Safe investigation design and data critique

Safe investigation design starts from a testable hypothesis and a plan in which every measured quantity is tied to the question. Before measuring, identify hazards (electricity, hot surfaces, chemicals, lasers, heavy loads) and replace or isolate them; if a hazard cannot be removed, use a simulation. The design must explicitly state the independent variable $x$ that you change, the dependent variable $y$ that you measure, and the controlled variables that stay constant. For reliability, plan repetitions, randomization, and blind procedures where possible; record the instrument uncertainty $\Delta x$ and the units. Critiquing data requires checking calibration, units, outliers, and systematic errors, not only the mean $\bar{x}$. A conclusion is justified only if the data are reproducible and alternative explanations have been tested.

A student plans to heat 100 mL of water in a glass beaker on a hot plate and record the temperature every minute. List three hazards and a control for each. Identify the independent variable, dependent variable, and two controlled variables.

Six repeated current measurements at a fixed voltage are 0.50, 0.51, 0.49, 0.52, 0.53, and 1.50 A. Calculate the mean and the sample standard deviation $s$. Flag any outlier using $|x_i-\bar{x}|>2s$. Then state one safety action and one data-critique action before repeating.

You want to test whether the rate of a chemical reaction increases with acid concentration. The reaction produces hydrogen gas and uses a strong acid. Design a safe investigation or simulation. State variables, controls, repetitions, units, and one data-critique rule.

Use a free circuit simulation (for example, PhET Ohm’s Law). Choose a fixed resistor and vary the voltage from 0 to 5 V in steps of 0.5 V, recording the current. Then deliberately insert one incorrect value into the table. Before starting, list the hazards of a real circuit (short circuit, burn, overheating) and explain why the simulation is used. Take at least six repeated current measurements at one voltage: for $n=3$ the maximum possible deviation from the mean is $2s/\sqrt{3}\approx 1.155s$, so the criterion $|x_i-\bar{x}|>2s$ can never flag an outlier, whereas for $n\ge 6$ the criterion works. Calculate the mean current and flag any outlier using $|x_i-\bar{x}|>2s$. Write 5 sentences of critique: units, calibration, repetitions, outlier, possible systematic error.

Show how hypothesis, hazard check, variables, procedure, data, and the decision to conclude or redesign are connected.

Flowchart: “Hypothesis” → “Hazard check” → “Variables ($x$, $y$, controls)” → “Safe procedure or simulation” → “Data table” → “Check units and calibration” → “Outlier and uncertainty” → “Conclude or redesign”.

A student tests whether light warm-up improves reaction. A partner holds a $30$ cm ruler so its lower edge is level with the thumb and releases it without warning; the student catches it with the same hand. Before and after $5$ minutes of warm-up they record $10$ trials each. Safety: warm-up without running through the lab, the ruler falls away from the face, and there are no bags around to trip over. For a fall distance $d=0{,}18$ m the reaction time is $t=\sqrt{2d/g}=\sqrt{2\cdot0{,}18/9{,}8}\approx0{,}19$ s; for $d=0{,}25$ m it becomes $\approx0{,}23$ s.

This tests safe design: controlled drop height, one hand, the same partner, no obstacles. Data critique is needed to notice an outlier: one trial with $d=0{,}32$ m gives $t\approx0{,}26$ s and is probably caused by distraction; it must not be silently averaged in. Repeats and spread show random error.

A cyclist of mass $60$ kg rides along a marked straight at $15$ km/h $=4{,}17$ m/s and brakes with only the front brake to a full stop. On dry asphalt three braking distances are $3{,}1$, $3{,}0$, $3{,}2$ m; on wet asphalt they are $4{,}8$, $6{,}2$, $5{,}1$ m. Safety: helmet, closed area without cars, a $10$ m wet patch, speed no higher than $15$ km/h, and walking the bicycle back after each braking. Means: dry $3{,}1$ m, wet $5{,}4$ m.

The scenario uses risk assessment and control of variables: the same tyres, pressure, mass and speed. Data critique requires comparing repeats and explaining the outlier $6{,}2$ m — perhaps the puddle is deeper; without repeats the conclusion 'wet is always $1{,}7$ times longer' would be unjustified. The spread gives the uncertainty of the mean.

In a kitchen they test whether salt changes the boiling point. In $250$ ml of water at $101$ kPa they boil pure water, then add $10$ g of table salt and bring it to boiling again. The thermometer is fixed so that it does not touch the bottom. Pure water: $100{,}0$ °C; with salt: $100{,}5$ °C, $101{,}2$ °C, $100{,}6$ °C. Safety: goggles, a glove for hot cookware, the stove cord away from water, and no tasting of the solution.

This is safe design: fixed volume, pressure, thermometer position, and burn protection. Data critique reveals a systematic error: if the thermometer touches the bottom, it reads $103$ °C, and that is not the boiling point. The reading $101{,}2$ °C is checked by repeating the measurement; the mean of the two agreeing values is $\approx100{,}55$ °C.