stat_quiz.txt

15 questions quiz in statistics
by Keith McNulty
https://keith-mcnulty.medium.com/fifteen-questions-to-test-your-statistics-knowledge-da4d74742abc

The Quiz

1. Fill in the gap: The standard deviation of a sample
is the square root of the ______ of that sample.

2. What is the difference between the formulas for the
standard deviation of a sample and the standard
deviation of a population?

3. What statistical hypothesis test can be applied to
two samples of categorical data with the same
categories to determine if the frequency distributions
are significantly different?

4. What does the term heteroscedastic mean?

5. Name the following theorem:  P(B)P(A|B) = P(A)P(B|A)

6. A statistician used linear regression to model a
dependent variable which was a survey rating on a
Likert scale from 1 to 5. Name one reason why linear
regression is a poor choice of regression model in
this case.

7. Describe how to calculate the R-squared value in a
linear regression model.

8. Describe the relationship between the Poisson
distribution and the Exponential distribution.

9. What distribution is typically used to estimate the
mean of a normally distributed population when its
standard deviation is unknown?

10. Fill in the gap: Maximum Likelihood Estimation
typically uses a ________ approximation of the log-
likelihood function.

11. Fill in the gap: A multivariate model is a model
involving more than one ______ variable.

12. Fill in the gap: Any ________ transformation of a
normally distributed variable is also normally
distributed.

13. Fill in the gap: _________ regression can be used
to specify the conditional median function of a
dependent variable.

14. What is the common term for the difference between
the means of two samples, divided by the standard
deviation of the combined samples?

15. In typical statistical model outputs, what does
three asterisks (***) usually represent?


The Answers

1. Variance

2. The denominator in a population standard deviation
is the population size. The denominator in a sample
standard deviation is the sample size minus 1. This is
known as Bessel’s correction, to correct a bias of
underestimation of the variance of the population. As
samples get larger this difference becomes less
important.

3. Chi-square test

4. Of unequal variance

5. Bayes’ Theorem

6. Any one from: a) the dependent variable is not
continuous, b) the dependent variable is bounded in
scale, c) you would be interpreting an ordinal
variable as a continuous variable.

7. Calculate the sum of the squared residuals of the
model, then calculate the variance of the dependent
variable. Divide the two and subtract from 1.

8. Both deal with the likelihood of occurrences of an
event over time. Poisson deals with the number of
occurrences in a fixed period of time, while
exponential deals with the time between successive
occurrences.

9. The t-distribution

10. Quadratic

11. Dependent (or outcome/response/target)

12. Linear

13. Quantile

14. Effect size (or Cohen’s effect size or Cohen’s d)

15. It indicates that the p-value of the associated
hypothesis test is less than 0.001.

How did you do?

You scored 0–3. Hmmm, you really need to do some work
on your stats knowledge so you have a better idea of
what’s going on in your modeling.

You scored 4–6. You know some of the basics, but you
could do with strengthening your knowledge, especially
if you are doing more than simple descriptive
statistics.

You scored 7–10. Not bad at at all. You are clearly no
slouch when it comes to stats. There’s room for
improvement though.

You scored 11–13. Very impressive, your statistical
knowledge means you must be a go to person for many of
your colleagues. Nice work!

You scored 14–15. Wow! You hit this out of the park.
Walk tall in the knowledge that you are a true
statistics expert!