  # 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