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Statistical tests (Basics (Scales of measurement (Nominal - categorical,…

- - - - Probability of falsely rejecting the null: a (alpha)
      - Conventional alpha level = .05 or .01
      - Probability of correctly accepting the null: 1 - a
    - - Probability of falsely accepting the null: beta
      - Probability of correctly rejecting the null: Power(1 - beta)
    - - Alpha
      - Sample size
      - Effect size (d)
        
        (Mean of experimental group - Mean of control group) / Standard deviation
        
        0.2 - 0.5 = small;
        0.5 - 0.8 = medium; >0.8 = large
- - - - Categorical IV, continuous DV
      - Assumptions
        
        Sampling distribution: normal distribution
        
        If violated:
        
        Independent t-test: Mann-Whitney test or Wilcoxon rank-sum test
        
        Repeated measures t-test; Wilcoxon signed-ranked test
        
        DV must be continuous
        
        Independent
        
        Homogeneity of variences
        
        Levene's p>.05
        
        Repeated measures
        
        paired sample correlations
        
        p<.05
      - Independent t-test
        
        Assumptions: Normality and Levene's
        
        t-stats, p-value t(df2)=t-stat, p=..
        
        Descriptive stat (M=..., SD=...)
      - Repeated measures t-test
        
        Assumptions: Normality and paired samples correlation
        
        t-stat, p-value
        
        Descriptive stat
    - - Conducting multiple t-tests increases type I error
      - Assumptions:
        
        Nominal IV; continuous DV
        
        Scores are independent from each other
        
        Normal sampling distribution
        
        Homogeneity of variance
        
        Levene's p>.05
        
        If violated: Welch's F (Brown-Forsythe F)
        
        ANOVA is robust, results still interpretable even when certain assumptions are violated
      - Between subject ANOVA
        
        Levene's p>.05
        
        F-statistic, p-value F(df between, df within)=f-stat, p=...
        
        Descriptive stat
        
        Post hoc
        
        Only for more than 2 levels of IV and significant F-stat
      - Repeated measures 1-way ANOVA
        
        Assumptions: Mauchly's p>.05 chi-square (df)=approx chi-square, p=...
        
        Not assumed:
        
        Greenhouse-Geisser
        
        Huynh Feldt
        
        Lower-bound
        
        F-stat, p-value
        
        Descriptive stat
        
        Post hoc
  - - - Assumptions
        
        Nominal IV, interval/ratio DV
        
        Normality
        
        Independence
        
        Homogeneity of variances
      - Reading output
        
        Descriptive stat
        
        Levene's
        
        If violated, assuming that sample sizes are equal and large, ANOVA is robust to violation
        
        F-stat, p-value
        
        Post hoc
        
        Pairwise comparisons
        
        Multiple comparisons
    - - Assumptions
        
        Nominal IV, interval/ratio DV
        
        Normality
        
        Sphericity
      - Reading output
        
        Descriptive stat
        
        Mauchly's
        
        Not assumed
        
        Greenhouse-Geisser
        
        Huynh Feldt
        
        F-stat, p-value
        
        Post hoc
  - - - Categorical IV, continuous CV and DV
      - Assumptions
        
        Correlation between CV and DV
        
        Pearson's r
        
        Homogeneity of regression slopes
        
        Correlation between CV and DV are not different across groups
        
        No interaction between IV and CV on DV
    - - Multivariate effect: effect of IVs and their interactions on combination of DVs
      - Univariate effect: effect of IVs and their interactions on each DV. Examined only when multivariate effects are significant
      - Running multiple ANOVAs results in accumulation of Type I error
      - Assumptions
        
        Multivariate normality (normality test for each DV)
        
        Moderate correlation between DVs (r-value: +.3 -.9/ up to -.4
        
        Homogeneity of variance-covariance matrices between groups
        
        Box's M-test p>.001
        
        If violated: Pillai's criterion
        
        Commonly used test: Wilk's lambda
        
        Homogeneity of between groups variance
        
        Levene's
        
        Sphericity of within groups variance (if more than 2 levels)
        
        Mauchly's
- - - - Relationship between predictor and criterion is linear
      - Outcome variable scores are normally distributed
    - - F-value and p-value F(df Regression, df Residual) = f-stat, p=...
      - Beta, t-value and p-value beta = beta coefficient, t(df) = t-value, p=...
      - Regression equation Read from unstandardized coefficient column
  - - - Correlation matrix correlation between predictors (r>.8)
      - Model summary
        
        R square
        
        R square change and F change
      - ANOVA overall fit of model
        
        F and p values
      - Coefficients
        
        Unstandardized coefficient (b)
        
        Standardized coefficient (Beta)
        
        t and p values
    - - Forced entry
      - Hierarchical
      - Stepwise
    - - Linearity
      - Normally distributed residuals
      - No multicollinearity
        
        Pearson's r <.8
        
        Variance Inflation Factor (VIF) <10
        
        Tolerance >.2
      - Homoscendasticity
      - Independence of errors
        
        Durbin-Watson value should be close to 2