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Introduction to Independent-Measures Design, Confidence Intervals,…

- - - - or
        (M₁-M₂) - (μ₁ - μ₂) / ˢ(M₁-M₂)
        
        M₁-M₂ obtained from sample data
        
        μ₁ - μ₂ obtained from null hypothesis
        
        estimated standard error of M₁-M₂
        
        ˢ(M₁-M₂)
        
        amount of error expected between sample mean difference and population mean difference
        
        when H₀ is true, measures average size to expect between two sample means
        
        combine formulas √(s₁²/n₁ + s₂²/n₂)
        
        corrected formula
        
        ˢ(M₁-M₂) = √(sₚ²/n₁ + sₚ² /n₂)
        
        for M₁, ˢM = √s₁²/n₁*
        for M₂, ˢM= √s₂²/n₂
        
        t = (data- hypothesis)/ error
  - - - EX. If two people estimate the same value (how much you weigh), reasonable to average estimates.
        If two people estimate two different things, it is meaningless to average the numbers!
      - check using
        
        Hartley's F- Max Test
        
        H₀: population variances are equal, therefore sample variances should be similar
        
        preferred outcome of test is to fail to reject!
        
        Procedure:
        
        compute sample variance for each separate sample
        
        select the largest and smallest sample variances and compute:
        
        F-Max = s²(largest)/s²(smallest)
        
        large value indicates large difference between sample variances, small value (near 1.00) indicates similar sample variances and homogeneity assumption is reasonable
        
        Compare F-Max value achieved to critical value in table.
        
        to locate critical value you need
        a. k = number of separate samples (2 for independent measures)
        b. df = n-1 for EACH sample variance
        c. alpha level