research27 min studyLesson 960 in Engineering

Publish an energy result another experiment can challenge

Match workload and instrumentation, preserve raw evidence, and separate repeatability from systematic uncertainty.

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What you’ll understand

  • Design matched, completion-aligned energy comparisons with traceable artifacts.
  • Calculate paired differences and a scoped standard-error estimate.
  • Propagate positive input ranges without mislabeling them as confidence intervals.

An energy claim becomes useful when its workload, electrical boundary, instruments, and uncertainty can be inspected independently. A repeatable script is necessary but insufficient: it can reproducibly integrate stale sensor values, stop before a device finishes, or compare unequal quality. Freeze the workload contract and record the measurement path with the implementation. Then separate variation among repeated runs from uncertainty that repeats do not remove, and preserve enough raw evidence to explain a reversal under another representative condition.

Match the experiment, not just the command line

Record code and model artifacts, tokenizer and data versions, useful-output counts, precision, batch policy, cache state, concurrency, and quality checks. Hold service constraints and the completed work definition fixed, or report intentional changes explicitly. Warmup and compilation belong either inside the declared measured service or in a separately documented amortization. An identical shell command can still execute a different workload when remote data, model versions, or runtime defaults change.

Record meter placement or API scope, device identity, driver and interface versions, counter epoch, timestamps, integration method, and start/stop synchronization. Confirm that asynchronous work has completed before closing the intended window. Preserve invalid reads and counter resets as diagnostic events rather than replacing them with zero. For facility or emissions accounts, store allocation policies and immutable factor versions with their units, geography, time resolution, and gas scope. This separates reproducible arithmetic from unsupported input assumptions.

Di=EA,i−EB,i,D‾=1n∑i=1nDi,SE^(D‾)=sDnD_i=E_{A,i}-E_{B,i},\qquad \overline D=\frac1n\sum_{i=1}^{n}D_i,\qquad \widehat{\mathrm{SE}}(\overline D)=\frac{s_D}{\sqrt n}
n≥2 matched pairs use the same energy unit and declared boundaries. sD is the sample standard deviation of paired differences with denominator n−1. The standard-error expression assumes independent representative pair differences with common finite variance. It is an estimate of random sampling variation, not a calibration bound or automatically a confidence interval.↔ Scroll wide equations horizontally.

Use repeats to answer a repeatability question

Pair runs under comparable conditions and randomize or counterbalance their order when appropriate. Thermal drift, background activity, and time-of-day effects can otherwise become confounded with implementation. Independence across pairs is an assumption to examine; rapid repeats with shared cache state or common external load can be correlated. A small standard error from many dependent runs is not evidence that the absolute energy measurement is accurate.

NIST’s uncertainty guidance distinguishes evaluations based on statistical observations from those based on other information such as calibration. A persistent meter bias does not generally shrink as the number of repeated runs grows. A common additive bias can cancel in a paired difference if it truly applies equally, while a differential bias can remain. State which uncertainty sources are shared and which are not instead of claiming either universal cancellation or universal independence.

E∈[E−,E+],I∈[I−,I+]⟹EI∈[E−I−,E+I+]E\in[E_-,E_+],\quad I\in[I_-,I_+]\quad\Longrightarrow\quad EI\in[E_-I_-,E_+I_+]
All four endpoints are finite and nonnegative with each lower endpoint no larger than its upper endpoint. E is kWh and I is kg CO2e/kWh under compatible boundaries, giving kg CO2e. This is an outer range conditional on both inputs lying in their intervals; independence is unnecessary. It is not automatically a calibrated probability interval.↔ Scroll wide equations horizontally.

Report the conclusion at the supported precision

Publish gross totals, useful-work denominators, run-level observations, and rejected-run reasons before compressing the study into one ratio. Report uncertainty sources separately when combining them would require unjustified distributional assumptions. A narrow repeatability estimate can coexist with a wide factor or calibration range. Rounding a final number appropriately is more honest than retaining every decimal from multiplication when the dominant input came from a coarse assumed factor.

A robust comparison also explains its scope of generalization. One matched input mix, device generation, facility period, and driver version do not establish a universal ranking. Reproduce the relevant result on other representative workloads when making broader claims, and record failures as well as wins. Preserve configuration and data snapshots so the experiment can be rerun after an implementation change. The objective is an auditable decision with stated limits, not an unchallengeable environmental label.

