The Three E’s of Quantitative Research: Estimand, Estimator, Estimate

The Three E’s of Quantitative Research

Term	One-line definition	Where it “lives”	Simple example (blood-pressure drug)
Estimand	The scientific question expressed as a precise quantity you want to know.	Before data are collected.	“The average reduction in systolic BP (mm Hg) if every adult took Drug X instead of placebo for 12 weeks.”
Estimator	The recipe or formula you will apply to data to target the estimand.	In your analysis plan / code.	“Difference in sample means between the Drug X group and placebo group (unadjusted).”
Estimate	The numerical answer you get after running the estimator on the actual dataset.	In your results table.	“–7.4 mm Hg (95 % CI –9.1 to –5.7).”

How they fit together

1. Start with the estimand.

   • Clarifies what effect, in whom, and under which conditions you care about.

2. Choose an estimator that is valid if the required causal/statistical assumptions hold.

   • Could be as simple as a risk difference, or as complex as a targeted-maximum-likelihood algorithm.

3. Compute the estimate once you have data.

   • This single number (plus its uncertainty) is what you report.

Key points to remember

• Estimand ≠ Estimator: The former is a target; the latter is a tool.

• Different estimators (e.g., regression with covariate adjustment, IPW, G-computation) can aim at the same estimand.

• The estimate is data-dependent and will change with a new sample; the estimand and estimator do not.

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Augmented Article

Estimand, Estimator, and Estimate

Quantitative research often appears technical, but at its core it follows a simple intellectual flow. Every well-designed study answers three fundamental questions:

1. What exactly do we want to know?

2. How will we calculate it from data?

3. What number do we finally obtain?

These questions correspond to the Three E’s of Quantitative Research:

• Estimand

• Estimator

• Estimate

Understanding the distinction between them is essential for designing valid studies, interpreting results correctly, and avoiding common methodological mistakes.

1. Estimand: What do we expect to estimate?

Definition

The estimand is the scientific question expressed as a precise quantity. It defines the target of inference—what we truly want to learn about the population, independent of any particular dataset.

In causal and clinical research, the estimand answers:

• What effect?

• In whom?

• Under what conditions?

• Over what time frame?

Importantly, the estimand is defined before any data are collected.

Where it “lives”

• In the research question

• In the study protocol

• In the methods section, conceptually
  

Simple clinical example (blood-pressure drug)

“The average reduction in systolic blood pressure (mm Hg) if every adult with hypertension were treated with Drug X instead of placebo for 12 weeks.”

This statement already clarifies:

• Population (adults with hypertension)

• Intervention (Drug X)

• Comparator (placebo)

• Outcome (systolic BP reduction)

• Time horizon (12 weeks)
  

Why the estimand matters

Without a clearly defined estimand:

• Different readers may interpret the same results differently

• Analyses may drift away from the original clinical question

• Methodological choices become arbitrary

🔍 Key insight: The estimand is not a statistical formula—it is a clinical–scientific target.

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2. Estimator: What method or statistic do we use?

Definition

The estimator is the statistical recipe or algorithm used to approximate the estimand using observed data.

It specifies how we will transform raw data into a quantity that targets the estimand, assuming certain statistical or causal assumptions hold.

Where it “lives”

• In the analysis plan

• In statistical code

• In the methods subsection of analysis

Simple clinical example

“The unadjusted difference in mean systolic blood pressure between the Drug X group and the placebo group.”

Other valid estimators for the same estimand might include:

• Regression-adjusted mean difference

• Inverse probability–weighted estimator

• G-computation

• Targeted maximum likelihood estimation (TMLE)
  

Why the estimator matters

• Different estimators can target the same estimand

• Some estimators are more robust to confounding, missing data, or model misspecification

• The estimator determines validity, precision, and bias
  

🔍 Key insight: The estimator is a tool, not the goal. A sophisticated estimator cannot rescue a poorly defined estimand.

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3. Estimate: What result do we actually obtain?

Definition

The estimate is the numerical value produced when the estimator is applied to the observed dataset.

It is the concrete answer that appears in tables, figures, and abstracts.

Where it “lives”

• In the results section

• In tables and figures

• In confidence intervals
  

Simple clinical example

“–7.4 mm Hg (95% CI: –9.1 to –5.7)”

This value depends on:

• The specific sample

• Random variation

• Measurement error

• Missing data patterns
  

Why the estimate matters (and why it can disappoint)

The estimate:

• May differ from expectations

• May be imprecise

• May be clinically small even if statistically significant

🔍 Key insight: The estimate is data-dependent. With a new sample, the estimate will change—but the estimand and estimator should not.

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How the Three E’s Fit Together

Step 1: Start with the estimand

Clarify the exact effect you care about. This anchors the entire study in a meaningful clinical or scientific question.

Step 2: Choose an estimator

Select a statistical method that can validly target the estimand if its assumptions are met.

• Simple question → simple estimator

• Complex causal question → advanced causal estimators
  

Step 3: Compute the estimate

Apply the estimator to your data to obtain a numerical result with uncertainty.

This final number—the estimate—is what you report, interpret, and debate.

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Common Pitfalls to Avoid

• Confusing estimand with estimator A regression model is not the research question.

• Changing the estimand after seeing the data This undermines scientific credibility.

• Overinterpreting the estimate Statistical significance does not guarantee clinical importance.

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Summary: The Three E’s at a Glance

Term	What it answers	Stability
Estimand	What do we want to know?	Fixed
Estimator	How do we calculate it?	Fixed
Estimate	What number did we get?	Sample-dependent

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Final Takeaway

Good quantitative research is not about producing impressive numbers. It is about alignment:

A well-defined estimand,matched with a valid estimator,producing an interpretable estimate.

When these three are aligned, your results become not only statistically sound, but clinically meaningful.