Hello Chantel:
When comparing averages or medians, especially when dealing with socioeconomic data like the percent of the population below the poverty line in different counties, it's crucial to choose the right statistical measure based on the characteristics of your data. Here's how you can compare averages and medians in this context:
1. **Comparing Averages (Mean):**
- **Advantages:**
- Sensitive to all data points, providing a comprehensive view.
- Suitable for normally distributed data.
- **Considerations:**
- Susceptible to extreme values (outliers) that can skew the results.
- May not accurately represent the central tendency for skewed distributions.
- **Procedure:**
- Calculate the mean percentage of the population below the poverty line for each county.
- Find the overall mean by averaging the county means.
2. **Comparing Medians:**
- **Advantages:**
- Resistant to extreme values, making it suitable for skewed distributions.
- Provides a more robust measure of central tendency in the presence of outliers.
- **Considerations:**
- Less sensitive to variations in the tails of the distribution.
- Does not utilize all data points, potentially overlooking information.
- **Procedure:**
- Calculate the median percentage of the population below the poverty line for each county.
- Compare the medians directly or find the overall median.
3. **Box Plots (Optional):**
- Use box plots to visually compare the central tendency, spread, and skewness of poverty percentage data for different counties.
- Identify outliers and assess the distributional characteristics.
4. **Percentile Comparison (Optional):**
- Analyze specific percentiles (e.g., 25th, 75th) in addition to the median to gain insights into the distribution.
- Useful for understanding the variation in poverty percentages among different counties.
5. **Statistical Tests (Optional):**
- If the number of counties is large and you want to test whether there are significant differences, consider using statistical tests such as ANOVA or Kruskal-Wallis, depending on the distribution of your data.
Ultimately, the choice between mean and median comparison depends on the characteristics of your data and the goals of your analysis. If the data is approximately normally distributed and not heavily skewed, comparing means may be appropriate. However, if the data is skewed or contains outliers, comparing medians may provide a more robust assessment of central tendency. Always consider the specific context of your study and the nature of the data you're working with.
