PSLE Science Reality Lab Vol No.029 | “70 of 100 Results Were Reported” — What Happened to the Missing 30?

PSLE-SCI-REALITY-0029

Wait, What? A blank space can change a scientific conclusion.

A report begins with 100 samples. Later, its results table contains only 70 rows. Fifty-six of those 70 reported samples show the expected result. The headline says:

“80% of samples succeeded.”

The arithmetic is correct: 56 ÷ 70 = 0.8, or 80%.

But the scientific question is not finished. The investigation started with 100 samples. Where are the other 30?

Were their labels damaged? Did an instrument fail? Were they excluded because a stated rule made them invalid? Were the results lost? Did the samples fail to produce a readable measurement? Or were inconvenient results quietly left out?

Those possibilities do not mean the same thing. Missing evidence is not automatically evidence of misconduct, and it is not automatically harmless. The reason the results are missing can determine whether the reported pattern is still a fair picture of the original investigation.

This is an advanced Reality Lab problem because it asks you to reason about information that is not present without inventing what the missing values were.

Quick Answer

When some expected scientific results are missing, first compare the number that should exist with the number actually reported. Then ask why the results are missing, whether the missingness could be connected to the outcome, which denominator the headline uses, and how much the conclusion could change under plausible possibilities for the missing results. Never fill unknown values with guesses just to complete the table.

Reality Lab rule: Missing is a state of the evidence record. Unknown must remain unknown until evidence resolves it.

The Owned Learner Job

This Reality Lab owns one job: how a Primary 5/6 learner should evaluate a real-world scientific claim when some expected observations, samples or responses are missing. It applies existing PSLE Science skills such as evidence checking, denominator tracking, evaluating methods and knowing when information is insufficient. It does not replace those canonical guides, and it does not become a standalone statistics page.

The Original Reality Lab Case: The Absorbent-Pad Trial

A fictional testing group compares 100 pieces cut from a new absorbent material. Each piece is supposed to receive the same 20 mL of water. A piece counts as a “success” if it absorbs all the water within 60 seconds without dripping.

The public summary says:

100 samples were prepared.
70 results were reported.
56 of the reported samples succeeded.
14 of the reported samples failed.
30 prepared samples do not appear in the result table.

The summary headline reads: “80% success rate.”

What can we conclude?

We can conclude that 56 out of the 70 reported results were successes. We cannot immediately conclude that 80 out of every 100 prepared samples would succeed. The other 30 samples are not successes and not failures in the evidence record we have. They are missing.

First Move: Reconstruct the Evidence Flow

Before interpreting a percentage, reconstruct what happened to the evidence.

100 prepared → 70 reported → 56 reported successes + 14 reported failures → 30 missing outcomes

This simple chain prevents a common mistake: treating the reported group as though it were automatically identical to the original group.

The Denominator Changes the Sentence

Consider three different statements:

56 of 70 reported results succeeded. This is known from the reported table.
56 of the original 100 samples are known successes. This is also true if all 100 were prepared as described.
80 of the original 100 samples succeeded. This is not established. It silently treats missing outcomes as though they followed the same pattern as the reported ones.

The number 80% can be mathematically correct for one denominator and scientifically misleading when the reader assumes another.

Why Are Results Missing? The Reason Matters

There are many ways a result can disappear from a final table. The important question is whether the reason could be related to the result itself.

Case 1: A random record was damaged

Imagine ten paper data sheets were soaked by a leaking bottle after the experiment. If the accident had nothing to do with whether those samples succeeded or failed, the missing records may not systematically favour one outcome. They still reduce how much information we have, but the reason for missingness is not obviously connected to success.

Case 2: The instrument failed only at extreme readings

Suppose a sensor stops recording whenever the measurement becomes unusually high. Missing results would now be linked to the outcome. The reported results could systematically under-represent extreme values.

Case 3: Invalid samples were removed using a rule decided in advance

Suppose the method states before testing that any sample with a visible tear must be excluded because the tear was caused during cutting, before the absorption trial began. If the same rule is applied consistently to every sample and the exclusions are reported transparently, this is different from silently removing disappointing outcomes after seeing the results.

Case 4: Failed trials were omitted because they looked bad

If results are hidden because they weaken the desired conclusion, the reported evidence is selected by outcome. Now the public summary can become much more favourable than the complete evidence.

The same final count—30 missing results—can therefore have very different scientific meanings.

Do Not Invent the Missing Values

A learner may be tempted to continue the observed pattern. If 80% of the reported samples succeeded, perhaps 80% of the missing samples also succeeded. That would predict 24 additional successes among the missing 30.

But prediction is not observation. Without additional evidence, those 24 successes do not exist in the data record. They are one possible model of what might have happened.

