Understanding the Question

When an interviewer asks, "How do you determine when to use parametric vs. non-parametric statistical tests?" they are inquiring about your understanding of statistical methodologies and your ability to apply the appropriate statistical tests based on the data characteristics and the research question at hand. This question tests your foundational knowledge in statistics, your analytical skills, and your practical experience in selecting the right tools for data analysis.

Parametric tests are based on assumptions about the distribution of the underlying population from which the sample is drawn (typically, that the data are normally distributed). They are used when these assumptions are met. Non-parametric tests, on the other hand, do not make such assumptions about the population's distribution and are often used when the data do not meet the assumptions required for parametric tests.

Interviewer's Goals

The interviewer aims to assess:

1. Your Knowledge Base: Do you understand the fundamental differences between parametric and non-parametric tests?
2. Analytical Skills: Can you correctly identify situations or data types where one type of test is preferable over the other?
3. Practical Application: Have you applied this knowledge in real-world data analysis scenarios, and can you provide examples?
4. Decision-Making Process: Are you able to articulate why you would choose one method over the other, considering the research question and data characteristics?

How to Approach Your Answer

To effectively answer this question, structure your response to cover:

1. Explanation of Key Differences: Briefly explain the main differences between parametric and non-parametric tests, focusing on assumptions about the data distribution.
2. Criteria for Selection: Discuss the criteria you use to decide between the two, such as the level of measurement of the data, distribution characteristics, sample size, and the presence of outliers.
3. Practical Examples: Provide examples from your experience where you had to choose between parametric and non-parametric tests, explaining your rationale.

Example Responses Relevant to Statistician

Here are example responses that could resonate well in an interview setting:

• "In determining whether to use a parametric or non-parametric statistical test, I first evaluate the distribution of the data. If the data follow a normal distribution and meet other assumptions such as homogeneity of variances and independence, I lean towards parametric tests because of their greater statistical power. For instance, when analyzing clinical trial data with normally distributed outcomes, I prefer using a t-test or ANOVA for comparing group means. However, if the data are skewed, have outliers, or the sample size is small, I might choose a non-parametric test like the Mann-Whitney U test or the Kruskal-Wallis test, which do not require normality. An example from my work was when I analyzed customer satisfaction scores, which were ordinal and not normally distributed. In that case, I opted for the Wilcoxon rank-sum test to compare two independent groups."

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• "When deciding between parametric and non-parametric tests, I consider the scale of measurement and sample size in addition to the distribution of the data. For ratio or interval data with a large enough sample size, the Central Limit Theorem suggests that the distribution of the sample means will tend toward normality, allowing for the use of parametric tests even if the original data are not perfectly normal. A practical application of this was when I analyzed a large dataset of online retail transactions to compare average purchase amounts between two different time periods. Despite the original transaction data not being normally distributed, the large sample size justified the use of a t-test."

Tips for Success

• Understand the Assumptions: Be clear about the assumptions underlying each type of test and be prepared to discuss how you would verify whether these assumptions are met in practice.
• Know the Alternatives: Be familiar with a range of both parametric and non-parametric tests and understand which scenarios each is best suited for.
• Illustrate with Examples: Use specific examples from your experience to illustrate your decision-making process. This demonstrates your practical skills in applying statistical tests.
• Keep Up-to-Date: Mention any recent advancements or considerations in the field of statistics that might influence the choice between parametric and non-parametric tests, showing that you stay current with your knowledge.
• Communicate Clearly: Use language that can be easily understood by someone who may not have a deep background in statistics, as interviewers can come from various backgrounds.