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Sad Analysis Techniques (Quantitative vs Nominal (ANOVA (Tests 3 or more…

- - - - H0: no effect of treatment/ no association between treatment and improvement
        
        Expected refers to values expected if null hypothesis is true
        
        there will be slight variability due to sampling variability
        
        Row total x column total
        ......................................
        Grand Total
    - - Small X^2 means null correct
      - Large value can be due to sampling variability alone or sampling variability and treatment effect
    - - Use Fischer's Exact test
        
        In 2x2 tables
        
        if total between 20-40 and one of the expected values in the cells is less than 5
        
        If population total less than 20
    - - if independence cant be assumed, we use McNemar's test
- - - - Always greater than one
        
        higher DF means closer to
    - - Variance of the two populations equal
        
        otherwise unequal-variance test used
      - Nonparametric: Man-Whitney U Test/ Wlcoxon rank sum test
    - - Before-after
        
        Twin data
        
        Matched-case control
      - The difference for the matched pairs follow a normal probability distribution
      - Nonparametric :Wilcoxon Signed-Rank Test
  - - - Graphical investigation
        
        multiple histograms
        
        side-by-side box plots
      - H0; the means of all the groups are equal
        
        Variation Between groups
        ..........................................
        Variation Within groups
        
        A larger F is evidence against the null
        
        More difference between groups than within groups
        (Larger/smaller by F times)
        
        P-value comes from (DFG,DFE)
        
        MSE-within (Xij-Xi)^2
        
        SSE
        ........
        DFE
        
        MSG-between (Xi-X)^2
        
        SSG
        ........
        DFG
      - F distribution is always a right tail test
      - Degrees of freedom
        
        Within groups: # of data values - # of groups
        
        Total: 1 - # of individuals
        
        Between groups: 1 - # of groups
      - R^2 gives the percent of variation due to between group variation
        
        The higher it is the bigger the effect
    - - Ratio of largest to smallest sample sd must be less than 2:1
    - - For dependent use Repeated-measures ANOVA
    - - P value threshold must be adjusted since multiple t-test increase chance of type 1 error
        
        Accumulation of type 1 error= Experimental-wide alpha level (EAL) = 1-(1-alpha)^c
        
        Post hoc t-test
        (tries to control for EAL)
        
        Scheffe test
        
        Uses a manipulation of the F-ratio
        
        Bonferroni correction
        
        Divides alpha by the number of contrasts
        (alpha/c)
        CI will be 1-(alpha/c)
    - - Different groups have same variation
      - Converts measurement observations to ranks
        
        smallest value gets rank 1
- - - - Pearsons correlation coefficient (r)
        
        Co-variance
        
        Cov(X,Y) = 0 ------independent
        
        Cov(X,Y) > 0 -----Positive correlation
        
        Cov(X,Y) < 0 ---------negative
        
        0.41-0.7
        
        0.7
        
        0.16-0.4
        
        0-0.15
      - Measures the strength of association linearly
    - - Method of least squares
        
        slope: how much Y changes for each on unit change in X
        
        Null is when slope = 0
        
        SS(total)= SS(reg) + SS(residual)
        
        SS(reg)
        
        SS(residual)
        
        SS(total)
        
        R^2= SS(reg)/SS(total)
        
        Tells how much of the total variance is explained by X
        
        Its the persons correlation coefficient squared
        
        SS(reg) is variability due to X
        
        SS(residual) is additional unexplained variability
        
        t=
        
        P values is being or more SE's away from mean of 0 on a normal curve
      - Multiple regressions
        
        Y= a + (bx1) + (cx2) + (dx3)
        
        Each regression coefficient is the change in outcome per unit change of predictor if all other variables were held constant
        
        Controls for confounders
        
        improve prediction
        
        test interactions between predictors
      - Makes an equation to help us predict changes that will happen to outcome if predictor increase by 1
    - - For regression residuals normally distributed
        
        Assumption may be checked using a Histogram or Q-plot.
        Also can use Goodness fit test (Kolmogrov-smirnov test)
      - For correlation both variables normally distributed
        
        Spearman rank correlation for non-normal