STT 411Design of Experiments

Review1

Basic computer skills:

  1. ability to interpret the standard output from R. (find out H0, H1, p-value, and the associations between numbers in the output. Eg, in Anova, the associationb/w Df, Sum Sq, mean Sq, and F-value. Draw non-statistical conclusions about the analysis based on the p-value)
  2. ability to use the R package (t.test, aov, anova) in the right way.
  3. Read the data into R, by hand and from a file.
  4. Understand how to use the following R commands: pnorm;qnorm; pt; qt; qqnorm; qqline;t.test; Bartlett test; pairwise t.test

Basic Statistical skills:

  1. Sampling distribution of sample average
  2. Steps for hypothesis testing
  3. model selection for a given problem with data

(One sample Z-test;CI for population avg when population SD is given;

One sample t-test; CI for population average when sample SD is given

Two sample Z-test;

Two sample t-test with equal variance assumption;CI for the diff of two population avg with equal variance assumption

Two sample t-test without equal variance assumption; CI for the diff of two population avg with equal variance assumption

ANOVA);

  1. ability to decompose the total deviation SST in Anova to SSE, SStreatment
  2. ability to find the degree of freedom for t-test and Anova
  3. **ability to prove the identities we proved in class or similar one.
  4. **find the p-value for the F-statistics Anova, and t-statistics for t-test, under certain Hypothesis.
  5. connection between t-test and Anova.
  6. From Anova to t-test, and pairwise-ttest.
  7. Check normality assumption
  8. Check equal variance assumption with Bartlett test.

Advanced Statistical skills:

  1. with a given problem without data, create a design that can successfully solve the problem. With the given conditions, you need to choose the right model and conduct the design by avoiding bias as much as possible.
  2. ## Advanced R programming ##.

Sample Problems:

  1. Homework problems.
  2. (30 points) The following is an output from R by doing one sample t-test.

One Sample t-test

data: x

t = -1.5815, df = 4, p-value = 0.9055

alternative hypothesis: true mean is greater than 23

95 percent confidence interval:

12.19929 Inf

sample estimates:

mean of x

18.4

  1. what is H0 and H1
  2. How many observations in the dataset x? ______
  3. What should be the reasonable alternative hypothesis if you see this output?
  4. According to the alternative hypothesis in c, should we reject H0 with alpha=0.10?
  5. What is the SD of the observations in the dataset?
  6. What should be the p-value if we do the two-sided t-test instead of one-sided?
  1. The following is an output from R by doing one sample t-test

Two Sample t-test

data: x and y

t = -2, df = 24, p-value = 0.028

alternative hypothesis: censored

sample estimates:

mean of x mean of y

84 86

Question:

  1. what is H0 and the should be H1?
  2. How many observations in the dataset x and y combined?
  3. should we reject H0?
  4. What is the SDpool if we assume that x and y share the same SD?