Describe the difference between a t-test and a chi-square test.

When you're interviewing for a data science role at a FAANG company, you may be asked to compare different statistical tests. Here's how you can address the question:

Explanation:

A t-test and a chi-square test are both statistical tests but are used for different types of data and hypotheses.

• T-Test: Used to determine if there is a significant difference between the means of two groups. It is applicable to continuous data and assumes a normal distribution.
• Chi-Square Test: Used to determine if there is a significant association between two categorical variables. It is applied to categorical data and compares observed frequencies to expected frequencies.

Key Talking Points:

• T-Test:
  • Compares means
  • Continuous data
  • Assumes normal distribution
• Chi-Square Test:
  • Compares frequencies
  • Categorical data
  • No assumption about data distribution

NOTES:

Reference Table:

• T-Test: If you want to compare the average points scored by two basketball teams over a season, you'd use a t-test because you are dealing with continuous data (points).
• Chi-Square Test: If you want to determine whether the distribution of players in different positions (e.g., forwards, guards) is the same for two teams, you'd use a chi-square test because you are dealing with categorical data (positions).

Follow-Up Questions and Answers:

• Question: What are the assumptions of a t-test?

  • Answer: The key assumptions are that the data is normally distributed, the samples are independent, and the variances of the two groups are equal (in the case of a two-sample t-test).

• Question: Can you perform a chi-square test on ordinal data?

  • Answer: Yes, you can perform a chi-square test on ordinal data, but it's typically used for nominal data. If the data has a natural order, other tests like the Mann-Whitney U test might be more appropriate.

• Question: How would you check the assumptions of a t-test in Python?

  • Answer: You can use visualizations like histograms or QQ plots to check for normality, and statistical tests like Levene's test to check for equality of variances. Here's a brief Python snippet for checking normality using the Shapiro-Wilk test:

from scipy.stats import shapiro, levene

# Check for normality
data = [sample_data]  # your data here
stat, p = shapiro(data)
print('Shapiro-Wilk Test: Statistics=%.3f, p=%.3f' % (stat, p))

# Check for equality of variances
stat, p = levene(group1, group2)
print('Levene’s Test: Statistics=%.3f, p=%.3f' % (stat, p))