Please enable JavaScript.

Coggle requires JavaScript to display documents.

T-test for Two Related Samples, Hypothesis Testing, Null Hypothesis = mean…

- - - - measures same participants twice (change over time)
        
        uses Difference Scores between two samples X₁ and X₂
        
        aka D = X₂- X₁
        
        symbolized as D
        
        Scores tell both amount of change and direction (+ or -)
        
        Advantages
        
        fewer participants required
        
        reduces/eliminates individual difference problems (less variability)
        
        likely to have greater power (likelihood of detecting real treatment effect)
        
        Disadvantages
        
        time-related factors (other than treatment) can cause score changes
        
        Order Effect (when 1st treatment affects score of 2nd treatment)
        
        must counterbalance with randomized order of treatment
      - aka "within subjects design"
      - Formulas
        
        single sample t-statistic (previous): t= M- μ/ sM
        
        New repeated measures t-statistic:
        t = MD - μD/ sMD
        
        MD= Sample Mean Difference
        
        μD = Population Mean Difference
        
        sMD = estimated standard error of MD
        
        computing standard deviation of D scores is same
        
        s² = SS/(n-1)
        
        1 more item...
        
        OR t = actual difference between sample (MD) and the hypothesis (μD)/ expected difference between MD and μD with no treatment effect
    - - aka "Between Subjects" design
      - measures and compares multiple groups of different participants/samples
        
        Null Hypothesis = No difference between population means OR
        H₀: μ₁ - μ₂ = 0
        
        Alternative Hypothesis= There IS a mean difference between the populations OR
        H₁: μ₁ - μ₂* ≠ 0
        
        Disadvantages
        
        more participants required
        
        Individual differences can skew sample data from independent groups
        
        use Matched-Subjects design (still randomized, but group members are matched to another in opposite group based on shared traits)
- - - - Make a Decision
        
        if t- statistic falls in Critical region, reject H₀ (likely treatment effect)
        
        if t-statistic is outside the critical region, do not reject H₀ (likely no effect)
- - - - estimated d = sample mean difference / sample standard deviation
        OR
        MD/s