# Chapter 9: Robust estimation

Quizzes are available to test your understanding of the key concepts covered in each chapter. Click on the quiz below to get started.

1. Which of the following is not a source of concern in interpreting summary statistics across different groups of a variable?

1. Positively skewed distributions
2. Extreme scores
3. Large standard errors
4. Similar medians across the groups

The correct answer is D. Outliers and asymmetrical or non-normally shaped distributions can heavily affect point estimates such as the mean and confidence intervals. If we detect heavily skewed distributions, outliers or large standard errors, it is likely that our estimates and variance will be biased.

2. Which of the following is the most accurate statement about how a mixed normal distribution affect our conclusions?

1. The mean is affected by heavily skewed distributions
2. The standard error is larger in the overall distribution
3. Point estimates and the dispersion of the distribution can be biased
4. Extreme scores are less likely to affect the shape of the distribution

The correct answer is C. An apparently normal distribution can be made of several other distributions with extreme scores which will, in turn, have an influence in accurately estimating any of the parameters and the associated measures of dispersion.

3. How does a log transformation help in reducing bias?

1. It reduces the impact of negative and positive extreme scores in a distribution
2. It makes the distribution look more normal by eliminating outliers
3. It reduces the impact of negatively skewed distributions
4. It reduces the impact of heavy-tailed distributions and outliers

The correct answer is D. log-transformation can only be applied to positive non-zero numbers. It removes positive skewness and the influence of outliers on the distribution.

4. What is the effect on the point estimates and dispersion after trimming the data?

1. The mean shifts to the left and the variance stays the same
2. The mean shifts to either right or left and the variance decreases
3. The mean shifts to either right or left and the variance increases
4. The mean and variance decrease

The correct answer is B. After removing a specific percentage of cases on the tails, the mean will shift to either up or down depending on the weight of the outlier on each of the tales in the original distribution, while the variance will become more accurate (i.e., smaller).

5. Bootstrapping offers more robust parameter estimates than winsorizing because:

1. It uses the entire sample without transforming the data
2. It computes the mean only for the middle 90% of the cases
3. It assumes the data is normally distributed
4. It is less likely to choose extreme scores

The correct answer is A. The bootstrapping technique uses the data collected to create bootstrap samples from which parameter estimates such as the mean are calculated. Thus, it does not transform the original sample, and it works with any extreme scores.