Revision 7T · Full Tutorial Edition · Updated 1 September 2026
PWR-125 · SELF GUIDED full tutorial
Detect predeclared outliers in synthetic sensor data without calling them threats
An anomaly is a value that differs from a declared reference; it is not automatically an error, fraud, disease or danger. This lesson uses synthetic temperature-sensor rows with known injected anomalies. The learner declares a range before viewing cases, flags values, checks a second measurement, reveals ground truth and reports hits, misses and false alarms at two prevalence levels.
What you will produceThe learner audits 60 synthetic rows and reports a full table of hits, misses, false alarms and correct rejections plus confirmation decisions for a predeclared anomaly rule.
Full step-by-step individual tutorial · TLU-PWR-125
The learner audits 60 synthetic rows and reports a full table of hits, misses, false alarms and correct rejections plus confirmation decisions for a predeclared anomaly rule.
Threshold and confirmation card: reference 3.0–5.0, noise allowance ±0.2, so flag below 2.8 or above 5.2. Repeat cards for flagged rows: A03→4.4, A05→2.6, A17→5.4, B07→4.2, B22→5.4.
Hidden injected-anomaly key and confusion sheet: true anomalies are A05, A17 and B22; A03 and B07 are noise, so Block A prevalence is 2/30 and Block B prevalence 1/30. Reveal this key only after every classification and confirmation.
Before you start
Write that all data and devices are fictional.
Declare normal reference, anomaly threshold and confirmatory rule before opening the rows.
Set equal review time for both prevalence blocks.
Have a helper copy the row blocks and repeat cards while keeping the injected-anomaly key hidden. If you memorised the key while preparing it, use this packet as demonstration and obtain a fresh permuted set for scored practice.
3 · The method
Follow these steps in order
Define normal and anomaly
Write the reference interval, allowed measurement noise and exact flag rule.
Why: An anomaly exists only relative to a declared model.
Check: Another learner can reproduce the same flag from the rule.
Declare prevalence and costs
Read the supplied expected prevalence for block one and rank the fictional cost of miss versus false alarm.
Why: Base rate and costs affect a useful review design.
Check: The record states expected targets and cost priority.
Inspect order and local context
Before classifying, note whether each value stands alone, follows a gradual drift or occurs beside a missing reading. Keep the numerical threshold unchanged.
Why: Sequence context can suggest noise or system change without turning an anomaly into a cause.
Check: Every flag records its preceding value and data-quality status as context, not as proof.
Classify the anomaly shape
Label a confirmed flag as an isolated point, a sustained level shift, a trend or an unresolved data-quality break using the supplied synthetic sequence rules.
Why: Different shapes call for different confirmation questions even when the numerical threshold is identical.
Check: The shape label follows the fixture rule and remains separate from any claim about cause or danger.
Inspect blinded rows
Apply the rule to each row once and mark flag or clear without seeing the key.
Why: A blinded pass preserves detection evidence.
Check: All rows receive one committed classification.
Confirm before interpreting
For each flag, open the supplied repeat-measurement card and label confirmed, not confirmed or unresolved.
Why: Independent measurement can distinguish anomaly from noise.
Check: No flag is called a cause or threat.
Reveal and score
Compare with injected ground truth and count hits, misses, false alarms and correct rejections.
Why: All four outcomes are needed when targets are rare.
Check: The matrix totals every row.
Change prevalence, not the rule
Run block two with rarer anomalies using the same threshold and time, then compare miss and false-alarm rates.
Why: Rare targets can be missed even when the detector has extensive exposure.
Check: The report shows performance by prevalence without threshold drift.
4 · Worked example
See the whole method used once
Scenario
A fictional cold-room sensor normally reads 3.0–5.0 units with ±0.2 measurement noise; the predeclared flag rule is below 2.8 or above 5.2.
Walkthrough
Inez writes the interval and rule before opening 30 rows.
She flags 5.6 and 2.7 but clears 5.1 because it stays inside the noise boundary.
