Summary: Basic Statistics

Read the summary and the most important questions on Basic statistics

• 1 Week 1

• 1.1 Day 3: Probability Distributions

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• Name 3 important probability distributions (shows how it differs) + short description:

  normal (continuous, symmetric outcome), poisson (count data) and binomial distribution (binary outcome (two classes), ratios, hidden ratios).
  
  Normal (continuous, symmetric, tail area decreases exponentially)
  Poisson (discrete, non-negative, right skewed especially for small λ)
  Binomial (discrete, bounded on [0, n], can be left or right-skewed)

• The Poisson distribution (with count data) is discrete. Meaning?

  Counts can only take on certain values. 0,1,2,3..

• 2 Week 2

• 2.1 Day 4: Simple linear regression

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• Fill in the values for simple linear regression formula.

  To summarize, a simple linear model estimates an intercept and a slope based on the residuals. We can express the uncertainty of these estimates with a confidence interval, and we can predict new observations with a prediction interval.

• Name the assumtions (that contain diagnostic plots) of a simple linear model, and how they can be checked visually.

  - Linearity (residuals vs fitted)
  - Normality (QQ-plot)
  - Constant variance (scale-location)
  - No influential outliers (residuals vs leverage)
  
  Others (that don't have plots):
  - Independence
  - No colinearity

• What are Std. Error, t value and p-value?

  Std. Error: Measurement of uncertainty, also computes t-value
  T value: Measure of evidence against the null-hypothesis (H0) that the estimate is 0, used to compute p-value
  P value: If H0 were true, what is the chance of finding this large an estimate in a sample? Computed from the t-value

• From this regression table, give explanation for residual standard error, multiple r squared, adjusted r squared and f statistic

  Call: Shows you what formula was fitted.
  Residuals: Simple summary statistics of the residuals (better do diagnostics)
  Signif. Codes: Simplification of the p-values
  Residual standard error: Misnomer, should say residual standard deviation
  Multiple R-squared: The variance in the outcome explained by this model
  Adjusted R-squared: Adjusted for model complexity, used to compare models
  F statistic: An omnibus test: does my model have any explanatory value?

• What is a confidence interval (CI)? And a prediction interval (PI)?

  Confidence interval: A range of plausible values for an estimate
  Prediction interval: Where you should expect future observations

• 2.2 Day 5: GLM

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• Name the 3 parts that make up a Generalized Linear Model (GLM) and their meanings:

  Error structure: a probability distribution in the exponential dispersion family (normal, poisson, binomial)
  Linear part: linear relationship between the explanatory variables and n
  Link function: translation from n to the expected value of the outcome
  
  
  Extra info: 
  Error structure: a sensible choice for the probability distribution of the outcome, given the explanatory effects. The whole reason we're using GLM.
  Linear part: How do explanatory variables affect the mean of the error structure?
  Link function: How do we transform the linear part, such that it actually corresponds to the mean of the error structure?

• Name the 4 generalized linear models (normal, poisson, binomial) key assumptions:

  independent observations, conditional probability distribution, linearity, mean-variance relationship

• Plot alternative for GLM is randomized quantile residuals. Use DHARMa package for diagnostics GLM. Describe the following of QQ plot residuals: The line: KS test:Dispersion test:Outlier test:

  
  The line: Deviations from the line are deviations from the chosen probability distribution
  KS test: Significance test for deviation from the chosen probability distribution
  Dispersion test: Significance test for over- or underdispersion
  Outlier test: Significance test for presence of outliers