Scientific Studies cheat sheet

Independent variable: the factor deliberately changed by the experimenter; dependent variable: the factor measured as the outcome; controlled variables are held constant to prevent confounding.

Control group receives no treatment or a placebo; it establishes the baseline against which the experimental group's change is compared.

Random assignment of subjects to groups reduces selection bias and distributes unknown confounding variables roughly evenly across groups.

A hypothesis must be testable and falsifiable: it predicts a specific, observable outcome that could prove it wrong.

Replication (repeated trials) and repetition by independent researchers both reduce the influence of random error and increase confidence in a result.

Blinding: single-blind hides treatment status from subjects; double-blind hides it from both subjects and experimenters, reducing expectancy bias.

Correlation does not establish causation; a causal claim requires controlled manipulation or a strong quasi-experimental design ruling out alternatives.

Sample size and statistical power: larger samples shrink random error, so small effects require larger samples to be detected reliably.

A scientific model or theory is a well-supported explanatory framework, not a guess; it must be revised when reliable evidence conflicts with it.

Mean = sum of values divided by n; median = middle value of ordered data; mode = most frequent value; median resists outliers, mean does not.

Standard deviation quantifies spread around the mean; about 68% of normal data lie within 1 SD and about 95% within 2 SD of the mean.

A p-value is the probability of data at least as extreme as observed if the null hypothesis is true; it is not the probability the null is true.

Statistical significance (commonly p < 0.05) differs from practical significance: a tiny effect can be significant with a very large sample.

Linear relationship: y = mx + b, where m is slope (change in y per unit x) and b is the y-intercept (value of y when x = 0).

Accuracy is closeness to the true value; precision is closeness of repeated measurements to one another; random error affects precision, systematic error affects accuracy.

Outliers should be investigated, not automatically deleted; report whether they were retained and justify any exclusion.

Units, significant figures, and error bars must be reported with data; error bars may show standard deviation, standard error, or a confidence interval, and these are not interchangeable.

Newton's second law: F = ma; net force in newtons equals mass in kilograms times acceleration in m/s².

Conservation of energy: energy is neither created nor destroyed, only transformed; total energy in a closed system stays constant.

Density = mass / volume; an object floats in a fluid when its average density is less than the fluid's density.

Speed = distance / time; velocity adds direction; acceleration is the rate of change of velocity (Δv / Δt).

Ohm's law: V = IR; power P = IV; in a series circuit current is the same everywhere, in parallel circuits voltage is the same across branches.

Wavelength × frequency = wave speed (v = fλ); for light in vacuum c ≈ 3.0 × 10⁸ m/s.

Chemical reaction signs include color change, gas production, precipitate formation, and temperature change; conservation of mass holds in a closed system.

pH scale: pH < 7 acidic, pH = 7 neutral, pH > 7 basic; each unit represents a tenfold change in hydrogen ion concentration.

Phase changes: melting, freezing, evaporation, condensation, sublimation, deposition; during a phase change temperature stays constant while energy is absorbed or released.

Cell theory: all living things are made of cells, the cell is the basic unit of life, and new cells arise from existing cells.

DNA replication is semi-conservative; transcription makes mRNA from DNA; translation at ribosomes builds protein from mRNA using codons.

Photosynthesis: 6CO₂ + 6H₂O + light → C₆H₁₂O₆ + 6O₂, occurring in chloroplasts; cellular respiration is roughly the reverse, occurring in mitochondria.

Mitosis produces two genetically identical diploid cells for growth and repair; meiosis produces four genetically varied haploid gametes.

Natural selection requires heritable variation, differential survival or reproduction, and change in trait frequency across generations.

Homeostasis is maintenance of a stable internal environment via negative feedback loops that counteract deviations from a set point.

Food webs: producers capture energy, consumers transfer it; roughly 10% of energy passes to the next trophic level, so food chains are short.

Dominant alleles mask recessive alleles in heterozygotes; a recessive trait appears only when both alleles are recessive.

Enzymes are biological catalysts that lower activation energy; each has an optimal temperature and pH at which reaction rate peaks.

Earth's layers: crust, mantle, outer core (liquid), inner core (solid); the liquid outer core generates the magnetic field via the geodynamo.

Plate tectonics: divergent boundaries create new crust (mid-ocean ridges), convergent boundaries produce subduction, mountains, or volcanoes, transform boundaries cause earthquakes.

Rock types: igneous forms from cooled magma or lava, sedimentary from compacted deposited material, metamorphic from heat and pressure altering existing rock.

The rock cycle and the water cycle are both driven by energy: internal heat drives tectonics, solar energy drives weather, evaporation, and the water cycle.

Earth's axial tilt of about 23.5° causes seasons; distance from the Sun is not the cause of seasonal temperature change.

Moon phases arise from the changing angle between Earth, Moon, and Sun; a solar eclipse requires a new moon aligned with Earth and Sun.

Kepler's third law: the square of orbital period is proportional to the cube of semi-major axis (P² ∝ a³) for bodies orbiting the same mass.

The Big Bang model is supported by cosmic microwave background radiation, redshift of distant galaxies, and abundance of light elements.

Weather occurs in the troposphere over short timescales; climate is long-term average conditions, typically assessed over 30 years.

Peer review is the process by which independent experts evaluate a study's methods and claims before publication; it reduces but does not eliminate error.

Informed consent requires that participants understand risks, benefits, and their right to withdraw; vulnerable populations need extra protections.

Conflict of interest exists when financial or personal interests could bias research design, interpretation, or reporting, and must be disclosed.

Technology assessment weighs benefits against risks, costs, and equity; risk is often expressed as probability × consequence.

Scientific consensus emerges from converging independent lines of evidence, not from a single study or authority.

Renewable energy sources (solar, wind, hydro, geothermal) are replenished naturally; fossil fuels are finite and release stored carbon when burned.

Correlation-based public claims should be checked for sample representativeness, funding source, and whether the effect size is meaningful.

Data privacy and reproducibility: sharing anonymized data supports verification, while personal identifiers must be protected under research ethics rules.

Science informs policy but does not dictate values; decisions combine evidence with economic, ethical, and social considerations.