AC9S9I03 · YEAR 9 · INQUIRY

Precision, Sample Size and Replication

ACARA v9 CONTENT DESCRIPTION select and use equipment to generate and record data with precision to obtain useful sample sizes and replicable data, using digital tools as appropriate
Builds on generating data with precision. Once you can read an instrument carefully, the next step is making the result trustworthy: taking enough repeats to form a useful sample size, reporting data others can reproduce, and letting digital tools log many readings without a slow or biased hand.

Precision is where it starts, but one reading is not enough

Suppose you measure how long a small electric motor runs before a fixed battery is drained. A data logger reading the voltage to a hundredth of a volt every second gives precise, finely numbered values, far beyond what a glance at a clock could offer. Yet precision alone does not settle the answer. A single run might give a typical result or a stray one, and from one number you cannot tell which. The cure is to repeat: a useful sample size lets the real value emerge from the natural scatter between runs.

Drain time across more and more repeats
The same motor and battery were tested many times. The bars show the running average of the drain time after 1 run, then 3, 5, 8 and 12 runs. Watch how it settles.
After a single run the average is whatever that one run happened to give. As more repeats are added, the running average stops jumping about and settles near 38 seconds. A larger sample size pulls the mean toward the true value and lets one odd run sway it far less.

Sample size, repeats and the value you report

Each repeat carries a little random scatter from tiny differences you cannot control. Average a handful of runs and that scatter partly cancels; average many and it cancels further, so the mean settles close to the true value. This is why a larger sample size gives a steadier, more reliable result. A data logger makes the repeats cheap: it records every reading at a fixed interval, evenly spaced and unbiased, so you can gather a useful sample without a slow hand losing track. Recording the real values from every run, rather than rounding them all to look alike, lets you average them honestly.

Twelve logged runs of the same test
Each bar is one logged run of the motor drain time. The runs cluster, but no two are identical. Switch between the table and a graph.
The twelve runs spread from 36 to 41 seconds with no single fixed answer. That scatter is normal. Because every run was logged honestly, you can average the whole sample to about 38 seconds rather than trusting any one run on its own.

Spot the run that does not belong

Even with careful logging, a single careless moment can plant an odd value: a loose battery clip, a probe that slipped, or a mistyped entry. A run that sits well outside the cluster of the others is the cue to check the apparatus and the record on the spot, while the test is still set up, rather than after everything is packed away. The odd value is noted and investigated, never quietly deleted, so that the sample you report stays honest.

A series of logged drain times: find the stray run
Twelve runs of the same test were logged in order. One value sits far outside the cluster, most likely a slipped connection or a mistyped entry.
Click the point that does not fit the pattern of the others.

What makes data replicable?

Data is replicable when another group, following your method with their own equipment, can reproduce a result that agrees with yours within reason. That independent agreement is what builds trust in a finding. Replication depends on choices you make while gathering the data: a faithful record of the apparatus and settings, an honest log of every run, and a sample large enough to be meaningful. Sort each practice below by whether it genuinely makes the investigation replicable, or whether it would quietly make it impossible to reproduce.

Judge the case for replicable data
The claim: this investigation produces replicable data that another group could reproduce. Decide which practices support it.
Claim: This investigation produces data that an independent group could replicate.
The equipment, the logger interval and the battery type are all written down with the results.
Every run is logged and kept, including the ones that came out a little high or low.
Only the three runs closest to the expected answer are reported, and the rest are dropped.
Enough repeats are taken to form a useful sample, and the full set is averaged.
The method is left vague so each group can quietly do it their own way.
Decide whether each statement is evidence for the claim, or not.

Why this matters

A conclusion is only as sound as the data behind it, and sound data is more than a precise instrument. It comes from enough repeats to form a useful sample, an honest record of every run, and a method clear enough that others can reproduce the result. Digital tools make the repeats easy to gather and log without bias, but the judgement about sample size, honesty and replicability stays with the investigator.

Quick self-check
1. You are timing how long a small motor takes to drain a battery and want a precise record across many runs. Which digital tool gives the most precise readings?
2. You measure the drain time once and get 41 seconds. Why is one reading a weak basis for a conclusion?
3. You run the same test ten times instead of three. What does the larger sample size mainly buy you?
4. Another class repeats your method with their own gear and gets results close to yours. This shows your data is...
5. To make your investigation easy for others to replicate, you should record...