Statistic Reasoning with R Exam 1 Note for Printing

Causal Inference

Specific causal question (SCQ)

• SCQ four components
• • • intervention ("what is the impact of xxx", x)
    • event & purpose ("of xxx", x improves y )
    • who ("for xxx", group_A, a group )
    • alternative or the control ("relative to xxx", x_control )
  • Example output: What is the impact of x on improving y for group_A relative to x_control.
  • Define y: continues variable, each individual of group_A has a y

Hypothesis

The researchers hypothesize that x will improve y for group_A.

Potential Outcomes of One Treatment (total count = 2)

• What would the outcome of y be if one of group_A (a individual of group_A) was subjected under x_control.
• What would the outcome of y be if one of group_A was subjected under x.

Average Factual Outcome (for treatment effect x)

What is the average y after individuals in group_A are subjected under x.

Average missing counterfactual (for treatment effect x)

What would have been the average y for individuals in group_A are subjected under x_control instead of x but all else remained the same.

Randomization

• Randomization ensures the average difference in outcome of y between x and x_control is only due to the treatment because the two groups are on average identical to each others in all other pretreatment characteristic.
• Ensures internal validity
• lacks in external validity, where the conclusion can only be generalized for this experiment.

Observational

• Not randomized
• estimated average MCF using group_A who received x_control, but cannot guarantee unbiased
• To be unbiased: no other features systematically differ between those who was subjected under x and those who was subjected under x_control

Confounders, covariate

• Systematic difference
• Two conditions for cofounder
• • related or predicts the outcome of y and not observed
  • difference in baseline covariate of the x group and the x_control group

Univariate Summary Statistics And Figures

Want to find out what values they take; the frequency of each value or each range of values: central tendency, spread, shape, notable features.

Variables to identify

• continuous
• discret
• • dichotomous (use mean)
  • categorical (use mode for central tendency)
  • ordinal (use median ): categorical with meaningful order
  • continuous variable (mean and median): numeric variable

Quantiles:

• Univariate variable (median: average of middle-most two values, or middle-most)
• mean: more sensitive to outliers than median
• mode: the most frequently appearing variable
• first quartile (lower quartile): the first 25% of the data
• second quartile: the first 50% of the data, which is the median
• third quartile (upper quartile): the first 75% of the data
• interquartile range: diff between upper and lower quart. and measures the spread
• root mean square: abs. magnitude change in proportion
• standard deviation: the proportion of y subjected to x is approx. sd() away from its mean.

Plots

• Bar plots: Summarize the distribution (0.3, 0.4, etc.), or dichotomous var, of a proportion var or char. var with multiple categories.
• Histogram: (For numeric vals) First, discretize by creating bins; second, calculate the density of each bin; third, use density as the height of the bin.
• Box plot: shows distribution of numeric values; best to show variables side-by-side; visualizes median, upper q., lower q., and IQR together

Bivariate Relationships

• Scatter Plot: Bivariate only; shows relationship between two continuous values.

Types:

• dichotomous vs. categorical: grounded bar plot
• dichotomous vs. continuous : two bar plots, overlaid or side-by-side histograms
• categorical vs. continuous : two box plots side-by-side
• continuous vs. continuous : scatter