Top 10 Statistics Position Interview Questions [Updated 2024]

Sample Answer
A p-value is a probability that provides a measure of the evidence against the null hypothesis in a statistical test. It quantifies the strength of evidence in support of a null hypothesis, which is the assumption that there is no effect or relationship between variables. In hypothesis testing, we compare the p-value to our significance level, often denoted by α. If the p-value is less than or equal to α, we reject the null hypothesis in favor of the alternative hypothesis. For example, if we have a significance level of 0.05, and our p-value is 0.03, we would reject the null hypothesis, suggesting that there is a statistically significant effect or relationship.

Sample Answer
Statistical power is the probability that a statistical test will reject the null hypothesis when the null hypothesis is actually false. In other words, it measures the test’s ability to correctly detect an effect if there is one. It is important in hypothesis testing because it helps us understand the likelihood of our study finding a significant effect if one truly exists. For instance, if we have a high statistical power, say 0.8 or 80%, it means we have an 80% chance of finding a significant difference if there indeed is a real difference. Having a high statistical power is crucial to avoid Type II errors – failing to reject the null hypothesis when it is false.

Sample Answer
Type I and Type II errors are potential errors that can occur in hypothesis testing. A Type I error, also known as a ‘false positive’, occurs when we reject a true null hypothesis. An example could be if a drug test comes out positive for a person who has not taken any drugs. On the other hand, a Type II error, or a ‘false negative’, occurs when we fail to reject a false null hypothesis. An example could be if the same drug test comes out negative for a person who has actually taken drugs. The probability of Type I error occurring is denoted by alpha (α), while the probability of Type II error occurring is denoted by beta (β).

Sample Answer
A confidence interval is a range of values, derived from a data set, which is likely to contain the value of an unknown population parameter. It’s calculated from the observed data and represents a range within which we are certain the population parameter lies, given a certain level of confidence, often 95%. The wider the confidence interval, the greater the uncertainty about the value of the population parameter. In statistics, we use confidence intervals to indicate the reliability of an estimate. For instance, if we are conducting a study on the average height of a certain population, the confidence interval might tell us that we are 95% confident that the average height is between 5.5 and 6 feet.

Sample Answer
The Central Limit Theorem is a fundamental theorem in probability theory and statistics that states that, given a sufficiently large sample size, the distribution of the sample means will approach a normal distribution, regardless of the shape of the population distribution. This is significant because it allows statisticians to make inferences about population parameters using the properties of a normal distribution. For instance, it underpins many statistical methods including confidence intervals and hypothesis testing.

Sample Answer
The chi-square test is a statistical test used to determine if there is a significant association between two categorical variables in a sample. It’s often used in research studies to examine the relationship between variables that are divided into categories, such as gender and voting behavior. For example, if you wanted to know whether men and women have different preferences for political parties, you could use a chi-square test to compare the proportions of men and women who vote for each party. If the test results in a chi-square statistic that is larger than the critical value, we would reject the null hypothesis and conclude that there is a significant association between the variables.

Sample Answer
A Z-score, also known as a standard score, is a measurement that describes a data point’s position in relation to the mean of a group of data points. It is calculated by subtracting the mean from the data point and then dividing the result by the standard deviation. Z-scores are used in statistics to identify how far away a specific data point is from the mean, measured in standard deviations. They are particularly useful in comparing data points from different sets of data, because they normalize the data. For example, if we have test scores from two different classes and we want to know how a particular student in one class compares to students in the other class, we could use Z-scores to make this comparison.

Sample Answer
Bayesian Inference is a statistical method based on Bayes’ theorem, which updates the probability for a hypothesis as more evidence or information becomes available. It is different from traditional statistical methods, which are typically based on frequency or proportion in a sample. The main difference lies in how probability is interpreted: Bayesian Inference interprets probability as a measure of believability in an event, while traditional statistics interprets it as long-term frequencies of events. As for application, Bayesian Inference is particularly useful in scenarios where we have prior knowledge about the event. For instance, it is heavily used in machine learning algorithms to update the probability as more data becomes available.

Sample Answer
Multicollinearity is a situation in multiple regression where two or more independent variables are highly correlated with each other. This high correlation can lead to unreliable and unstable estimates of the regression coefficients, which makes it difficult to assess the effect of independent variables on the dependent variable. There are several methods to detect multicollinearity. For instance, a Variance Inflation Factor (VIF) that is greater than 5 or 10 indicates a problematic amount of multicollinearity. Tolerance is another measure used, which is just the reciprocal of VIF. A tolerance value below 0.2 or 0.1 indicates a multicollinearity problem. Another method is to examine the correlation matrix of the independent variables. High correlation coefficients between variables may indicate the presence of multicollinearity. Finally, Eigenvalues from the correlation matrix can also be used. If the Eigenvalues are close to zero, this indicates the presence of multicollinearity.

Sample Answer
Survival analysis is used to analyze the time until the occurrence of an event. The event can be death, occurrence of a disease, marriage, divorce, etc. It is called ‘survival analysis’ because it was first developed by medical researchers and statisticians who were interested in predicting patient survival in medical studies. A real-world scenario where survival analysis would be applicable is in customer churn prediction. For example, in a telecom company, survival analysis can be used to predict the time until a customer cancels their subscription. The analysis can take into account various factors such as the customer’s usage pattern, complaints, payment history, etc. The results can help the company identify customers who are at risk of canceling their subscription and take preventative measures.