Analyze and Evaluate Scientific Explanations and Predictions - MCAT Chemical and Physical Foundations of Biological Systems

No linear association is present. A correlation of $r=0$ signifies no linear relationship between variables, though nonlinear associations may still exist.

Precision. Precision reflects the reproducibility of measurements, indicating low variability regardless of proximity to the true value.

The explanation is invalid unless assumptions or measurements are corrected. Conservation laws are fundamental principles; violations indicate flaws in the explanation or underlying assumptions.

$\rho=\frac{m}{V}$. Density relates mass to volume, enabling evaluation of material properties and consistency in physical models.

Doubling $x$ should double $y$. Proportionality implies a linear relationship through the origin, so scaling the input directly scales the output.

Unpredictable variation that reduces precision but not accuracy on average. Random error arises from unpredictable fluctuations, averaging to zero over many trials but increasing variability.

Causal inference (association does not imply causation). An unmeasured third variable can create spurious associations, preventing valid causal conclusions from correlational data.

Provide a baseline for comparison to isolate the tested effect. Control groups eliminate alternative explanations by providing a reference point without the experimental treatment.

Dependent variable. The dependent variable reflects changes resulting from alterations in the independent variable, serving as the key outcome metric.

Independent variable. The independent variable is controlled by the researcher to examine its causal impact on other factors.

The specific, measurable way a variable is defined and assessed. Operational definitions ensure variables are concretely specified for reliable measurement and replication in experiments.

A falsifiable, testable proposed explanation for an observation. A hypothesis must be empirically testable and potentially disprovable to qualify as scientific, allowing for experimental validation or refutation.

Consistent bias that shifts results away from the true value. Systematic error introduces consistent deviation due to flaws in methodology or instrumentation, affecting all measurements uniformly.

A causal account specifying intermediate steps linking cause to effect. Mechanism-based explanations enhance understanding by detailing the underlying processes and causal pathways in systems.

The finding is reproducible (greater reliability). Replication across independent studies strengthens confidence in the result's validity and reduces the likelihood of artifacts.

$\left|\frac{\text{exp}-\text{acc}}{\text{acc}}\right|\times 100%$. Percent error quantifies the relative discrepancy between measured and true values, assessing experimental accuracy.

As $x$ increases, $y$ tends to decrease. A negative slope in regression indicates an inverse linear relationship, where increases in $x$ correspond to decreases in $y$.

The mean difference is statistically significant at $\alpha=0.05$. Exclusion of zero in a 95% CI implies the difference is unlikely due to chance, supporting rejection of the null at $\alpha=0.05$.

A range expected to contain the true parameter at a stated confidence. Confidence intervals provide a plausible range for the population parameter, with the level indicating long-run coverage probability.

Type II error (false negative). Type II error occurs when an actual effect is missed, often due to insufficient power or sample size.

Type I error (false positive). Type I error represents the risk of falsely detecting an effect when none exists, controlled by the significance level.

Data are unlikely under $H_0$ at the $5%$ level. A $p<0.05$ threshold indicates sufficient evidence to reject the null hypothesis at the 5% significance level.

Probability of results at least as extreme, assuming $H_0$ is true. The $p$-value quantifies the evidence against the null hypothesis by calculating the likelihood of observed data under its assumption.

Accuracy. Accuracy measures the closeness of results to the actual value, distinguishing it from mere consistency.