Statistical Tricks

If Z causes both X and Y, but X doesn’t cause Y, and Y doesn’t cause X, then _______ .

• (a) the correlation between X and Y must be zero

• (b) any correlation between X and Y would be spurious

• (c) both of the above

• (d) neither of the above

Can you tell which has the strongest correlation? Why?

A research team is conducting a survey to determine the favorite sports of students in a large university. They decide to distribute their survey only in the university's sports arena during a basketball game. What type of bias might be introduced into their survey?

• a) Observer bias

• b) Selection bias

• c) Measurement error

• d) Non-response bias

A company conducts a series of experiments to test the effectiveness of a new dietary supplement. After many experiments, they find one test where the supplement had a significant effect on a specific health parameter. They focus on this single result and use it to market the supplement as a miracle product. What is the primary problem with the company's approach?

• a) Their experiments do not show any useful information.

• b) They have not conducted a comprehensive review of all experiments.

• c) They are not accurately representing the overall results of their experiments.

• d) The supplement has consistently demonstrated no health benefits in all experiments.

A cosmetic advertisement claims, "Experimental results show that our product can remove 80% of facial wrinkles and improve skin in just 10 days." If we assume these data indeed originate from an experiment, can we trust these numbers, and why? (Open-ended question)

As a transportation department staff, you plan to report to the mayor the average funding amount for the national investment in 26 road projects in your city. One new road project has a construction investment of 22 million RMB, while the other 25 projects range from 200,000 to 1 million RMB. The median is 250,000 RMB, the mean is 1 million RMB, and the mode is 200,000 RMB. Which statistical measure would you choose to represent the national investment in each project, and what are the drawbacks of using this measure? (Open-ended question)

You are flipping a fair coin, and it has landed on heads five times in a row. What do you expect the outcome of the next flip to be?

• a) Heads

• b) Tails

• c) The probability is the same for both outcomes

You are investigating the admission data for a Law School and a Business School, focusing on gender-based admission rates. Is there gender bias in the admission and why? (Open-ended question)

In causal inference, what is the fundamental problem when dealing with counterfactuals?

• a) The inability to observe multiple outcomes for the same individual simultaneously

• b) The lack of suitable statistical models to estimate counterfactual outcomes

• c) The absence of a clear definition for counterfactuals

• d) The difficulty in defining treatment and control groups

What is the primary purpose of a randomized controlled trial (RCT)?

• a. To determine the correlation between two variables

• b. To establish a causal relationship between two variables

• c. To control for all confounding variables

• d. To prove that correlation implies causation