1. IEE 380 Review

2. Outline Probability (Chapter 3) Statistical Tests (Chapter 4&5)
Regression, Design of Experiments, Statistical Process Control (Chapter 6, 7 & 8)

3. Probability (Chapter 3)
Discrete vs Continuous
PMF, PDF, CDF
Identification of relationships

4. Discrete Distributions
Discrete Random Variable: A random variable that has a finite number of values across a finite interval of its range
Probability Mass Function (pmf): probability that X equals a specific value
Cumulative Density function (cdf): The probability that a random variable, X, is less that or equal to a specific numerical value x
Types of distributions: Uniform, Bernoulli, Binomial, Poisson,

5. Continuous Distributions
Continuous Random Variable: A random variable that has an infinite number of values across a finite interval of its range
Probability Density Function (pdf): Distribution of probability over the range of X
Cumulative Density Function (cdf): Probability that a random variable, X, is less than or equal to a specific numerical value of x
Types of distributions: Uniform, Exponential, Normal. Standard normal

6. Statistical Tests (Chapter 4 & 5)
Fail to Reject H0 vs Reject H0
If the p-value is low the null must go
One sided vs two sided
Statistical Inference: used to determine information about a population based upon data taken from a sample of size n of that population

7. Type 1 and Type 2 Error
Type 1 error: Reject the null hypothesis when it is True (false positive) α
α = the probability that the test statistic (z0) will fall outside the acceptance region of H0
Type 2 error: Fail to reject the null hypothesis, when it is False (false negative) β

8. One Sample Tests (Chapter 4)
Case 1- Test of hypothesis on µ with known σ
Case 2- Test of hypothesis on the µ with σ unknown
Case 3- Test of Hypothesis on σ or σ2
Case 4: Test of hypothesis on p (population)

9. Two Sample Tests (Chapter 5)
Case 1: Test the difference between two means with known variances
Case 5: Test the equality of two variances
Case 2: Test the difference between two means variance unknown and equal
Case 3: Test the difference between two means variance unknown and unequal
Case 4: Test mean difference of two treatments (one population) variance unknown
Case 6: Test the equality of two populations

10. Decision tree for picking the right test
Is the Variance known?
Yes: Case 1- 2 sample Z test
No: Case 5: test the variances equality
Are the variances equal?`
Yes: Case 2- 2 sample t-test Pooled: yes
No: Case 3 2 sample t-test Pooled: no

11. Analysis of Variance (ANOVA)
Testing to see if there is a statistical difference between treatments
Completely randomized : 3 types of medicines used on 12 random people
Randomized block: 4 people try 3 different medicines (eliminating the difference by person)

12. Regression
Two parts: ANOVA and Hypothesis test on significance of individual regressors
ANOVA: Is there at least one independent variable that Is significant
Hypothesis test on significance of individual regressors: Which independent variables are significant

13. Design of Experiments
2k factor design is one that has two factors (denoted A and B) each with k levels
Factor A/B are run at two levels: “low” and “high”
Each combination of factor levels are called treatments
A/B/AB denote the (estimated) main effect of the factors
+ and - denote the factor setting for a run + high – Low
Main Effect (A/B/AB) equals the difference of the mean of the favor on high and low

14. Design of Experiments cont.

15. Statistical Process Control
Use of X-bar and R charts
X-bar chart: sample mean
R chart: sample range
Do not throw out of control data until an assignable cause is found