Hypothesis Testing
      The second type of inferential statistics
  Hypothesis testing is a statistical method used to 
  make comparisons between a single sample and a 
  population, or between 2 or more samples.
  The result of a statistical hypothesis test is a 
  probability, called a p-value, of obtaining the results 
  (or more extreme results) from tests of samples, if 
  the results really weren’t true in the population. 
   Commonly Used Statistical 
              Tests
  Tests for quantitative data (i.e. comparing means):
   Two groups:  t-test  (paired or 2-sample)
   Two or more groups (ANOVA: analysis of variance)
  Tests for categorical (nominal, ordinal) data (i.e. 
   comparing proportions):
   Chi-square, Fisher’s exact test
  Tests for association between two quantitative 
   variables:
   Correlation and regression
               Hypothesis Testing
          In all hypothesis testing, the numerical result from the 
        statistical test is compared to a probability distribution to 
     determine the probability of obtaining the result if the result is 
                        not true in the population. 
     Examples of                    normal 
     two                            distribution 
     probability                                             t distribution
     distributions:
     the normal 
     and   t-
     distributions
                                   -4  -3   -2  -1   0   1    2   3    4
       Steps in Statistical 
       Hypothesis Testing
  1.  Formulate null and research hypotheses
  2. Set alpha error (Type I error) and beta 
    error (Type II error)
  3. Compute statistical test and determine 
    statistical significance
  4.  Draw conclusion
           Step 1:  Formulate Null 
       and Research Hypotheses
     Null Hypothesis (H0):
        There is no difference between groups; 
        there is no relationship between the independent 
        and dependent variable(s).
        Research Hypothesis (H ):
                                       R
           There is a difference between groups;
           there is a relationship between the 
        independent
           and dependent variable(s).