# Verification of Contractor Test Results

How agencies verify contractor QC results before using them in acceptance: independent samples, the F-test and t-test, split samples, and failed comparisons.

- Canonical URL: https://pavementinteractive.org/reference-desk/qc-qa/statistical-acceptance/verification-of-contractor-test-results/
- Last updated: 2026-11-01
- Standards: ASTM D3665

Many agencies use the contractor's [quality control](https://pavementinteractive.org/glossary/quality-control/) test results as part of [acceptance](https://pavementinteractive.org/glossary/acceptance/). Federal rules allow this on federal-aid projects only if the agency **verifies** the contractor's results with its own sampling and testing. Verification asks one question: do the contractor's results and the agency's results look as if they came from the same material? If they do, the contractor's larger set of tests can be used to judge the lot. If they don't, they can't (Federal Highway Administration, 2004[^1]).

This article explains what the rules require and how the usual statistical comparison works. Acceptance plans in general are covered in [Acceptance Plan Basics](https://pavementinteractive.org/reference-desk/qc-qa/statistical-acceptance/acceptance-plan-basics/) and [Acceptance Plan Components](https://pavementinteractive.org/reference-desk/qc-qa/statistical-acceptance/acceptance-plan-components/).

## What the Regulation Requires

The federal quality assurance rule, 23 CFR Part 637 Subpart B, says in summary (Code of Federal Regulations, 23 CFR 637[^2]):

- contractor test results may be used in the acceptance decision only when they are validated by the agency's verification sampling and testing;
- verification samples are taken **independently** of the contractor's samples, by agency staff or their representatives;
- the testing is done by qualified personnel in qualified laboratories; and
- the agency has an [independent assurance](https://pavementinteractive.org/glossary/independent-assurance/) program covering the people and equipment doing the tests.

FHWA's technical advisory on the subject stresses the difference between **independent** samples and [split samples](https://pavementinteractive.org/glossary/split-sample/). Independent samples are taken separately, at their own random locations, and so include the variability of sampling as well as testing; only they show whether the two sets of results describe the same material. Split samples, one sample divided between the two laboratories, show only whether the two laboratories test alike. Split samples belong to independent assurance and to resolving disputes, not to verification (Federal Highway Administration, 2004[^1]).

## The F-Test and t-Test

The recommended comparison uses two classical tests together, on independent samples from the same lot or set of lots (Burati et al., 2003[^3]):

1. **The F-test** compares the variability of the two data sets. It is run first.
2. **The t-test** compares their averages.

The F statistic is the ratio of the two sample variances, larger over smaller:

$$F = \frac{s_1^2}{s_2^2}, \quad s_1^2 \ge s_2^2$$

where:

- $$s_1^2, s_2^2$$ = sample variances of the two data sets

If F exceeds the critical value for the chosen level of significance and the two sets' degrees of freedom, the variabilities are significantly different and the results are not validated, whatever the averages show.

If the variances are not significantly different, they are pooled and the t statistic compares the means:

$$t = \frac{|\bar{x}_c - \bar{x}_a|}{\sqrt{s_p^2\left(\frac{1}{n_c} + \frac{1}{n_a}\right)}}$$

where:

- $$\bar{x}_c, \bar{x}_a$$ = averages of the contractor and agency results
- $$n_c, n_a$$ = number of contractor and agency results
- $$s_p^2$$ = pooled variance of the two data sets

$$s_p^2 = \frac{(n_c - 1)\,s_c^2 + (n_a - 1)\,s_a^2}{n_c + n_a - 2}$$

If t exceeds the critical value for $$n_c + n_a - 2$$ degrees of freedom, the averages are significantly different. When the F-test shows different variances, a modified t-test that doesn't pool the variances is used instead (Burati et al., 2003[^3]).

The level of significance (α) is the agency's choice; it sets the risk of declaring a real match "different". FHWA's guidance leaves the value to the agency, and many agencies use 0.01 (Federal Highway Administration, 2004[^1]).

Calculator: Contractor versus agency verification (F and t tests) — https://pavementinteractive.org/tools/qa-verification/

## How Many Tests

The comparison is only as strong as the data. With a handful of agency tests, even a real difference between the contractor's and the agency's results can go undetected. The FHWA research shows the power of the F and t tests climbing as the number of agency tests rises, with sample sizes on the order of 10 to 20 or more needed for good protection. For this reason many agencies compare results over several lots, using a moving set of the most recent tests, rather than lot by lot (Burati et al., 2003[^3]; Federal Highway Administration, 2004[^1]).

Comparing a single agency test against the contractor's results for one lot is discouraged: one test says very little about either the mean or the variability.

## When Results Don't Verify

A failed comparison is a signal to investigate, not a verdict on who is right. Typical steps are:

- check both laboratories' calculations, equipment calibration and procedures, often by testing split samples;
- check how the samples were taken: the random locations, the sampling method and the sample handling;
- look for a real change in the material between the times each party sampled.

Until the cause is found and corrected, agencies typically base acceptance on their own test results only (Federal Highway Administration, 2004[^1]).

## Random Sampling

Verification only works if both parties' samples are random. Random locations and times are generated from random numbers within each lot or sublot, following ASTM D3665 or an agency procedure, and are not revealed to the contractor in advance (Texas DOT, 2016[^4]). The ideas behind random sampling are explained in [Acceptance Plan Basics](https://pavementinteractive.org/reference-desk/qc-qa/statistical-acceptance/acceptance-plan-basics/).

## Standard Practices

- ASTM D3665: Random sampling of construction materials
- 23 CFR Part 637, Subpart B: Quality assurance procedures for construction

## Sources

[^1]: Federal Highway Administration (FHWA) (2004). Use of Contractor Test Results in the Acceptance Decision, Recommended Quality Measures, and the Identification of Contractor/Department Risks. Technical Advisory T 6120.3. Federal Highway Administration. Washington, D.C. https://www.fhwa.dot.gov/construction/t61203.cfm
[^2]: Code of Federal Regulations (current). 23 CFR Part 637: Construction Inspection and Approval (Subpart B, Quality Assurance Procedures for Construction). Electronic Code of Federal Regulations. U.S. Government Publishing Office. https://www.ecfr.gov/current/title-23/chapter-I/subchapter-G/part-637
[^3]: Burati, J.L.; Weed, R.M.; Hughes, C.S. and Hill, H.S. (2003). Optimal Procedures for Quality Assurance Specifications. FHWA-RD-02-095. Federal Highway Administration. McLean, VA. https://www.fhwa.dot.gov/publications/research/infrastructure/pavements/pccp/02095/appf.cfm
[^4]: Texas Department of Transportation (TxDOT) (2016). Random Selection of Bituminous Mixture Samples (Tex-225-F). Materials and Tests Division, Texas Department of Transportation. Austin, TX. https://ftp.dot.state.tx.us/pub/txdot-info/cst/TMS/200-F_series/pdfs/bit225.pdf