Types of Measurement Error and Statistical Analysis

Flashcards covering types of measurement error (systematic, random), uncertainty (absolute, relative, percent), methods for estimating uncertainty, and basic statistics including average, standard deviation, confidence intervals, and the t-test for comparing means.

Systematic error

A flaw in equipment or design where the error is reproducible.

Random error

Caused by uncontrolled (sometimes controllable) variables, with an equal chance of being positive or negative.

Absolute uncertainty

The margin of uncertainty associated with a measurement, often expressed as ± a value (e.g., 70 ± 5°F).

Relative uncertainty

The size of uncertainty with respect to the actual measurement, calculated as absolute uncertainty divided by the measurement.

Percent uncertainty

Relative uncertainty multiplied by 100.

Estimating Uncertainty (Estimated Digit)

The estimated digit corresponds to 1/10 of the smallest mark on a measuring device.

Estimating Uncertainty (Numerical Readouts)

For balances or numerical readouts, uncertainty is assumed to be in the last digit (e.g., mass 3.62(3)g).

Estimating Uncertainty (Smallest Mark Convention)

A common convention is to estimate uncertainty as 1/2 of the smallest mark on a measuring device.

Estimating Uncertainty (Balance/Numerical Read Out - Convention)

For a single measurement from a balance or numerical readout, assume +/- 1 in the last digit (e.g., 1.7346 ± 0.0001g).

Average (Mean)

The sum of all values divided by the number of measurements (Σxi / n).

Standard Deviation (STDEV)

A statistical measure of how closely the data cluster around the mean.

Population Standard Deviation (STDEV. P)

Standard deviation calculated from data representing the entire population.

Sample Standard Deviation (STDEV. S)

Standard deviation calculated from data representing a sample of a larger population, typically larger than population STDEV.

Confidence Intervals

The probability that a population parameter will fall between a set of specified values.

One Standard Deviation Confidence

Indicates that approximately 68% of the data falls within one standard deviation of the mean.

Two Standard Deviations Confidence

Indicates that approximately 95% of the data falls within two standard deviations of the mean.

Three Standard Deviations Confidence

Indicates that approximately 99.7% of the data falls within three standard deviations of the mean.

t-test

A statistical test used to determine if there is a statistically significant difference between two average values, particularly when the standard deviations are assumed to be equal.

Statistically Different Results (t-test)

If the calculated t-value (tcalculated) is greater than the critical t-value from the table (ttable) for the given degrees of freedom and confidence level, the two results are considered statistically different.

Degrees of Freedom (t-test)

For a comparison of two means, it is calculated as n1 + n2 - 2, where n1 and n2 are the number of measurements in each sample.

STDEV pooled

A combined standard deviation used in the t-test formula when the standard deviations of the two data sets are different, calculated as [(STDEV₁)²(n₁-1) + (STDEV₂)²(n₂-1)] / (n₁ + n₂ - 2).