applied statistician Interview Questions and Answers

1. What is the difference between descriptive and inferential statistics?

   • Answer: Descriptive statistics summarizes and describes the main features of a dataset, using measures like mean, median, mode, and standard deviation. Inferential statistics uses sample data to make inferences and draw conclusions about a larger population, employing techniques like hypothesis testing and confidence intervals.

2. Explain the central limit theorem.

   • Answer: The central limit theorem states that the distribution of the sample means approximates a normal distribution as the sample size gets larger, regardless of the shape of the population distribution. This is crucial for hypothesis testing and confidence interval construction.

3. What are the assumptions of linear regression?

   • Answer: Linear regression assumes linearity, independence of errors, homoscedasticity (constant variance of errors), normality of errors, and no multicollinearity (low correlation between predictor variables).

4. How do you handle missing data?

   • Answer: Methods for handling missing data include deletion (listwise or pairwise), imputation (mean, median, mode imputation, regression imputation, k-nearest neighbors), and model-based approaches. The best method depends on the nature and extent of missingness (MCAR, MAR, MNAR) and the dataset.

5. Explain the difference between Type I and Type II errors.

   • Answer: Type I error (false positive) occurs when we reject a true null hypothesis. Type II error (false negative) occurs when we fail to reject a false null hypothesis. The probability of Type I error is denoted by α, and the probability of Type II error is denoted by β.

6. What is p-value?

   • Answer: The p-value is the probability of obtaining results as extreme as, or more extreme than, the observed results, assuming the null hypothesis is true. A small p-value (typically below a significance level, such as 0.05) provides evidence against the null hypothesis.

7. What is a confidence interval?

   • Answer: A confidence interval is a range of values that is likely to contain the true population parameter with a certain level of confidence (e.g., 95%). It provides a measure of uncertainty around the point estimate.

8. Explain the difference between correlation and causation.

   • Answer: Correlation measures the association between two variables, while causation implies that one variable directly influences another. Correlation does not imply causation; a correlation between two variables could be due to a third, unobserved variable (confounding variable).

9. What is A/B testing?

   • Answer: A/B testing is a randomized experiment used to compare two versions of something (e.g., a website, an advertisement) to determine which performs better. It's a key method in evaluating marketing and product designs.

10. What is Bayesian statistics?

    • Answer: Bayesian statistics updates prior beliefs about a parameter with new data to obtain a posterior distribution. It uses Bayes' theorem to combine prior knowledge with observed data to make inferences.

11. What are some common data visualization techniques?

    • Answer: Common data visualization techniques include histograms, scatter plots, box plots, bar charts, line charts, heatmaps, and treemaps. The choice of technique depends on the type of data and the message to be conveyed.

12. Explain the difference between parametric and non-parametric methods.

    • Answer: Parametric methods assume a specific probability distribution for the data, while non-parametric methods make no such assumption. Non-parametric methods are more robust to violations of assumptions but may be less powerful if the assumptions of parametric methods are met.

13. What is logistic regression?

    • Answer: Logistic regression is a statistical model used to predict the probability of a binary outcome (0 or 1) based on one or more predictor variables. It uses a sigmoid function to model the probability.

14. What is time series analysis?

    • Answer: Time series analysis is a statistical technique used to analyze data points collected over time. It aims to understand patterns, trends, and seasonality in the data and to forecast future values.

15. What is clustering?

    • Answer: Clustering is a machine learning technique used to group similar data points together. Common clustering algorithms include k-means, hierarchical clustering, and DBSCAN.

16. What is principal component analysis (PCA)?

    • Answer: PCA is a dimensionality reduction technique used to transform a large number of correlated variables into a smaller number of uncorrelated variables called principal components.

17. What is the difference between supervised and unsupervised learning?

    • Answer: Supervised learning uses labeled data (data with known outcomes) to train a model to predict outcomes on new data. Unsupervised learning uses unlabeled data to discover patterns and structures in the data.

18. Explain the bias-variance tradeoff.

    • Answer: The bias-variance tradeoff refers to the balance between model complexity and its ability to generalize to new data. High bias leads to underfitting (high error on training data), while high variance leads to overfitting (high error on test data). The goal is to find a model with a good balance between bias and variance.

19. What is regularization?

    • Answer: Regularization is a technique used to prevent overfitting in statistical models by adding a penalty term to the model's loss function. Common regularization techniques include L1 (LASSO) and L2 (Ridge) regularization.

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