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Statistics Boot Camp - Coggle Diagram

- - - - Probability that a population parameter will fall between the Lower and Upper Confidence Limits
  - - - Standard Error = SD / sqrt(n)
        where:
        SD = standard deviation
        n = sample size
    - - Standard Error = sqrt( ((P)(1-P)) / n)
        where:
        P = population proportion
        n = sample size
  - - - States that the sampling distribution of the sample means approaches a normal distribution as the sample size gets larger, even if the population distribution is not normal.
      - This fact holds especially true for sample sizes over 30.
- - - - Vector: 1D
        (1.2 p21-37)
      - Matrix: 2D
        (1.2 p51-55)
      - Array: Multi D
    - - List: 1D
        (1.2 p42-47)
      - Data Frame: 2D
        (1.2 p58-70)
    - - For categorical data
  - - - Iterating over data
    - - Managing data
- - - - Null Hypothesis
        
        A precise and testable statement
        
        Assumes no relationship between the variables
      - Alternative Hypothesis
        
        A statement that is being tested against the null hypothesis
    - - Probability of rejecting the null hypothesis when it is true
    - - Variable of interest (y) is Continuous of Categorical?
        
        Continuous
        
        1 Sample
        (3.1 p24-53)
        
        Population SD known and sample size > 30
        
        Single Sample Z-Test
        
        Population SD unknown or sample size < 30
        
        Single Sample T-Test
        
        2 Samples
        (3.1 p54)
        
        Independent Samples
        (3.1 p55-59)
        
        Population SD known and sample size > 30
        
        2 Samples Z-Test
        
        Population SD unknown or sample size < 30
        
        2 Samples T-Test
        
        Paired Samples
        (3.1 p60-62)
        
        Population SD known and sample size > 30
        
        Paired Z-Test
        
        Population SD unknown or sample size < 30
        
        Paired T-Test
        
        Many Independent Samples
        
        2 Independent Variables
        
        Two-way ANOVA
        (3.2 p29-43)
        
        https://www.statology.org/two-way-anova/
        
        3 p-values, 2 for the independent variables, 1 for the interaction between the 2 variables
        
        1 Independent Variable
        
        One-way ANOVA
        (3.2 p9-28)
        
        Hypotheses
        
        2 more items...
        
        https://www.statology.org/one-way-anova/
        
        Multiple Comparison Tests
        (3.2 p24-27)
        
        2 more items...
        
        Categorical or Proportional
        
        1 Sample and 2 Options
        
        One Proportion Z-Test
        (3.1 p64-66)
  - - - Probability of a Type I error = alpha, α (significance level)
      - Reject the null hypothesis when it is actually true
    - - Fail to reject the null hypothesis when it is actually false
      - Probability of a Type II error = Beta, β
    - - Null: No COVID
        Alternate: COVID positive
      - Type I error: Tested COVID positive (reject null) when no COVID
      - Type II error: Tested negative (do not reject null) when is COVID positive
  - - - Hypothesis involves making a “greater than” or “less than ” statement
    - - Hypothesis involves making an “equal to” or “not equal to” statement.
- - - - Groups must be mutually
        exclusive and exhaustive
  - - - Steps
        
        Data Exploration
        
        Check correlation
        (4.1 p9-20)
        
        Pearson correlation coefficient (r) > 0.7 for correlation to be considered strong
        
        Do scatter plot of Y vs X
        
        Check linear relationship between X and Y
        
        If non-linear, can try to perform transformation to become linear
        (5.2 p9)
        
        Identify and deal with outliers
        
        Check interaction effects
        (5.1 p21-24)
        
        how the y reacts to different levels or level combinations of predictors (Xs)
        
        interaction is significant
        
        when interaction p-value < 0.05
        
        predictor must stay in the model, even if the individual p-value is not significant
        
        using interaction plots
        
        Check distribution of Y
        
        Transform if not normal
        
        Check for outliers
        
        Build model
        
        Fit linear regression
        (4.1 p24-27)
        
        Split to train and test dataset
        
        Evaluation of model
        
        Do residuals analysis
        
        Linearity using Residuals VS Fitted Plot
        (4.1 p43)
        
        Normality
        
        Q-Q Plot
        (4.1 p44)
        
        Shapiro-Wilk Test p-value < 0.05
        (4.1 p41)
        
        Equal variance using Scale-Location Plot
        (4.1 p45)
        
        Outliers check using Residuals vs Leverage Plot
        (4.1 p46)
        
        Ensure variables are significant
        
        p-value for coefficients < 0.05
        
        Check Goodness of fit of model
        (4.1 p28-32)
        
        Adjusted R-squared > 0.7 is a good model fit
        
        Check multicollinearity
        
        All variables are Continuous
        
        Correlation matrix
        (4.2 p6)
        
        eliminate variables which are highly correlated keeping the one with highest correlation with y
        
        VIF
        (4.2 p7)
        
        If VIF for a variable > 5, the variable is highly correlated with the other variables
        
        If multiple variables with VIF > 5, drop the variable with the highest VIF, run the multi regression, get the VIF and drop the next highest VIF.
        
        Contains Categorical variables
        
        Continuous-Categorical
        
        1 Categorical
        
        1 more item...
        
        2 Categorical
        
        1 more item...
        
        Perform one-hot encoding
        (5.1 p6-14)
        
        Categorical-Categorical
        
        Chi-Square
        (5.1 p17)
        
        If the predictor variables are highly correlated
        
        Ensure model is better than null model
        
        p-value for model < 0.05
        
        Model testing using test data
      - Algorithms to improve regression accuracy
        
        Variables selection methods
        
        Backward elimination
        (4.2 p24)
        
        Stepwise
        (4.2 p24)
        
        Forward selection
        (4.2 p23)
        
        Cross-Validation