Foundations for Experimental Research
These notes supply the probability and classical inference needed before causal estimators are introduced.
See
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Probability and Sampling Distributions
- Means, variances, standard errors, the central limit theorem, and reference distributions.
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Hypothesis Tests for Experimental Research
- One- and two-sample tests for means and proportions, including paired tests.
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Confidence Intervals for Experimental Research
- Interval estimates for means, proportions, and differences.
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ANOVA for Experimental Research
- Decomposition of total variation into between- and within-group components.
Why these foundations matter
Experimental estimators are statistics computed from outcomes and treatment assignments. Their uncertainty is described by a sampling or randomization distribution. Standard errors, test statistics, confidence intervals, and ANOVA all formalize how much an estimate would vary under repetition.
Worked problems and practice
Foundations Exam Workshop combines test selection, confidence intervals, paired designs, proportions, and a complete ANOVA table. It includes multi-part exercises with numerical solution checks.