Statistics Interview Questions for Expert Level

35. What is Sampling Bias? How would you avoid bias in your dataset?

Sampling bias refers to distortion in the composition of a sample collected from a population which leads to results that do not accurately represent the population. To avoid having bias in your dataset, you can implement the following:

• Random Sampling method: This ensures that the sample is representative of the population by giving equal chance of selection for each member in that population.
• Stratified Sampling method: Another way where you divide the population based on certain groups and randomly select a member from the groups for the sample.
• Blinding: Blinding refers to the technique of keeping certain aspects of the experiment hidden from either researcher or the population. if it is hidden from both of them it is called Double Blinding.

36. What is meant by Type I and Type II error? How does it affect your decision making?

Type I error: Type I error occurs when a null hypothesis that is actually true is rejected. This means that the researcher believed that there was a significant effect/relationship when in actuality there wasn’t. In other words, it is a false positive result.

Type II error: Type II error occurs when a null hypothesis that is actually false is not rejected. This means that the researcher believed that there was no significant effect/relationship when in actuality there was. In other words, it is a false negative result.

37. What is Statistical Significance ? How does Hypothesis Testing help prove statistical Significance? Illustrate the steps in doing so.

Statistical significance assesses whether an observed effect or relationship in data is unlikely to have occurred by random chance. This is used in Hypothesis Testing for drawing conclusions about our Null Hypothesis. The results interpreted in your testing is said to be valid and statistically significant when your p-value is less than or equal to the predetermined Significance level (i.e., you reject the null hypothesis). In other case, the The Steps involved in doing so are:

• Formulate your null and alternate hypothesis
• Select a statistical significance value
• perform the test and find out the p-value
• Interpret the result

38. What is p-value? How is its value related to Confidence Interval?

p-value, short for probability value, is a statistical measure which is used to evaluate our hypothesis. If p-value is less than or equal to the pre-determined significance level, the null hypothesis is rejected and we conclude that there is relationship/effect between the variable. The smaller the p-value, the stronger the evidence against null hypothesis.

Confidence interval, on the other hand, is a range of values that is calculated from sample data and is used to estimate an unknown population parameter with certain level of confidence. Wider confidence intervals indicate greater uncertainty about the parameter estimate, while narrower intervals indicate greater precision.

Now, suppose you are checking your hypothesis for a value. If that value is not in the confidence interval range, you have an evidence now that you can use to reject the null hypothesis. This is similar to having a small p-value. In this way, you can use both p-value and Confidence interval to test your hypothesis.

39. What is the difference between t-score and z-score?

40. What is One sample test? How is it different from Two Sample test? Give a scenario for each of these types of hypothesis testing?

41. What are the assumptions made in One sample Z-test?

Following are the assumptions that are made in One sample Z-test:

• Normality : the true population distribution is normal.
• Independence : the observations in your data set are not correlated with each other, they should be independent.
• Known Standard Deviation : the true standard deviation of the population is known.

42. What is the difference between One tailed and Two tailed test?

43. Why is t-test not used for Two sampling test of Proportions?

t-test is designed for normal continuous distributions or numerical data like means, score, etc. Proportions on the other hand represents categorical data. Categorical data cannot be plotted as a continuous distribution and do not follow normality. That is why t-test is not suitable for Proportions test. For that, we can use other tests like Z-test and Chi-square test.

44. What are the assumptions made in Chi-square test?

Following are the assumptions made in Chi-square test:

• Categorical : It is considered that the value is categorical in nature. (like gender, age, education level, etc.)
• Independent : It is considered that the value is independent
• Mutually exclusive : The samples/values should be mutually exclusive, i.e., they belong to only one category

45. What are the assumptions made in t-test hypothesis testing?

The following assumptions are made in a t-test:

• Normality : It is assumed that the data distribution is normal
• Independence : The observation of the two samples are different and not dependent
• Homogeneity of variance : Both have approximately same variance
• Random Sampling : The samples taken are randomly sampled.
  