The disciplined response is:

“Among the 70 reported results, 56 succeeded. The outcomes of the remaining 30 samples are unknown from the information provided.”

That sentence is less dramatic than “80% success”, but it keeps observation and inference separate.

A Powerful Advanced Move: Bound the Possible Result

You may not know the missing outcomes, but sometimes you can calculate the range of what is still possible.

In our case, 56 of 100 original samples are known successes. Thirty outcomes are missing.

Lowest possible success count

If all 30 missing samples failed, there would be 56 successes out of 100: 56%.

Highest possible success count

If all 30 missing samples succeeded, there would be 86 successes out of 100: 86%.

Without knowing more, the complete-sample success rate could therefore lie anywhere from 56% to 86%.

This does not tell us the true value. It tells us what the available evidence has not ruled out. That is a sophisticated scientific habit: use known constraints to bound uncertainty without pretending to know the missing facts.

When Missing Results Matter Less—and When They Matter More

Missingness is more worrying when:

a large fraction of expected results is absent;
the reason for missingness is unclear;
missingness could depend on the outcome;
different comparison groups lose different fractions of their results;
the headline uses only the remaining data without mentioning the missing cases;
the conclusion changes substantially under reasonable possibilities for the missing outcomes.

Missingness may be easier to interpret when:

the missing count is small;
the reason is known and unrelated to the outcome;
the same transparent exclusion rule was set before results were known;
all expected counts are reported;
the conclusion remains similar even under unfavourable assumptions about the missing cases.

“Easier to interpret” still does not mean “safe to ignore”. The evidence record should preserve what was missing and why.

Missing Results Are Different From Failed Results

This distinction is essential.

State	What we know
Success	The stated success condition was observed.
Failure	The stated success condition was not met.
Missing	The outcome is unavailable or not validly recorded from the information supplied.

Turning every missing value into a failure may unfairly lower the result. Turning every missing value into a success may unfairly raise it. The correct state is often simply: unknown.

Missing Results Are Also Different From Anomalous Results

An anomalous result is still a recorded result. It may look unusual, but it exists and deserves investigation. A missing result is absent from the usable evidence record. You should not erase an anomaly by relabelling it “missing” simply because it is inconvenient.

That connects to eduKate’s guide on handling an anomalous PSLE Science result without deleting it because it looks wrong.

The Missing-Evidence Audit

How many observations or samples were expected?
How many usable results were actually reported?
How many are missing?
Why are they missing?
Was that reason decided before or after outcomes were known?
Could the reason be connected to success, failure or measurement size?
Which denominator does the reported percentage use?
Would the conclusion change if the missing outcomes were mostly unfavourable?
Does the public claim tell readers that evidence is missing?

This audit turns an invisible gap into an explicit part of the scientific reasoning.

Worked Case 1: A Broken Timer

A class plans 20 trials measuring how long a toy car takes to travel down a ramp. During three randomly chosen trials, the timer fails to record any value. The timer failures occur before the student sees the travel time.

There are 17 usable times and three missing results. The missing trials reduce the amount of evidence. Because the timer failure does not obviously depend on whether the car was fast or slow, the missingness does not automatically favour one travel-time outcome. The class should still report that only 17 of 20 planned trials produced usable measurements.

Worked Case 2: A Sensor That Stops at High Values

A temperature sensor can display only up to 50°C. A heating investigation includes several conditions that may exceed this limit. The report includes exact values for low-temperature trials but simply leaves high-temperature trials blank.

The missing values are connected to the measurement size: hotter cases are more likely to be missing. Calculating an average from only the recorded values could make the whole experiment look cooler than it really was. This is not ordinary random loss; the instrument limit selects which results remain visible.

Worked Case 3: The Online Poll

A science club sends a questionnaire to 200 students asking whether a new classroom fan makes the room feel more comfortable. Eighty students reply; 64 say yes. A post says, “80% of students prefer the new fan.”

The known result is that 64 of the 80 respondents answered yes. We do not know how the 120 non-respondents would have answered. Perhaps students with strong opinions were more likely to reply. The missing responses limit how confidently the result can be extended to all 200 students.

Worked Case 4: The Exclusion Rule Was Written First

A seed-germination investigation says before testing begins: “Any seed found cracked before the experiment starts will not be included because it was physically damaged before treatment.” Five cracked seeds are identified and recorded before conditions are assigned.

This is different from waiting until after germination and removing seeds that did not produce the desired result. A pre-stated, scientifically relevant rule can make an exclusion traceable and auditable. The report should still say how many seeds were excluded and why.

Selective Reporting: When the Evidence Window Is Chosen After Seeing the Result

Selective reporting happens when some outcomes, analyses, times or results are emphasised while others are omitted in a way that can distort the apparent evidence. Researchers and evidence-review organisations treat this as an important source of bias because the visible results may differ systematically from the full set that could have been reported.

