面试题与答案

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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?

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.

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.

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.

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.