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Quantitative Statistical Tests - Coggle Diagram

- - - - Coping with unmet assumptions
        
        Normality; if group sizes are equal it is robust. apply a transformation, use a non-parametric test (The Kruskal-Wallis H test/"one-way ANOVA on ranks")
        
        Variance; if group sizes are equal it is robust, apply a transformation, Choose an F that has been corrected for variance inequality, like Welch or Brown-Forsythe
        
        Sphericity; Choose an F that has been corrected for deviations from sphericity, like the Greenhouse-Geisser
    - - Post-hoc comparisons
        when you haven't hypothesised specific differences - tests all pairs of groups
        
        can control for experiment-wise error rate
        
        Bonferroni
        
        Tukeys
        
        Scheffe
      - Planned comparisons
        when you have hypothesised specific group comparisons
    - - It is used to analyse effect on more than 1 DV
        
        The MANOVA will for look overall mean differences for the Factor in all DVs combined
      - MANOVA reduces Type 1 error rate in comparison to separate ANOVAs for each of these DVs
      - Example:
        We could look at the impact of Type of Intervention (CBT v Mindfulness) on heart rate, mood and sleep quality.
    - - MANCOVA compares two or more continuous dependant variables (e.g. Test Scores and Annual Income) by levels of a independent variable (e.g. Level of Education), controlling for a covariate (e.g. Number of Hours Spent Studying).
- - - - What does r actually mean? (only for Pearsons)
        
        The best way to interpret r is to square it to r2
        
        r = -0.6 ==> r2 = -0.36 : 36% of the variance in X can be explained by variation in Y. 36% of the variance in Y can be explained by variation in X. More simply, 36% of the variance is shared between X and Y
        
        Between 0 and 1
        
        The fraction of the variance in the 2 variables that is shared = covariance
      - Assumptions
        
        Level of measurement should be continuous
        
        Homoscedasticity; the variation in the residuals (or amount of error in the model) is similar at each point across the model
        
        There must be a linear relationship between variables
        
        Paired observations mean that every data point must be in pairs. That is, for every observation of the independent variable, there must be a corresponding observation of the dependent variable.
        
        No outliers must be present in the data. A data point thats beyond +3.29 or -3.29 standard deviations away, it is considered to be an outlier.
  - - - Variables
        
        The two variables should be measured at an ordinal or nominal level (i.e., categorical data).
        
        The two variable should consist of two or more categorical, independent groups. Example independent variables that meet this criterion include gender (2 groups: Males and Females), ethnicity (e.g., 3 groups: Caucasian, African American and Hispanic), physical activity level (e.g., 4 groups: sedentary, low, moderate and high) and so forth
        
        Each level of the categorical variable had an expected frequency count of at least 5.
        
        What if expected frequency count is less than 5?
        
        The chi-squared statistic is only an approximation
        -The larger the sample, the better the approximation becomes as the sampling distribution is close enough to the chi-squared distribution
        
        In smaller samples, the approximation is not good enough, making significance test inaccurate as sampling distribution is too deviant from chi-squared distribution to be accurate
        
        Fishers Exact test
        
        A way to compute the exact probability in chi-squared statistic in small samples
        
        Used on 2x2 contingency tables with small samples
      - Independence
        
        Each item must only contribute to once cell of the contingency table
        
        Independence of observations (no repeated measures)
        
        Mutually exclusive categories (no case should belong to more than 1 category on each variable)
        
        Therefore cannot be used on a repeated measures design > would have to use a generalised linear mixed model
    - - Phi
        -The measure of the strength of association between 2 categorical variables
        
        Used with 2-2 contingency tables (2 variables each with 2 categories)
      - Cramers V
        
        The measure of stregnth of association between variables that have more than 2 categories
        
        Used instead of Phi in these situations as Phi fails to reach minimum value of 0 (indicating no association)
- - - - Sobell test
        
        A significant test of mediation
        
        It tests whether the relationship between the predictor and outcome is significantly reduced when a mediator is included in the model
        
        Tests the indirect effect of the predictor on the outcome
      - Bootstrapping
        
        Consists of artificially recreating a population that you resample from, based on your initial sample