QC Sec 4 Science & Tech cheat sheet

In a table, identify the independent variable column (the one the experimenter set) and the dependent variable column (the one measured); rows usually hold replicates of one condition.

Line graphs suit continuous independent variables; bar charts suit categorical or discrete conditions; scatter plots suit paired measurements where neither variable is controlled.

Slope of a linear graph equals the rate of change of the dependent variable per unit of the independent variable; its units are (y-units)/(x-units).

Error bars showing ±1 standard error indicate precision of the mean; non-overlapping 95% confidence intervals suggest a statistically detectable difference.

A logarithmic axis compresses large ranges; equal vertical distances represent equal ratios, so a straight line on a log axis means exponential change.

In a phase or cycle diagram (e.g., a heating curve), a flat segment marks a change of state where added energy breaks intermolecular forces rather than raising temperature.

Read values from the axis gridlines, not from the plotted point marker, and record the smallest grid division to set the reading's precision.

When a trend line is drawn, check for outliers before fitting: a single distant point can dominate a least-squares slope.

Correlation between two variables does not establish causation; a third confounding variable or reverse causation must be excluded by design or analysis.

A hypothesis is falsifiable if some conceivable observation would contradict it; unfalsifiable claims lie outside empirical testing.

Anecdotal evidence (single cases, testimonials) lacks a comparison group and cannot establish a general effect.

Sample size affects precision: the standard error of a mean is s/√n, so quadrupling n halves the standard error.

Statistical significance (a small p-value) addresses chance, not effect size or practical importance; report both.

Peer review screens for methodological and logical flaws but does not replicate results; independent replication is the stronger evidence.

A controlled experiment changes one variable at a time; an observational study compares existing groups and supports association only.

Evaluate a claim by asking what evidence would refute it, whether the sample is representative, and whether the measurement instrument was valid.

Independent variable: the factor deliberately changed; dependent variable: the factor measured as the response; controlled variables: factors held constant.

A control group receives no treatment or a placebo so the effect of the treatment can be separated from other influences.

Random assignment to treatment groups reduces systematic bias; random sampling makes results generalizable to the population.

Blinding (single or double) prevents expectation effects from influencing participants or observers.

A fair test changes only the independent variable; if two factors change together, the cause of any effect is confounded.

Replication within an experiment estimates variability; repetition of the whole experiment by others tests reliability.

A negative control should show no effect; a positive control should show a known effect, confirming the method works.

Validity means the measurement actually measures the intended quantity; reliability means repeated measurements agree.

A system has inputs, a process, outputs and often feedback; negative feedback opposes the change and stabilizes, positive feedback amplifies it.

Efficiency = useful output energy ÷ total input energy × 100%; the remainder is usually lost as heat through friction or resistance.

In a series circuit, current is the same through all components and voltages add; in a parallel circuit, voltage is the same and currents add.

Ohm's law V = IR and power P = VI allow sizing of components; a fuse or breaker protects by opening the circuit above a current limit.

Digital signals encode information as discrete levels (bits), making them more resistant to noise than continuous analog signals.

A sensor converts a physical quantity (temperature, light, pressure) into an electrical signal that a controller can process.

Mechanical advantage = load force ÷ effort force; for a lever it equals effort arm ÷ load arm, and no machine creates energy.

Troubleshooting follows a divide-and-conquer logic: test at midpoints of the system to isolate the faulty subsystem before replacing parts.

Report measurements with the correct number of significant figures; the last digit reported should be the first uncertain one.

Use SI units and prefixes consistently: k = 10³, m = 10⁻³, μ = 10⁻⁶, n = 10⁻⁹; convert before calculating.

A complete data statement includes the quantity, value, unit and uncertainty, e.g., 25.4 ± 0.2 cm.

Scientific notation expresses very large or small values as a × 10ⁿ with 1 ≤ |a| < 10, preserving significant figures.

Distinguish a model from reality: models simplify to make predictions and are judged by predictive accuracy, not by literal truth.

Cite the source of data and describe the method so another person could reproduce the result.

Graphs need labeled axes with units, a title, and a legend when more than one data series is shown.

When reporting a mean, state n and the spread (standard deviation or standard error) so readers can judge precision.

Accuracy is closeness to the true value; precision is closeness of repeated measurements to each other.

For an analog scale, the reading uncertainty is typically half the smallest division; for a digital display, it is ±1 in the last digit.

When adding or subtracting, absolute uncertainties add; when multiplying or dividing, percentage (relative) uncertainties add.

Percentage error = |measured − accepted| ÷ accepted × 100%.

Density = mass ÷ volume; speed = distance ÷ time; these ratios give units that can be checked by dimensional analysis.

Convert with unit factors: 1 km = 1000 m, 1 h = 3600 s, 1 L = 1000 cm³, so 1 m/s = 3.6 km/h.

Order-of-magnitude estimation uses rounded values and known reference quantities to check whether a calculated answer is plausible.

Random errors scatter symmetrically and are reduced by averaging; systematic errors shift all readings the same way and require calibration.

The greenhouse effect: atmospheric gases absorb outgoing infrared radiation and re-emit it, warming the surface; CO₂, CH₄ and H₂O are the main contributors.

The carbon cycle exchanges carbon among the atmosphere, oceans, biosphere and lithosphere; burning fossil fuels moves stored carbon into the atmosphere.

Energy flow through ecosystems is one-way and inefficient: roughly 10% transfers between trophic levels, so food chains are short.

Eutrophication follows nutrient (nitrogen, phosphorus) runoff, causing algal blooms, oxygen depletion and dead zones.

The water cycle: evaporation, condensation, precipitation, runoff and infiltration; groundwater recharge depends on infiltration rate.

Plate tectonics explains earthquakes, volcanoes and mountain belts at convergent, divergent and transform boundaries.

Renewable resources (solar, wind, hydro) are replenished on human timescales; fossil fuels are finite and non-renewable.

Bioaccumulation is the buildup of persistent pollutants along a food chain, reaching highest concentrations in top predators.