Treatment Effect Estimation

How can we estimate treatment effect?

Example: Suppose you decided to test whether the new method improves test scores. They randomly assign 10 of your students to the new method (Treatment Group) and 10 students to the regular method (Control Group).

Group Test Scores
Treatment Group 88, 90, 85, 92, 87, 91, 89, 93, 90, 88
Control Group 80, 82, 78, 85, 81, 79, 83, 84, 82, 80

How can you evaluate the effect of the new method (treatment)?

TipTreatment effect estimation

After performing a randomized experiment, we can directly compare the two groups by looking at the difference in their average outcomes.

Step 1: Calculate the average score

  • Treatment Group average:
    \[\frac{88 + 90 + 85 + 92 + 87 + 91 + 89 + 93 + 90 + 88}{10} = 89.3\]

  • Control Group average:
    \[ \frac{80 + 82 + 78 + 85 + 81 + 79 + 83 + 84 + 82 + 80}{10} = 81.4 \]

Step 2: Compare the averages

The difference is:
\(89.3 - 81.4 = 7.9 \text{ points}\)

Since the students were randomly assigned, we can be confident that this difference is caused by the new study program rather than other factors.

You can use the following code chunks as a calculator: just press the Run Code button.

Warning

This gives us a single-number estimate of the difference between the groups. However, we can’t yet conclude whether this difference is statistically significant. Don’t worry β€” future statistics classes will teach us how to test that! πŸ™‚

Try it yourself!

Example: A botanist wants to test whether a new fertilizer helps plants grow taller. She randomly assigns 12 plants to receive the new fertilizer (Treatment Group) and 12 plants to receive regular soil (Control Group).

Group Plant Height (cm)
Treatment Group 25, 27, 26, 28, 24, 27, 26, 29, 25, 28, 27, 26
Control Group 20, 22, 21, 19, 21, 20, 22, 19, 21, 20, 21, 20
  1. What is the average height of the Treatment Group? Enter your answer with one decimal place (tenth place).

Feel free to add calculations to the code chunk below or use an external calculator.

  1. What is the average height of the Control Group? Enter your answer with one decimal place (tenth place).

  1. Estimate the treatment effect? Enter your answer with one decimal place (tenth place).