Statistics Interview Questions and Answers
Intermediate / 1 to 5 years experienced level questions & answers
Ques 1. Explain the central limit theorem.
The central limit theorem states that the distribution of the sum or average of a large number of independent, identically distributed random variables approaches a normal distribution, regardless of the original distribution.
Example:
If you roll a fair six-sided die many times and calculate the average, the distribution of those averages will be approximately normal.
Ques 2. What is regression analysis?
Regression analysis is a statistical technique used to model the relationship between a dependent variable and one or more independent variables by fitting a linear or nonlinear equation to the observed data.
Example:
Predicting house prices based on factors like square footage, number of bedrooms, and location.
Ques 3. What is the purpose of hypothesis testing?
Hypothesis testing is used to make inferences about a population based on a sample of data. It involves comparing observed data with the results that would be expected if a specific null hypothesis were true.
Example:
Testing whether a new drug has a significant effect by comparing the outcomes of treated and untreated groups.
Ques 4. Differentiate between correlation and causation.
Correlation implies a relationship between two variables, but it does not imply causation. Causation indicates that one variable directly influences the other.
Example:
There is a correlation between ice cream sales and drowning incidents, but one doesn't cause the other; both are influenced by warm weather.
Ques 5. What is a confidence interval?
A confidence interval is a range of values that is likely to contain the true unknown parameter, with a certain level of confidence based on the sample data.
Example:
A 95% confidence interval for the average height of a population is 160 to 170 cm.
Ques 6. Define type I and type II errors.
Type I error occurs when a true null hypothesis is incorrectly rejected. Type II error occurs when a false null hypothesis is not rejected.
Example:
Type I: Concluding a new drug is effective when it is not. Type II: Concluding a new drug is not effective when it is.
Ques 7. What is ANOVA?
Analysis of Variance (ANOVA) is a statistical method used to determine if there are any statistically significant differences between the means of three or more independent groups.
Example:
Comparing the average scores of students in three different teaching methods.
Ques 8. Explain the concept of p-hacking.
P-hacking refers to the manipulation of statistical analyses, methods, or data to produce statistically significant results, often by testing multiple hypotheses until one reaches significance.
Example:
Conducting multiple tests on the same data until a significant result is found and then reporting only that result.
Ques 9. What is the difference between correlation and covariance?
Correlation is a standardized measure of the strength and direction of the linear relationship between two variables. Covariance measures the extent to which two variables change together, but it is not standardized.
Example:
Correlation coefficient ranges from -1 to 1; covariance can take any value.
Ques 10. Define multicollinearity in regression analysis.
Multicollinearity occurs when two or more independent variables in a regression model are highly correlated, making it difficult to identify the individual effect of each variable on the dependent variable.
Example:
In a regression predicting house prices, if square footage and number of bedrooms are strongly correlated, multicollinearity may occur.
Ques 11. What is a Q-Q plot used for?
A Q-Q plot (Quantile-Quantile plot) is used to assess whether a dataset follows a particular theoretical distribution, like the normal distribution. It compares the quantiles of the observed data to the quantiles of the expected distribution.
Example:
Checking if a set of exam scores follows a normal distribution using a Q-Q plot.
Ques 12. Explain the term 'power' in statistics.
Power is the probability that a statistical test will correctly reject a false null hypothesis. It is the ability of a test to detect an effect, given that the effect truly exists.
Example:
A study with a larger sample size generally has higher power to detect a true effect.
Ques 13. What is the purpose of a chi-squared test?
A chi-squared test is used to determine if there is a significant association between two categorical variables. It compares the observed frequencies with the expected frequencies.
Example:
Testing if there is a significant association between gender and voting preference.
Ques 14. Explain the difference between a one-tailed and a two-tailed test.
In a one-tailed test, the critical region is on one side of the distribution (either the right or left). In a two-tailed test, the critical region is on both sides.
Example:
One-tailed test: Does a new drug increase performance? Two-tailed test: Does a new drug have any effect on performance?
Ques 15. What is the coefficient of determination (R-squared) in regression analysis?
The coefficient of determination, denoted as R-squared, measures the proportion of the variance in the dependent variable that is predictable from the independent variables. It ranges from 0 to 1.
Example:
If R-squared is 0.75, 75% of the variance in the dependent variable is explained by the independent variables.
Ques 16. Define skewness in statistics.
Skewness measures the asymmetry of the probability distribution of a real-valued random variable. A negative skewness indicates a distribution that is skewed to the left, and a positive skewness indicates a distribution that is skewed to the right.
Example:
A dataset with a long tail to the right has positive skewness.
Ques 17. What is the purpose of a t-test?
A t-test is used to determine if there is a significant difference between the means of two groups. It is often applied when the sample size is small and the population standard deviation is unknown.
Example:
Comparing the average scores of two groups of students who were taught using different methods.
Ques 18. Define outlier in the context of statistical analysis.
An outlier is an observation that lies an abnormal distance from other values in a random sample from a population. It may indicate a data entry error, measurement error, or a rare event.
Example:
In a dataset of exam scores, a score of 120 when others range from 50 to 100 may be an outlier.
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