Counts and denominators
About confidence intervals and independent results explains why counts, intervals and independence matter.
How rows are counted
Section titled “How rows are counted”| Group | Meaning |
|---|---|
| Included | Not excluded and not flagged |
| Excluded | Excluded with a reason. Listed in the report, left out of the analysis |
| Flagged | Still included and marked: blank, <0.5 or text |
Results gives the counts, for example 19 analyzed · 2 excluded. Several rows can belong to one specimen or subject.
How n is counted
Section titled “How n is counted”Observations are rows. They come from independent units: specimens, subjects, materials, pools, days or runs. Repeats add observations but no units.
| Study type | Counted unit |
|---|---|
| Descriptive summary | Estimates use every included row. A limit counts distinct specimen IDs |
| Repeatability | Each replicate of the one material at that level |
| Bias against an assigned value | Each replicate of the one material at that level when all share one recorded day and run; otherwise one material, so no mean or bias interval |
| Multi-day precision | Replicates within runs within days. The mean CI uses day means |
| Method comparison, instrument comparison | Specimens, with replicates averaged first. In instrument comparison, every specimen counts toward each analyzer's specimen rule, even one with a missing result; a specimen whose rows on one analyzer are all excluded with a reason leaves only that analyzer's count |
| Reagent lot comparison | Patient specimens, with replicates averaged per lot. QC material is excluded. A specimen measured on one lot only still counts toward the specimen rule, as not evaluated |
| Linearity | Replicates at each level. The fit uses level means |
| Reference interval | Subjects. Repeat draws from one subject count once, as their mean |
| Qualitative agreement | Specimens, one initial result each |
| Near-cutoff precision | Replicate results at each concentration |
| Limit of blank | Blank results. Blank materials are counted separately |
| Stability | Materials (paired design) or specimens (independent design) at each time |
The count strip and study notes show which count was used. The example bias file has 10 results from 1 control material, all on day 1, run 1, so its mean CI is calculated for that run; the same 10 results spread over five days get no interval.
Confidence levels
Section titled “Confidence levels”Confidence level under Calculation settings on Set up is 90%, 95% or 99%. It sets the confidence for the study's estimate intervals, including Wilson score intervals for agreement percentages and exact rank-based intervals for nonparametric reference limits. Manufacturer-claim verification has its own confidence setting, and the calibration-verification precision index uses a 90% interval.
descriptive.csv holds five results (2, 4, 6, 8 and 10 mg/dL) from five specimens. As a descriptive summary:
| Confidence level | Mean | Sample SD | CI for the mean |
|---|---|---|---|
| 90% | 6.0 mg/dL | 3.16 mg/dL | 3.0–9.0 mg/dL |
| 95% | 6.0 mg/dL | 3.16 mg/dL | 2.1–9.9 mg/dL |
| 99% | 6.0 mg/dL | 3.16 mg/dL | −0.5 to 12.5 mg/dL |
Only the width changes. The 99% interval goes below zero and is reported as calculated.
When an interval is not estimated
Section titled “When an interval is not estimated”The interval reads Not estimated, and the study notes and report give the reason. In a descriptive, repeatability or bias summary:
| Situation | Reason given |
|---|---|
| Only one result | One result gives no SD, CV or mean CI |
| Several rows share a specimen ID (in a bias check: across days or runs, or without a recorded day and run) | Results from one specimen are not independent |
| All results identical | The basic mean CI is not estimated because the SD is zero |
| Study type | Interval rule |
|---|---|
| Limit of blank | At 95% confidence, at least 72 blank results for the upper confidence limit of the 95th percentile |
| Method comparison | At least 2 independent specimen pairs with nonzero spread for a mean-difference CI; at least 3 for slope and intercept CIs |
| Interference, stability | A zero-width effect interval is kept when identical rounded measurements support it |
A limit that depends on a missing interval is Undecided.
Which denominator a percentage uses
Section titled “Which denominator a percentage uses”| Percentage | Denominator | Not calculated when |
|---|---|---|
| CV | The mean: CV% = 100 × SD / mean |
Interval scale; fewer than 2 results; mean zero or negative; any negative result |
| Percent bias against an assigned value | The assigned value: 100 × (mean − assigned) / assigned |
Interval scale; assigned value zero or negative |
| Recovery | The assigned value: 100 × mean / assigned |
As for percent bias |
| Relative difference, method comparison | |comparative result| | The comparative result is exactly zero |
| Mean relative bias criterion, method comparison | |comparative result| | The comparative result is exactly zero |
| Percentage specimen limit, method and instrument comparison | Each specimen's comparative (reference-analyzer) result: allowance = P × result / 100 | The result is zero or negative, or the scale is interval. That specimen is not evaluated |
| Percentage limit, reagent lot comparison | Each specimen's previous-lot result: allowance = P × previous / 100 | As for the specimen limit |
| Descriptive percentage difference, reagent lot comparison | The mean of the two lot results: 100 × (new − previous) / ((new + previous) / 2) |
Interval scale; a negative lot result; pair mean zero |
| Bias at a medical decision level, percentage limit | The decision level | Interval scale; decision level 0 |
| Overall percent agreement | Reportable pairs | Always calculated. Nonreportable pairs are listed separately |
| All-pairs agreement | All paired specimens, nonreportable counted as non-agreement | Always calculated |
In the example qualitative agreement study, 40 specimens were paired and 37 were reportable on both methods. Overall agreement is 34/37 = 91.9% and all-pairs agreement 34/40 = 85.0%.