For a Primary 5/6 learner, the transferable idea is simple:

If the result helped decide whether it would be shown, then the shown results may no longer be a fair picture of all the results.

That is why Reality Lab Vol No.009 asks whether “every trial worked” only because failed trials disappeared from view.

PSLE Science Transfer: The Blank Table Cell

Suppose a PSLE-style table gives values at 10°C, 20°C, 30°C and 50°C, but the 40°C cell is blank. Can you fill it by drawing a smooth line between the other points?

Only if the question explicitly gives enough information to justify that inference. A missing measurement is not automatically the same as an unlabelled answer waiting to be calculated. eduKate’s guide on when a missing PSLE Science table value can be inferred—and when it must stay unknown owns that micro-skill.

A Second Advanced Move: Test the Conclusion Under Different Missing-Result Scenarios

You can sometimes pressure-test a claim without pretending to know the missing values.

Return to the absorbent-pad trial:

Known successes: 56
Known failures: 14
Missing outcomes: 30

Ask:

If every missing result were a failure, would the headline still sound reasonable?
If every missing result were a success, how high could the complete-sample success rate be?
If the main conclusion changes completely between these two limits, how much confidence should we place in the headline before the missing outcomes are explained?

This is not guessing the missing data. It is testing how sensitive the conclusion is to what we do not know.

Tempting Reasoning That Fails

“If it is missing, it must have failed.” Not necessarily. Missing and failed are different evidence states.
“The reported 70 are enough, so the missing 30 do not matter.” That depends on why they are missing and whether the conclusion is sensitive to them.
“80% of the reported cases succeeded, so 80% of the original cases succeeded.” The denominator has silently changed.
“We can estimate every missing value from the trend.” Only if a justified model and the question permit that inference.
“Any exclusion is suspicious.” Transparent, pre-specified scientific exclusion rules can be legitimate.
“If some data are missing, nothing can be concluded.” Too strong. You may still have useful evidence, but its scope and uncertainty must be stated honestly.

Practice 1: The 90% Claim

An investigation prepares 50 samples. Results are reported for 40. Thirty-six of those 40 succeed. A poster says “90% success”. What is the strongest precise statement you can make from the information given?

Answer: Thirty-six of the 40 reported results succeeded, which is 90% of the reported results. The outcomes of 10 prepared samples are missing, so the complete-sample success percentage is not known from the information given.

Practice 2: Bound the Unknown

Using the same 50-sample investigation, what is the lowest possible complete-sample success percentage if all 10 missing outcomes were failures? What is the highest if all 10 were successes?

Answer: Lowest: 36/50 = 72%. Highest: 46/50 = 92%. The actual value cannot be determined without the missing outcomes, but these limits show the range still compatible with what is known.

Practice 3: The Broken Sensor

A sensor fails only whenever the measured value is above its maximum range. Would averaging the remaining readable measurements fairly represent all trials?

Answer: Probably not. High values are systematically more likely to be missing, so the remaining measurements are not a neutral subset of all trials.

Practice 4: The Pre-Stated Rule

A test states in advance that samples contaminated before the investigation starts will be excluded. Three are later found to meet that condition. Is excluding them automatically selective reporting?

Answer: No. A transparent rule defined before outcomes are known can be scientifically justified. The report should still disclose the exclusions and their reason.

Delayed Independent Return

The next time a chart, poll, product test or science story gives a percentage, ask for two counts before trusting the percentage:

How many cases were supposed to be in the evidence set?
How many cases actually appear in the reported result?

If those counts differ, do not panic and do not fill the gap. Ask what happened between the two numbers.

Where to Route Next

Teaching Guide for Parents and Tutors

A simple way to teach this is to draw 10 boxes representing 10 planned trials. Mark six as success, two as failure and leave two blank. Ask the learner to describe what is known without converting the blank boxes into an outcome.

Then ask how the conclusion changes if the two blanks are both successes, both failures, or one of each. The goal is not to teach formal missing-data statistics. It is to teach evidence discipline: preserve the unknown, track denominators, and test whether a conclusion is robust to missing information.

The earliest weak link is often linguistic rather than mathematical. Listen for phrases such as “the other 30 probably did the same thing” or “missing means failed”. Stop there. Ask, “Where did that outcome enter the evidence?” If the learner cannot point to an observation, they have crossed from evidence into assumption.

Authoritative Sources

The Quiet Return

Science is not only about the numbers you can see. It is also about keeping track of which observations were expected, which were actually obtained, which were excluded for declared reasons and which remain unknown.

The next time a neat percentage appears, look behind it. Ask how many cases entered the investigation, how many reached the final result, and what happened to the rest. Sometimes the most important scientific information is the space where a number should have been.

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