for determining the probability of receiving future donations from existing donors, as it incorporates individual donation histories and their relationship to the overall donor pool. In contrast, R-squared, F-statistic, and median each lack the necessary focus on individual donor behavior and probability assessment, rendering them ineffective for this specific purpose.