"Master Hypothesis Testing in Field Experiments"

Hypothesis testing in field experiments is a statistical approach to evaluate cause-and-effect relationships by analyzing real-world data to determine the significance of observed outcomes. It involves defining null and alternative hypotheses, designing randomized experiments, collecting data, and using statistical tests like t-tests or regression for result interpretation.


Aspect Description
Definition
Hypothesis testing is a statistical method used to make decisions or inferences about a population parameter based on sample data. In the context of a field experiment, it involves testing a specific assumption or claim (the hypothesis) about the behavior, outcome, or effect of a variable in a real-world environment.
Purpose
The objective is to evaluate whether the observed results in the field experiment are statistically significant or if they could have occurred by random chance. This helps in determining the cause-and-effect relationship between variables in a natural setting.
Null Hypothesis (H0)
The null hypothesis represents the default position or assumption that there is no effect, no difference, or no relationship between the variables being studied. For example, "The new method has no impact on productivity."
Alternative Hypothesis (H1)
The alternative hypothesis is the claim that contradicts the null hypothesis, suggesting that there is an effect, a difference, or a relationship. For example, "The new method improves productivity."
Experiment Design
In a field experiment, the design involves randomizing participants or observations into treatment and control groups to test the hypothesis. This ensures that the results are not biased and can be attributed to the intervention or variable being tested.
Data Collection
Data is collected directly from the real-world context where the experiment is conducted. This can include observational data, surveys, or performance metrics, depending on the hypothesis being tested.
Statistical Testing
Statistical methods such as t-tests, chi-square tests, or regression analysis are used to analyze the data. These tests determine whether the observed differences or effects are statistically significant.
Results Interpretation
Based on the p-value and confidence level, the null hypothesis is either rejected or not rejected. Rejecting the null hypothesis indicates that the alternative hypothesis is supported by the data, whereas failing to reject it suggests otherwise.

Infographic: The Path of Statistical Inference

The Path of Statistical Inference

From a Small Sample to a Big Conclusion

🎯

The Goal

We want to understand a whole **population**, but we can only study a small **sample**. Statistical inference is the science of using that sample data to make educated guesses about the population.

👥

Population

(Everyone)

→
🧑‍🤝‍🧑

Sample

(A Small Group)

🌉

The Bridge: Central Limit Theorem

If we take many random samples and plot their average values, they form a predictable bell curve called a **sampling distribution**. This allows us to use the properties of the normal distribution to make inferences.

📜

The Framework: Hypothesis Testing

This is the formal process for testing a claim.

1️⃣

State Hypotheses

Define the Null (H₀, no effect) and Alternative (Hₐ, an effect) hypotheses.

2️⃣

Set the Standard

Choose a significance level (α), usually 5% (0.05).

3️⃣

Analyze Data

Calculate a test statistic from your sample data.

4️⃣

Make a Decision

Compare your result (p-value) to your standard (α).

⚖️

The Verdict

The **p-value** is the probability of seeing your data if the null hypothesis is true. We compare it to alpha (α) to make a decision.

IF p-value ≤ α

💥

Reject the Null Hypothesis

(The result is statistically significant)

IF p-value > α

🤷

Fail to Reject the Null

(The result is not statistically significant)

⚠️

The Risks: Errors

Since we're dealing with probability, we can make two kinds of mistakes.

Actual Reality
H₀ is True H₀ is False
Our Decision Type I Error False Positive Correct! True Positive
Reject H₀ Correct! True Negative Type II Error False Negative
📏

The Uncertainty

A **confidence interval** gives a range of plausible values for the true population parameter, quantifying the uncertainty around our sample estimate.

Sample Mean: 105

99 111

95% Confidence Interval: [99, 111]

We are 95% confident the true population mean lies between 99 and 111.

2-causal-inference    3-hypothesis-testing    4-covariates    5-one-sided-compliance   

Topic

  • Home

  • 2-causal-inference

  • 3-hypothesis-testing

  • 4-covariates

  • 5-one-sided-compliance

    Read more