HYPOTHESIS TESTING

Approaches to Hypothesis Testing

• Classical Statistics
  
  • sampling-theory approach
    
  • objective view of probability
    
  • decision making rests on analysis of available sampling data
    
• Bayesian Statistics
  
  • extension of classical statistics
    
  • consider all other available information
    

Types of Hypotheses

• Null
  
  • that no statistically significant difference exists between the parameter and the statistic being compared
    
• Alternative
  
  • logical opposite of the null hypothesis
    
  • that a statistically significant difference does exist between the parameter and the statistic being compared.
    

Logic of Hypothesis Testing

• Two tailed test
  
  • no directional test
    
  • considers two possibilities
    
• One tailed test
  
  • directional test
    
  • places entire probability of an unlikely outcome to the tail specified by the alternative hypothesis
    

Decision Errors in Testing

• Type I error
  
  • a true null hypothesis is rejected
    
• Type II error    
  
  • one fails to reject a false null hypothesis
    

Testing for Statistical Significance

• State the null hypothesis
  
• Choose the statistical test
  
• Select the desired level of significance
  
• Compute the calculated difference value
  
• Obtain the critical value
  
• Interpret the test
  

Classes of Significance Tests

• Parametric tests
  
  • Z or t test is used to determine the statistical significance between a sample distribution mean and a population parameter
    
• Assumptions:
  
  • independent observations
    
  • normal distributions
    
  • populations have equal variances
    
  • at least interval data measurement scale
    

Classes of Significance Tests

• Nonparametric tests
  
  • Chi-square test is used for situations in which a test for differences between samples is required
    
• Assumptions
  
  • independent observations for some tests
    
  • normal distribution not necessary
    
  • homogeneity of variance not necessary
    
  • appropriate for nominal and ordinal data, may be used for interval or ratio data
    

How to Test the Null Hypothesis

• Analysis of variance (ANOVA)
  
  • the statistical method for testing the null hypothesis that means of several populations are equal
    

Multiple Comparison Tests

• Multiple comparison procedures
  
  • test the difference between each pair of means and indicate significantly different group means at a specified alpha level (<.05)
    
  • use group means and incorporate the MSerror term of the F ratio
    

How to Select a Test

• Which does the test involve?        
  
  • one sample,
    
  • two samples
    
  • k samples
    
• If two or k samples,are the individual cases independent or related?
  
• Is the measurement scale nominal, ordinal, interval, or ratio?
  

K Related Samples Test

Use when:

• The grouping factor has more than two levels
  
• Observations or participants are
  
  • matched . . . or
    
  • the same participant is measured more than once
    
• Interval or ratio data