A repeat card shows 5.6 became 4.4, so she labels it not confirmed rather than dangerous.
The key shows 2.7 and the later 5.5 as Block A anomalies while 5.6 was noise; she records two hits, one false alarm and 27 correct rejections.
On rarer Block B she keeps the same rule, confirms B22 and reports one hit plus the B07 false alarm with the 1/30 prevalence rather than moving the threshold afterward.
Result
Inez detects and confirms synthetic outliers transparently. She has not diagnosed a device fault or demonstrated professional monitoring.
5 · Right and wrong
Compare correct or safer execution with the common wrong version
Right and wrong comparison
Moment
Right / safer
Wrong / riskier
Why it matters
Rule timing
Declare the range before viewing rows.
Circle unusual-looking values and invent a threshold later.
Post-hoc rules inflate discoveries.
Meaning
Call a value anomalous pending confirmation.
Call it fraud, danger or equipment failure.
An unusual observation does not identify a cause.
Scoring
Report misses and false alarms with prevalence.
Report 98% accuracy on mostly normal rows.
Overall accuracy can hide failure on rare targets.
Confirmation
Use an independent repeat measurement.
Re-read the same number until convinced.
Repeated interpretation is not independent evidence.
6 · Common mistakes
Spot the error and apply the correction
Common mistakes and corrections
Mistake
Fix
Noise allowance is ignored.
Build measurement uncertainty into the flag rule.
Unresolved flags are forced into true or false.
Keep a separate unresolved category until the key or repeat exists.
Block prevalence is omitted.
Record targets/rows for each block.
Threshold changes after a miss.
Preserve the original score and preregister any new rule for a fresh dataset.
7 · Practice
Turn the steps into a usable skill
First session
Define reference and rule.
Review one 30-row block.
Open confirmation cards.
Build the confusion matrix.
Review a second rarer block with the same rule.
Repeat plan
Use one new two-block synthetic dataset weekly for four weeks. Alternate normal-range width and prevalence, but declare both before inspection. On week four, preregister one revised threshold and test only on fresh rows.
Progress when
Rules reproduce exactly across rows.
Miss and false-alarm rates are both reported.
Flags trigger confirmation rather than causal claims.
Do not progress when
The dataset becomes real or consequential.
Thresholds are repeatedly moved to improve past scores.
Low prevalence creates fatigue that breaks the time or attention limit.
8 · Check the result
Measure what changed
Sensitivity and false-alarm rate for a predeclared synthetic anomaly rule.
How: From the keyed rows, calculate hits/(hits+misses), false alarms/(false alarms+correct rejections), prevalence, review time and confirmation outcomes.
Good result: All 60 rows and five repeat cards are accounted for, the confusion matrices reproduce the hidden key and the threshold never moves after reveal. Sensitivity and false-alarm rate are descriptive fixture results, not validated real-monitoring pass thresholds.
This does not prove: It does not validate a real detector, identify causes, support accusation or show performance in another base rate.
Self-check
What reference and noise model define anomaly?
Was the rule fixed before seeing data?
How many misses and false alarms occurred?
What independent confirmation follows a flag?
9 · Stop, adapt or get help
Keep the safety boundary practical
Stop and get help
Stop if real medical, fraud, threat or safety data enters the exercise.
Stop when fatigue or compulsive scanning breaks the review limit.
Route real anomaly systems to domain experts with calibrated thresholds, confirmation and appeal.
Accessibility and adaptations
Provide data as an accessible table with consistent row labels.
Use calculator or spreadsheet formulas with the rule visible.
Offer audio values or tactile plots while preserving identical rows and timing rules.
10 · Evidence and limits
Why these instructions are here
primary research
The ultra-rare-item effect persisted across millions of game trials, showing that very low prevalence can produce high miss rates.
Correctable-search research found interface conditions can reduce rare-target misses in bounded tasks, so the correction path is part of the configured system.
Progress is saved only in this browser on this device.
