(5-6) Parametric Tests

(5-6) Parametric Tests

1. One population

   • Large sample
     • z-test
   • Small sample
     • t-test
   • how to calculate p-value

2. Two populations

   • Independent
     • Large sample
       • z-test
     • Small sample
       • t-test
     • u1 - u2 = Do
   • Paired
     • Large sample
       • z-test
     • Small sample
       • paired t-test
     • ud = 0
   • Mixture model of two sub-populations (bimodal)
     • Do they come from the same sub-population?

3. Three or more populations

   • Independent
     • One-way ANOVA
       • Assumptions
   • Blocked (not independent)
     • Two/n-way ANOVA
   • SSTr and SSE
     • F
       • Should be equal to 1
     • DoF
       • Columns - 1
       • All boxes minus the above
   • ud = 0, F = MSTr/ MSE
   • Pair-wise comparisons
     • Bonferroni
     • Tukey

4. Hypothesis testing

   • Null hypothesis
   • Alternate hypothesis
   • Test statistic
     • p-value that measures the strength of evidence if null hypothesis is true
     • z-value or t value
   • Significance level
     • Area under the PDF lying above the rejection region
   • p-value
     • Alternative to pre-determined level of significance level
     • Smallest significance level for which null hypothesis can be rejected

5. Errors

   • Type I
   • Type II
   • Power