What are the qualities of a good statisticians?

Answer 1

A "Good" estimator is the one which provides an estimate with the following qualities:

Unbiasedness: An estimate is said to be an unbiased estimate of a given parameter when the expected value of that estimator can be shown to be equal to the parameter being estimated. For example, the mean of a sample is an unbiased estimate of the mean of the population from which the sample was drawn. Unbiasedness is a good quality for an estimate, since, in such a case, using weighted average of several estimates provides a better estimate than each one of those estimates. Therefore, unbiasedness allows us to upgrade our estimates. For example, if your estimates of the population mean µ are say, 10, and 11.2 from two independent samples of sizes 20, and 30 respectively, then a better estimate of the population mean µ based on both samples is [20 (10) + 30 (11.2)] (20 + 30) = 10.75.

Consistency: The standard deviation of an estimate is called the standard error of that estimate. The larger the standard error the more error in your estimate. The standard deviation of an estimate is a commonly used index of the error entailed in estimating a population parameter based on the information in a random sample of size n from the entire population.

An estimator is said to be "consistent" if increasing the sample size produces an estimate with smaller standard error. Therefore, your estimate is "consistent" with the sample size. That is, spending more money to obtain a larger sample produces a better estimate.

Efficiency: An efficient estimate is one which has the smallest standard error among all unbiased estimators.

The "best" estimator is the one which is the closest to the population parameter being estimated.

Answer 2

Beyond the technical expertise, the most desirable characteristics are good communication skills and the ability to identify the critical aspects of a specific instance and apply the principles correctly.

Due to the broad range of questions that statistics can be applied to, there is often not a pat answer. These types of questions require the ability to apply the principles of statistics rather than just the ability to use a formula.