Quantitative Methods II
Exam II
Monday, May 10  
8:00 pm 

You will need a calculator for this exam.  I will provide normal and t tables, as well as a list of useful formulas.


I. Data Collection (continued)

A. Data Collection: direct observation
    1. representative sample
    2. observations
       a. accuracy
       b. training, calibration

B. Experimental Design
    1. study and control groups
        a. random
        b. blind
    2. measurement needs to be double-blind
    3. results from poorly designed experiments are not meaningful
        a. placebo effect
        b. unconscious bias
    4. A well-designed experiment can show causation

II. Ethics
A. Honesty
    1. don't falsify data
    2. don't intentionally bias results
    3. don't suppress findings

B. Data collection
    1. do no harm
    2. manage risks to protect subjects
    3. informed consent
    4. confidentiality

C. Institutional Review Board (IRB)
    1. protect human subjects
    2. approval required for research

III. Estimation
A. sample statistics are estimators for population parameters
     1. imperfect estimates
     2. random error 

B. sampling errors
    1. standard error
        a. normally distributed
             i) central limit theorem
             ii) known variance
        b. calculations
            i) mean
            ii) proportion
    2. estimate intervals
    3. increasing sample size increases accuracy

C. confidence intervals
    1. calculating interval endpoints
        a. normal distribution
            i) large samples, or known variance
            ii) find z values in normal table
            iii) interval = mean plus/minus z standard errors
        b. t-distribution
            i) small samples, estimated variance
            ii) find t values (n-1) in t-table
            iii) interval = mean plus/minus t standard errors
    2. precision/ accuracy trade-off

IV.   Hypothesis Testing
A. answering questions about populations based on sample results
    1. base hypothesis on an idea
    2. uncertainty; use probability

B. Inference

1. specify null and alternative hypotheses
2. specify confidence level
3. calculate critical region
    a. standard error
    b. normal table or t-table
4. compare sample statistic to critical value
    a. reject null hypothesis
    b. don't reject null
5. testing
    a. two-tailed test
    b. one tailed test
C. Small populations
    a. possible to sample large fraction
    b. standard error is smaller
    c. finite population multiplier

D. Comparing groups
    1. difference of means
    2. difference of proportions

E. Regression
    1. typical test is there a statistically significant relation between Y and X ?
    2. null hypothesis b = 0
    3. use standard error of the coefficient to construct critical region
    4. reject if b is outside critical region

E. Significance versus Power of a test [if time]
    1. Type I error
    2. Type II error
 
 



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