46. What are different types of t-test?

The different types of t-test can be categorized into two:

• Based on samples:
  • One sample t-test: t-test done where a single sample is used to compare with a known value like population mean. For e.g., Testing if the average score of students in a class differs significantly from the national average score
  • Two sample t-test: It is done when comparing a value for two samples. For e.g., Comparing the test scores of students who received tutoring to those who did not to assess if tutoring has an effect.
• Based on Variance:
  • Student t-test: When two samples have equal variance, we do student’s t test. For e.g., Comparing the average weights of two groups of mice, assuming that the variances in weights are similar in both groups.
  • Welch t-test: When the two samples do not have equal variance, we use this method. For e.g., Comparing the test scores of students from two different schools where the variances in test scores are significantly different.

47. How can you determine if two samples have equal variance?

There are two possible methods to determine if two samples have equal variance:

• Variance rule of Thumb: if the ratio of larger variance to smaller variance is less than 4, it is assumed that the two samples have approximately equal variance.
• F-test: we can also use F-test to check whether the two variance are equal by using F-test, where we define our Null hypothesis to be both variance equal to each other.

48. What is F-test? What are the steps involved in an F-test?

F-test is a statistical test used to compare the variances of two or more groups or samples. This test helps in determining whether there is heteroscedasticity among two samples (they have different variance or not). To perform F-test, the following steps are taken:

• Formulate your Null and Alternate Hypothesis. Here, Null hypothesis is two samples have same variance and alternate hypothesis is they have different variance.
• Find the F-statistics which is calculated as : [Tex]F = \frac {\sigma_{1}^2}{\sigma_{2}^2} [/Tex]
• Calculate the degree of freedom for both the samples.
  • Degree of freedom for numerator: [Tex]df1 = n_{1} – 1 [/Tex], where n1 is the sample size of sample 1
  • Degree of freedom for denominator: [Tex]df2 = n_{2}-1 [/Tex], where n2 is the sample size of sample 2
• For the degree of freedoms as calculated, find the F-value for your selected significance level.
• Compare the value with the F-statistics found at step 2.
• Interpret the results. If the F-value is less that the F-statistics, you reject the null hypothesis and conclude that there is heteroscedasticity between the two samples.

49. What is the usage of Box plot in Statistical Analysis?

Box plots are visualization plots that can be considered an important part of statistics. It is helpful in giving the Measure of Center, Measure of Dispersion and Measure of Position for the data distribution. The following are some aspects in which Box plots help:

• Finding out the median
• Detecting Outlier
• Identifying Data Skewness
• Visualizing Data distribution
  

50. You are given a task to measure the average height of all the trees in the world. How would you approach this problem with the help of statistics?

Lets approach the problem step by step:

• First we define the proper problem statement. Here, it is calculating the height of all the trees in the world.
• Create a sample of the whole population such that the sample is representative of the population
• Find out the descriptive statistics (i.e., measure of central tendency, measure of position and measure of dispersion) for the sample chosen.
• Formulate your hypothesis and choose a significance level. Here your hypothesis would be about the height of the trees in the sample.
• Find the p-value using appropriate test metrics
• compare the p-value and your significance level.
• Interpret the results from it.
  

51. Explain different types of Sampling Biases in statistics.

Biases refer deviations from the truth that can occur at various stages of the data collection, analysis, or interpretation process. Sampling Bias occurs when a certain group of individuals get preferred/favored to be included in the research, thus making it not representative of the population as whole.

There are 3 types of Sampling Bias in Statistics:

• Selection Bias : Selection bias occurs when the process of selecting individuals for a sample is not random
• Survivorship Bias : Survivorship bias occurs when the analysis or study focuses only on the individuals that have “survived” or made it through a selection or filtering process.
• Undercoverage bias : Undercoverage bias happens when certain segments or subgroups of the population are inadequately represented or excluded from the sample

Conclusion

Well, this is the end of this write-up. Here we have compiled the most-asked interview questions for statistics. To gain all the information about the interview and its related questions. Explore the whole blog post and collect all the ideas about it.

Statistics is a branch of mathematics that deals with large amounts of data and the analysis of that data across various industries. Now, if you are looking for career opportunities as a data analyst or data scientist, then knowledge of statistics is very important. Because in most of these interviews, you will encounter statistical questions.

Hence, this blog post aims to explore some of the most frequently asked interview questions in statistics. By the end of this write-up, you will gain comprehensive insights at all levels, ranging from beginners to advanced statistical interview inquiries.