First Stage Instrument Strength

Compute the first-stage instrument-set F statistic from R-squared, sample size, and instrument count.

Description

A first-stage F statistic summarizes instrument-set predictive strength in a regression.

A first-stage F statistic summarizes instrument-set predictive strength in a regression. Strength does not establish the other assumptions required for causal inference.

Compute the first-stage instrument-set F statistic from R-squared, sample size, and instrument count.

When to use First Stage Instrument Strength

Use this for the following task: Compute the first-stage instrument-set F statistic from R-squared, sample size, and instrument count.

Prepare the observed records or explicit model parameters requested below. Keep probabilities as fractions and paired records aligned.

How to use First Stage Instrument Strength and understand its results

Prepare the observed records or explicit model parameters requested below. Keep probabilities as fractions and paired records aligned.
Enter firstStageRSquared, sampleSize, instrumentCount, minimumF using the field table, then run the tool.
Read fStatistic, strongByThreshold. Interpret flags, units, ordering and placeholder values using the rules below.
Review any reported issue or failed check, correct the supplied values when appropriate, and verify the result in its intended context.

Input field	Meaning	Value type and bounds	Requirement
firstStageRSquared	First stage r squared	number	Required
sampleSize	Sample size	integer	Required
instrumentCount	Instrument count	integer	Required
minimumF	Minimum f	number	Required

Require R squared in [0,1), a positive instrument count, n>k+1 and a nonnegative minimum F. Compute the statistic and compare inclusively.^[1]

F=(R²/k)/[(1−R²)/(n−k−1)]

This summarizes the declared operation. Units, indexing, inclusivity and exceptional cases are explained in the surrounding text.

Output field	Meaning	Value type
fStatistic	F statistic	number
strongByThreshold	Strong by threshold	boolean

json

{
  "input": {
    "firstStageRSquared": 0.1,
    "sampleSize": 100,
    "instrumentCount": 2,
    "minimumF": 10
  },
  "output": {
    "fStatistic": 5.388888888888889,
    "strongByThreshold": false
  }
}

Limitations and assumptions

The first-stage fit is supplied. Exclusion restrictions, confounding, causal validity and weak-instrument-specific inference are not tested.

The tool evaluates supplied observations or a declared model. It does not establish the biological cause of an observed pattern. Malformed requests produce input errors. A successfully evaluated request can still contain false flags, empty result lists or a result outside the supplied threshold; those outcomes have the meanings stated above.

Alternative or Complementary methods

Choose Expected Cell Count Audit for this operation: Audit expected contingency-cell counts against a caller-defined asymptotic adequacy criterion. For a complementary task, use Population PC Outliers for this operation: Flag population-PC1 outliers relative to an explicitly supplied reference mean and standard deviation.

The implementation reference documents the exact calculation, supported input shapes and returned fields.

References

First Stage Instrument Strength — tool.io

Similar or alternative tools

Expected Cell Count Audit
Audit expected contingency-cell counts against a caller-defined asymptotic adequacy criterion.
Population PC Outliers
Flag population-PC1 outliers relative to an explicitly supplied reference mean and standard deviation.