Step-by-step learner mode
Each activity includes its success check, a nearby accessible alternative and an “I’m stuck” correction path. Alternatives preserve the target where possible; when they change the task, Titan labels them as related rather than equivalent.
01
Define normal and anomaly
Write the reference interval, allowed measurement noise and exact flag rule.
Why this step exists
An anomaly exists only relative to a declared model.
Success check
Another learner can reproduce the same flag from the rule.
I’m stuck on this step
Reset: Re-read this authored instruction — “Write the reference interval, allowed measurement noise and exact flag rule.” — and its success check, then attempt only this step.
Possible snag: Noise allowance is ignored.
Correction: Build measurement uncertainty into the flag rule.
Stop / get help: Stop if real medical, fraud, threat or safety data enters the exercise.
02
Declare prevalence and costs
Read the supplied expected prevalence for block one and rank the fictional cost of miss versus false alarm.
Why this step exists
Base rate and costs affect a useful review design.
Success check
The record states expected targets and cost priority.
I’m stuck on this step
Reset: Re-read this authored instruction — “Read the supplied expected prevalence for block one and rank the fictional cost of miss versus false alarm.” — and its success check, then attempt only this step.
Possible snag: Block prevalence is omitted.
Correction: Record targets/rows for each block.
Stop / get help: Stop if real medical, fraud, threat or safety data enters the exercise.
03
Inspect order and local context
Before classifying, note whether each value stands alone, follows a gradual drift or occurs beside a missing reading. Keep the numerical threshold unchanged.
Why this step exists
Sequence context can suggest noise or system change without turning an anomaly into a cause.
Success check
Every flag records its preceding value and data-quality status as context, not as proof.
I’m stuck on this step
Reset: Re-read this authored instruction — “Before classifying, note whether each value stands alone, follows a gradual drift or occurs beside a missing reading. Keep the numerical threshold unchanged.” — and its success check, then attempt only this step.
Possible snag: The result from “Before classifying, note whether each value stands alone, follows a gradual drift or occurs beside a missing reading. Keep the numerical threshold unchanged.” does not yet meet this declared check: Every flag records its preceding value and data-quality status as context, not as proof.
Correction: Return to the start of “Inspect order and local context”, reduce complexity or pace, and repeat only the part needed to satisfy: “Every flag records its preceding value and data-quality status as context, not as proof.”
Stop / get help: Stop if real medical, fraud, threat or safety data enters the exercise.
04
Classify the anomaly shape
Label a confirmed flag as an isolated point, a sustained level shift, a trend or an unresolved data-quality break using the supplied synthetic sequence rules.
Why this step exists
Different shapes call for different confirmation questions even when the numerical threshold is identical.
Success check
The shape label follows the fixture rule and remains separate from any claim about cause or danger.
I’m stuck on this step
Reset: Re-read this authored instruction — “Label a confirmed flag as an isolated point, a sustained level shift, a trend or an unresolved data-quality break using the supplied synthetic sequence rules.” — and its success check, then attempt only this step.
Possible snag: The result from “Label a confirmed flag as an isolated point, a sustained level shift, a trend or an unresolved data-quality break using the supplied synthetic sequence rules.” does not yet meet this declared check: The shape label follows the fixture rule and remains separate from any claim about cause or danger.
Correction: Return to the start of “Classify the anomaly shape”, reduce complexity or pace, and repeat only the part needed to satisfy: “The shape label follows the fixture rule and remains separate from any claim about cause or danger.”
Stop / get help: Stop if real medical, fraud, threat or safety data enters the exercise.
05
Inspect blinded rows
Apply the rule to each row once and mark flag or clear without seeing the key.
Why this step exists
A blinded pass preserves detection evidence.
Success check
All rows receive one committed classification.
I’m stuck on this step
Reset: Re-read this authored instruction — “Apply the rule to each row once and mark flag or clear without seeing the key.” — and its success check, then attempt only this step.
Possible snag: The result from “Apply the rule to each row once and mark flag or clear without seeing the key.” does not yet meet this declared check: All rows receive one committed classification.
