Inferential Foundations for Experimental Research

The route

1. 01

   Module 1: Sampling variability and standard error

   A statistic computed from one sample would differ in another. Expectation, variance and conditional probability supply the notation; the sampling distribution and its standard error measure the variation.

   • 1
     Random Variables, Expectation and Variance

     • The learner can compute the expectation and variance of a discrete random variable by either route, and apply the linearity and scaling rules to a linear transformation of it.
   • 2
     Covariance, Independence and the Variance of a Sum

     • The learner can determine whether the variance of a sum decomposes, justifying the decision by the covariance term, and can distinguish independence from zero covariance by exhibiting or interpreting a pair that is uncorrelated yet dependent.
   • 3
     Conditional Probability, Total Probability and Bayes' Rule

     • The learner can compute a conditional probability from a joint table or mass function, apply the law of total probability, and obtain a posterior by Bayes' rule without inverting the conditioning or discarding the base rate.
   • 4
     Probability and Sampling Distributions

     • Given a described sampling situation, the learner can obtain the standard error of a mean, say what the central limit theorem does and does not claim, and identify when the independence the formula assumes fails.
2. 02

   Module 2: Hypothesis tests, confidence intervals and group comparisons

   An estimate, a null value and a standard error, assembled two ways. A test asks whether the data would be surprising under a hypothesis; an interval reports which parameter values the data are compatible with. ANOVA extends the comparison to several group means under one error rate.

   • 1
     Hypothesis Tests for Experimental Research

     • Given a described study, the learner can identify the unit of analysis and the data structure, paired or independent, one sample or two, and select a test whose standard error matches that design.
     • Given an estimate, a null value and the design's standard error, the learner can compute the standardized distance, name the reference distribution with its degrees of freedom, and state what the result does and does not establish, treating failure to reject as inconclusive rather than as evidence for the null.
   • 2
     Confidence Intervals for Experimental Research

     • Given an estimate and its standard error, the learner can construct the appropriate interval and state what the confidence level does and does not claim.
   • 3
     ANOVA for Experimental Research

     • Given an ANOVA table or a description of a multi-group comparison, the learner can read the decomposition, compute or check the statistic, and state precisely what rejection establishes.
3. 03

   Module 3: Fitting relationships

   Least squares turns a scatter of points into coefficients with standard errors, and the same machinery carries group comparisons, varying effects and binary outcomes. It supplies no warrant for reading a coefficient as an effect.

   • 1
     Linear Regression for Experimental Research

     • Given regression output, the learner can state what a coefficient means as an average change per unit of the predictor, conditional on the others in the model and with its units, and treat $R^2$ as in-sample explained variation rather than evidence of correctness.
     • Given regression output and a described study, the learner can identify the design or identification argument, not the fit, as the source of any causal reading, and say when the classical standard errors are inappropriate and what should replace them.
   • 2
     Indicator Variables and Interactions

     • Given a model containing indicators and interactions, the learner can state what each coefficient means, identify the reference point it depends on, and recover a quantity of interest from the parameterisation.
   • 3
     Binary Outcome Models for Experimental Research

     • Given a binary-outcome analysis, the learner can say what each model reports, convert or refuse to convert between scales, and identify a result stated on the wrong one.

What finishing means

Finishing this course means you have demonstrated the required skills with the level of support this course currently assesses.

12 required skills. If you reach a lesson without the background it assumes, you are pointed at the prerequisite first, and returned here afterwards.