Available Skills for Statistics Foundations

Institutions can select the skills to be included in the students’ assessment. Students are only tested on selected skills. Statistics Foundations consists of one or more questions to assess each skill and instructional web pages to teach and review each skill.

Probability

  1. Calculate the probability of an event
  2. Use the relation Pr(not A) = 1 - Pr(A)
  3. Recognize when events are mutually exclusive
  4. Apply Pr(A or B) = Pr(A) + Pr(B) for mutually exclusive events
  5. Apply Pr(A or B) = Pr(A) + Pr(B) - Pr(A & B)
  6. Recognize when events are independent
  7. Apply Pr(A and B) = Pr(A)Pr(B) for independent events
  8. Interpret the Pr(A|B) notation
  9. Apply Pr(A|B) = Pr(A) for independent events
  10. Calculate Pr(A|B) if A and B are not independent

Descriptive

  1. Calculate the mean (discrete trials)
  2. Calculate the median (discrete trials)
  3. Calculate the mode (discrete trials)
  4. Calculate the variance (discrete trials)
  5. Calculate the standard deviation (discrete trials sample)
  6. Calculate the standard deviation (population)
  7. Calculate a weighted average
  8. Define the term 'expected value'
  9. Read a histogram with absolute frequencies
  10. Read a histogram with relative frequencies
  11. Estimate a percentile statistic from a histogram
  12. Distinguish between a sample and a population
  13. Explain what sample bias is

Distributions

  1. Distinguish a discrete and a continuous distribution
  2. Distinguish a p.m.f. and a p.d.f.
  3. Calculate the probability from a p.m.f.
  4. Calculate probability from a p.d.f.
  5. Recognize the effect on a distribution plot of changing the mean
  6. Recognize the effect on a distribution plot of changing the std dev
  7. Distinguish median and mean on a distribution plot
  8. Identify a plot of a Normal distribution
  9. Calculate probability that a normal rand var is in certain range
  10. Define z-value
  11. Recognize probabilities corresponding to z-values 1, 2, 3
  12. Recognize z-values corresponding to probabilities 90%, 95%, 99%
  13. Apply the Central Limit Theorem
  14. Predict distribution of a sum or average of several independent rand vars
  15. Recognize a Bernoulli random variable
  16. Recognize a uniform distribution
  17. Recognize a Binomial random variable

Inferences

  1. Define confidence interval
  2. Define confidence level for a confidence interval
  3. Calculate a confidence interval for a mean with a large sample size
  4. Effect on a confidence interval of increasing the sample size
  5. Effect on a confidence interval of increasing the confidence level
  6. Calculate a confidence interval for a mean with a small sample size
  7. Calculate a confidence interval for the Bernoulli parameter
  8. Define null hypothesis
  9. Define test statistic in the context of hypothesis testing
  10. Define critical value in the context of hypothesis testing
  11. Interpret the meaning of significance at level alpha
  12. Define p - value
  13. Distinguish Type I errors from Type II errors
  14. Identify when one-tailed vs. two-tailed tests should be used
  15. Define control group in the context of testing
  16. Describe randomization in the context of testing
  17. Describe blocking in the context of testing
  18. Define placebo effect in the context of testing
  19. Describe double blind testing
  20. Calculate p-value
  21. Calculate the power of a test against an alternative hypothesis

Paired Data

  1. Distinguish data exhibiting positive negative and zero covariance
  2. Calculate covariance
  3. Explain the difference between covariance and correlation
  4. Distinguish strong weak and negligible correlation values
  5. Calculate correlation
  6. Calculate the mean of a sum of two random variables
  7. Calculate the standard deviation of a sum of two random variables
  8. Distinguish independent and dependent vars in a regression model
  9. Transform non-linear data into linear data for a regression
  10. Use a simple regression model for prediction
  11. Use a simple regression to predict impact of changes to independent variable
  12. Distinguish between small and large R2 values in plotted data
  13. Interpret the R2 value in a regression model
  14. Use a multiple regression model for prediction
  15. Use a multiple regression to predict impact of changes to independent variables
  16. Interpret the coefficient for the dummy variable
  17. Determine a confidence interval for a regression coefficient
  18. Determine the p-value for a regression coefficient
  19. Explain how the confidence in predictions of a multiple regression model can be improved