8 Interpreting and Communicating Quantitative Results Free Online FlashCards

What does dimensional analysis check?

Dimensional analysis checks that added or compared terms have the same units and that both sides of an equation have equivalent dimensions.

How do exact values, estimates, measurements, and predictions differ?

An exact value follows a definition or identity; an estimate comes from approximation; a measurement has instrument or natural variability; a model prediction depends on behavioral assumptions.

What does uncertainty describe?

Uncertainty describes incomplete knowledge or variability associated with a result; it is not necessarily a mistake.

What does $\pm$ fail to specify by itself?

The notation $x=\hat{x}\pm u$ gives an estimate and an uncertainty measure, but $\pm$ alone does not specify the probability or confidence associated with the interval.

How is output uncertainty approximately propagated from independent inputs?

For small, independent input uncertainties, $u_Y\approx\sqrt{\sum_i\left(\frac{\partial f}{\partial X_i}u_{X_i}\right)^2}$. Correlated inputs may require covariance terms.

How do sensitivity and uncertainty analysis differ?

Sensitivity asks which inputs influence an output most. Uncertainty analysis asks how uncertain the output is, given input and model uncertainty.

What does an elasticity measure?

Elasticity $S_i=\frac{x_i}{y}\frac{\partial y}{\partial x_i}$ approximates the percentage change in $y$ caused by a 1% change in $x_i$.

What question does model verification answer?

Verification asks whether the stated mathematical problem was implemented and solved correctly, using checks such as units, code, limiting cases, conservation laws, or numerical convergence.

What is model calibration?

Calibration adjusts model parameters so outputs agree with selected observations. It can improve fit but may also fit noise, especially in an overly flexible model.

What does model validation assess?

Validation compares predictions with independent observations or trusted reference results to assess whether a model is suitable for its intended use.

How should the slope $b_1$ be interpreted in a linear model?

For $\hat{y}=b_0+b_1x$, $b_1$ is the predicted change in $y$ for a one-unit increase in $x$, with appropriate units.

Why is extrapolation generally riskier than interpolation?

Interpolation estimates within the observed data range and is usually less risky. Extrapolation predicts beyond that range, where mechanisms or constraints may change.