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Glacius

Builds on probability

Statistics

Move from observations to estimates, inference, regression, and model evaluation.

Start with data variables 38 lessons · 12 units
Explore sample means

Inside this subject

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01Data and study design2 lessons
  1. 01
    Data variables

    Classify an observed variable by its numerical or categorical meaning.

  2. 02
    Populations and samples

    Identify the target population and observed sample in a study.

02Describing samples4 lessons
  1. 01
    Sample means

    Compute a sample arithmetic mean.

  2. 02
    Sample medians

    Compute a sample median using the stated even-size convention.

  3. 03
    Sample quantiles

    Locate a sample quantile under a supplied convention.

  4. 04
    Sample variance

    Compute sample variance using an explicitly stated denominator.

03Sampling properties2 lessons
  1. 01
    Estimators

    Distinguish a data-dependent estimator from its realized estimate.

  2. 02
    Sampling distributions

    Identify the distribution induced by repeatedly sampling an estimator.

04Likelihood estimation3 lessons
  1. 01
    Discrete likelihoods

    Evaluate candidate parameters using a fixed discrete sample's probability model.

  2. 02
    Continuous likelihoods

    Compare candidate parameters using a fixed continuous sample density.

  3. 03
    Log-likelihood

    Express an independent-sample likelihood as a sum of log terms.

05Bayesian estimation2 lessons
  1. 01
    MAP estimation

    Select a posterior mode from a supplied likelihood and prior.

  2. 02
    Grid posteriors

    Normalize posterior weights over a finite parameter grid.

06Uncertainty intervals5 lessons
  1. 01
    Standard errors

    Interpret the standard deviation of an estimator's sampling distribution.

  2. 02
    Confidence interval meaning

    Interpret confidence through repeated coverage of a fixed parameter.

  3. 03
    Mean intervals

    Construct a one-sample t interval under stated sampling conditions.

  4. 04
    Bootstrap resampling

    Construct a bootstrap sampling approximation for an IID sample statistic.

  5. 05
    Bootstrap intervals

    Read a percentile interval from supplied bootstrap replicates with stated limitations.

07Tests and errors3 lessons
  1. 01
    Null hypotheses

    Specify a null and alternative for a stated population claim.

  2. 02
    Test statistics

    Compute a supplied test statistic measuring discrepancy from a null.

  3. 03
    P-values

    Compute a tail probability under a specified null distribution.

08Comparisons and multiplicity2 lessons
  1. 01
    Effect sizes

    Interpret the magnitude of an effect in meaningful units.

  2. 02
    Multiple comparisons

    Apply a Bonferroni familywise-error bound to a stated test family.

09Linear regression4 lessons
  1. 01
    Linear regression models

    Specify a conditional mean model separating predictors from residual noise.

  2. 02
    Design matrices

    Encode supplied predictors and an intercept as a design matrix.

  3. 03
    Fitting regression

    Obtain coefficients for a full-rank regression using a supplied QR least-squares procedure.

  4. 04
    Regression residuals

    Compute residuals from fitted predictions and observations.

10Regression uncertainty and evaluation4 lessons
  1. 01
    Collinearity

    Diagnose coefficient instability caused by dependent or nearly dependent predictors.

  2. 02
    Holdout evaluation

    Separate model fitting from an independent evaluation set.

  3. 03
    Cross-validation

    Aggregate validation error from a supplied fold scheme without test-set reuse.

  4. 04
    Data leakage

    Identify preprocessing or selection that uses unavailable evaluation information.

11Probabilistic prediction3 lessons
  1. 01
    Logistic probabilities

    Convert a linear score to a probability through a supplied logistic link.

  2. 02
    Logistic log loss

    Compute binary negative log-likelihood for logistic predictions.

  3. 03
    Probability calibration

    Assess whether predicted probabilities match observed frequencies in supplied bins.

12Principal component analysis4 lessons
  1. 01
    Centering data

    Center each data feature using training-sample means.

  2. 02
    Principal components

    Find principal directions from a supplied SVD of centered data.

  3. 03
    Component scores

    Project centered observations into a chosen principal-component basis.

  4. 04
    Explained variance

    Compute a retained-variance fraction from supplied singular values.