CurriculumGrade 12Mathematics

Comparing Two Treatments

Aligned to S-IC.B.5 — Common Core State Standards for Mathematics.

What this lesson teaches

In a randomized experiment, compare the mean outcomes of two treatment groups. A difference is likely significant if it is larger than the variation you would expect from chance alone, which a simulation or randomization test can check.

Worked example

Group A (new drug) averages 8 fewer sick days than Group B (placebo). If randomly reshuffling the group labels rarely produces a gap as large as 8, then the observed difference is statistically significant.

Practice questions

  1. What does it mean for a difference to be statistically significant?
  2. Why compare the means of the treatment groups rather than individuals?
  3. How can a simulation test whether a difference is due to chance?

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Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.

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En español

Comparar dos tratamientos

En un experimento aleatorizado, compara los resultados promedio de dos grupos de tratamiento. Una diferencia probablemente es significativa si es mayor que la variación que esperarías solo por azar, lo cual una simulación o prueba de aleatorización puede comprobar.

Ejemplo: El grupo A (medicamento nuevo) promedia 8 días de enfermedad menos que el grupo B (placebo). Si reordenar al azar las etiquetas de los grupos rara vez produce una diferencia tan grande como 8, entonces la diferencia observada es estadísticamente significativa.

More Statistics & Probability lessons

Making Inferences from SamplesS-IC.B.4Normal Distributions and the Empirical RuleS-ID.A.4Making Inferences from SamplesS-IC.A.1Surveys, Experiments, and Observational StudiesS-IC.B.3Events, Unions, and ComplementsS-CP.A.1Independent EventsS-CP.A.2

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