Correction: Return to the start of “Inspect blinded rows”, reduce complexity or pace, and repeat only the part needed to satisfy: “All rows receive one committed classification.”
Stop / get help: Stop if real medical, fraud, threat or safety data enters the exercise.
06
Confirm before interpreting
For each flag, open the supplied repeat-measurement card and label confirmed, not confirmed or unresolved.
Why this step exists
Independent measurement can distinguish anomaly from noise.
Success check
No flag is called a cause or threat.
I’m stuck on this step
Reset: Re-read this authored instruction — “For each flag, open the supplied repeat-measurement card and label confirmed, not confirmed or unresolved.” — and its success check, then attempt only this step.
Possible snag: Unresolved flags are forced into true or false.
Correction: Keep a separate unresolved category until the key or repeat exists.
Stop / get help: Stop if real medical, fraud, threat or safety data enters the exercise.
07
Reveal and score
Compare with injected ground truth and count hits, misses, false alarms and correct rejections.
Why this step exists
All four outcomes are needed when targets are rare.
Success check
The matrix totals every row.
I’m stuck on this step
Reset: Re-read this authored instruction — “Compare with injected ground truth and count hits, misses, false alarms and correct rejections.” — and its success check, then attempt only this step.
Possible snag: The result from “Compare with injected ground truth and count hits, misses, false alarms and correct rejections.” does not yet meet this declared check: The matrix totals every row.
Correction: Return to the start of “Reveal and score”, reduce complexity or pace, and repeat only the part needed to satisfy: “The matrix totals every row.”
Stop / get help: Stop if real medical, fraud, threat or safety data enters the exercise.
08
Change prevalence, not the rule
Run block two with rarer anomalies using the same threshold and time, then compare miss and false-alarm rates.
Why this step exists
Rare targets can be missed even when the detector has extensive exposure.
Success check
The report shows performance by prevalence without threshold drift.
I’m stuck on this step
Reset: Re-read this authored instruction — “Run block two with rarer anomalies using the same threshold and time, then compare miss and false-alarm rates.” — and its success check, then attempt only this step.
Possible snag: Threshold changes after a miss.
Correction: Preserve the original score and preregister any new rule for a fresh dataset.
Stop / get help: Stop if real medical, fraud, threat or safety data enters the exercise.
Correct versus incorrect execution
These accessible process diagrams are built from the tutorial’s own right/wrong teaching. They are not anatomical illustrations and do not add technique beyond the canonical tutorial.
Rule timing — Post-hoc rules inflate discoveries.
Correct / safer
Declare the range before viewing rows.
Wrong / riskier
Circle unusual-looking values and invent a threshold later.
Meaning — An unusual observation does not identify a cause.
Correct / safer
Call a value anomalous pending confirmation.
Wrong / riskier
Call it fraud, danger or equipment failure.
Scoring — Overall accuracy can hide failure on rare targets.
Correct / safer
Report misses and false alarms with prevalence.
Wrong / riskier
Report 98% accuracy on mostly normal rows.
Confirmation — Repeated interpretation is not independent evidence.
Correct / safer
Use an independent repeat measurement.
Wrong / riskier
Re-read the same number until convinced.
Method-structure checklist
10 of 10 structural checks present
✓ Ordered, Power-specific instructions — present
✓ Every activity has a success check — present
✓ Materials or supplied records are declared — present
✓ Measurement or assessment rule is present — present
✓ Tutorial-specific troubleshooting is present — present
✓ Stopping or escalation boundary is present — present
✓ Every activity has an adjacent alternative — present
✓ Correct-versus-incorrect comparison is present — present
✓ Evidence context is bound to the Power record — present
✓ Planning metadata is present — present
The method-readiness band and presence checklist assess tutorial presentation and are separate from evidence quality for the underlying Power. They are automated editorial aids, not human approval.
Manual editorial sign-off: Pending. This tutorial must not display a human-approved state until an identified editor signs the exact content hash.