Compare treated and control event rates or average outcomes. The calculator reports the observed difference and relative change; causal interpretation requires appropriate study design and assumptions.

Compare the same yes/no outcome over the same follow-up period. Count each participant once in one group. This unadjusted difference estimates a causal effect only under appropriate study assumptions.

Average Treatment Effect Formula

The following difference-in-means formula can estimate the Average Treatment Effect (ATE) under appropriate study assumptions.

ATE = Mₜ - Mc

Variables:

  • M_t is the mean outcome for the treated group
  • M_c is the mean outcome for the control group

Subtract the control mean from the treated mean to calculate the observed group difference. For a binary outcome, each mean is event count divided by group total; multiplying their difference by 100 gives percentage points. Relative change divides the difference by the control outcome and multiplies by 100; it is undefined when control is zero.

What is the Average Treatment Effect?

The Average Treatment Effect (ATE) is the population average of the difference between each individual’s potential outcome with treatment and without treatment. An observed treated–control difference is not automatically causal. Causal identification requires assumptions such as exchangeability, consistency and positivity, with suitable sampling for the target population. This calculator reports an unadjusted comparison; it does not adjust for confounding, calculate uncertainty or establish statistical significance.

How to Calculate the Average Treatment Effect?

Select Average outcome for the steps below, using the same outcome scale and follow-up period. In Binary outcome mode, enter whole participant counts with each event count no greater than its group total. Count each participant once in one group. Select Calculate to view the observed difference; whether a higher outcome is beneficial depends on what was measured.

  1. First, determine the mean outcome for the treated group (M_t).
  2. Next, determine the mean outcome for the control group (M_c).
  3. Use the formula ATE = M_t – M_c.
  4. Finally, calculate the Average Treatment Effect (ATE).
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem:

Use the following variables as an example problem to test your knowledge.

Mean outcome for the treated group (M_t) = 75

Mean outcome for the control group (M_c) = 65. The observed difference is 75 − 65 = +10 outcome units; relative change is approximately +15.384615%.