AGENDA
Exam
3 Review
EXAM 3 REVIEW
Chi-squared goodness of fit test
U and H Rank Sum Tests
Linear Regression
GOODNESS OF FIT TESTS
Based on a comparison of observations between
Observed data
Theoretical data
The comparison utilizes a set of intervals or cells
Each cell has a lower and upper boundary values
The determination of the boundaries are a function of
Theoretical distribution
Number of observations in the sample
2 different approaches
Equi-interval
Equi-probable
CELLS AND BOUNDARIES
Maximum number of cells not to exceed 100
Expected number of observations needs to be at least 5
To calculate observed values in each cell, we must determine the actual x cell boundaries from the equiprobable cells
X cell boundaries depend on distribution
Normal
Exponential
Uniform
TEST STATISTIC
RANK SUM TESTS
Used when the sample data is either
Non-normal
To small to determine normality
U test
H test
RANK SUM U-TEST
Comparing 2 data sets
Alternative to:
Independent t test
Smith-Satherwaithe test
U test
Based on the rank order of sorted data sample rather than mean and standard deviation
Uses Z standard normal distribution for critical value
PERFORM CALCULATIONS
Calculate rank sums
W1 is the sum of the ranks of data from set 1
W2 is the sum of the ranks of data from set 2
Calculate Us
U1=W1-n1(n1+1)/2
U2=W2-n2(n2+1)/2
U1=min (U1,U2)
Next
NEXT
Calculate the mean of the ranks
u = n1*n2/2
Calculate the variance the of ranks
Sigma1 squared = n1*n2*(n1+n2+1)/12
Calculate the test statistic Z
Z = (U1-u) / sigma1
RANK SUM H-TEST
Comparing three or more data sets
Alternative to:
ANOVA (not covered in this class)
H test
Based on the rank order of sorted data sample rather than mean and standard deviation
Uses chi-squared distribution for critical value
H-TEST STATISTIC
LINEAR REGRESSION
Statistical method for determining a linear relationship between two variables assuming normality and independence
Two types of variables
Independent
Dependent
Method of least squares
Intercept and Coefficients
Significance
R squared
PREDICTION LINE
DETERMINING PREDICTION LINE
Calculate the total squared error between the
Actual value
Predicted value according to the prediction line
NORMAL EQUATIONS
With some rearrangement
Resulting linear equations are called normal equations
INTERCEPT AND SLOPE
Substitute x, y, xy, and x squared values in normal equations
Solve for a
Intercept with y axis at x=0
Solve for b
Coefficient of slope for x values
TEST FORMAT
20 2 point multiple choice
15 4 point multiple choice requiring calculations
Mostly eliminated none of the above
You can write in a different answer if you strongly disagree with the provided choices
Do not memorize equations with the exception of the sample variance
STUDY SUGGESTIONS
Get in a study group
Review class notes
Review homework problems
Lastly do practice test