Small run variation does not remove differential calibration uncertainty

Three fictional matched pairs measure A energies [100,110,105] J and B energies [90,100,96] J. Assume pair differences are independent observations for the repeatability calculation. Separately, the comparison has an uncanceled differential calibration-bias range of ±3 J that is not reduced by repeats.

  1. Paired differences A−B are [10,10,9] J. Their mean is 29/3≈9.6667 J, so B uses less measured energy in each of these matched pairs.

  2. Deviations from the mean are [1/3,1/3,−2/3] J. Their squared sum is 2/3 J²; dividing by n−1=2 gives sample variance 1/3 J². Thus sD≈0.57735 J and estimated standard error is 1/3 J.

  3. The ±3 J stipulated differential calibration range remains separate from the 0.3333 J random standard-error estimate. More independent repetitions reduce random error under the model but do not automatically remove that bias. No 95% interval is claimed from these three observations.

The result

The observed mean saving is approximately 9.667 J with a scoped random standard-error estimate of 0.333 J, alongside a separate ±3 J differential calibration range.

Explore the model

Interactive lab

Interactive lab · sampling

Independent averaging reduces one kind of variation

Reset, set Success probability p to 0.5 and Independent samples n to 20; predict sample-mean variance 0.0125 before Step. Reset, set p to 0.5 and n to 100; predict variance 0.0025 before Step. Playback highlights exact binomial outcomes, not fresh observations. This independent Bernoulli model illustrates random averaging only; it has no calibration bias, correlated energy traces, or measured device data.

Independent averaging reduces one kind of variationExact binomial masses for the mean of n independent Bernoulli trials, compared with normal mass between adjacent half-count boundaries; normal tails outside the finite support remain outside the bars. Playback highlights outcomes, not random samples. The Berry–Esseen bound applies to standardized CDFs, not individual bars or continuity-corrected errors. At p = 0 or 1, normal comparison and that bound are disabled. Normal-CDF evaluation uses a numerical approximation with absolute error below 7.5×10⁻⁸ (at most 1.5×10⁻⁷ per interval, before rounding). Current readings: Mean sample proportion: 0.5; Sample-mean variance: 0.0125; Uniform CDF error bound: ≤ 0.1062. All parameters are adjustable with the labeled controls below.Exact distribution of the mean of 20 independent Bernoulli variables with success probability 0.5; playback highlights outcome 0.00.250.50.75100.0580.1150.1730.23Sample mean · k / nProbability massNormal bin masses are an approximationk = 0 · exact probability = 9.54e-7
Exact binomial massNormal interval massHighlighted outcome / mean
Mean sample proportion
0.5
Sample-mean variance
0.0125
Uniform CDF error bound
≤ 0.1062
t = 0 s

Exact binomial masses for the mean of n independent Bernoulli trials, compared with normal mass between adjacent half-count boundaries; normal tails outside the finite support remain outside the bars. Playback highlights outcomes, not random samples. The Berry–Esseen bound applies to standardized CDFs, not individual bars or continuity-corrected errors. At p = 0 or 1, normal comparison and that bound are disabled. Normal-CDF evaluation uses a numerical approximation with absolute error below 7.5×10⁻⁸ (at most 1.5×10⁻⁷ per interval, before rounding). Parameter changes pause playback and recompute the model at the current elapsed time. Reset restores both parameters and returns time to zero. Playback starts paused. Adjust either parameter, then choose Play or Step.

Look forMore independent samples shrink modeled random variation, not every source of uncertainty.

Check your understanding

A large number of repeats makes a mean highly repeatable. What further claim is justified about an unchanged systematic calibration bias?

Try it yourself

A fictional compatible account has energy in [0.9,1.1] kWh and an emissions factor in [0.3,0.5] kg CO2e/kWh. Compute a guaranteed outer product range conditional on those input bounds. Is it automatically a 95% confidence interval?

Take a moment to make a prediction or work it out on paper. Open a hint when you need one.

Give me a hint

Both ranges are nonnegative, so multiply lower endpoints and upper endpoints.

Compare with the solution

The product lies in [0.9×0.3,1.1×0.5]=[0.27,0.55] kg CO2e if the actual inputs lie within the stated bounds. Input dependence can make some interior combinations unattainable, but the outer range remains valid. No confidence level follows unless the input intervals and their joint coverage have an appropriate probabilistic justification.

Take it with you

  • Match useful work, service constraints, electrical scope, and completion windows.
  • Separate random repeatability from calibration, allocation, and factor uncertainty.
  • Preserve raw traces and immutable inputs so another study can challenge the result.

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