Experimental Error & Statistics (L01; chptrs 3 & 4)

CHEM 310: Foundations of Analytical Chemistry

qualitative analysis

deals with the identification of objects; finding what elements or compounds are present in the sample to give us a descriptive and non-numerical result

quantitative analysis

concerned with the determination of how much of a particular substance (analyte) is present in a sample, and it gives us definite results (has numbers and units)

types of quantitative analysis according to sample amount

> 100 mg = macro

1-10 mg = micro

1 ug = ultramicro

types of quantitative analysis according to percent analyte

> 1% = major constituent

0.01-1% = minor constituent

<0.01% = trace constituent

Error

= Accepted Value - Experimental Value

Can be positive or negative depending on whether the experimental value is greater than or less than the accepted value

Systematic/Determinate Errors

• Arises from an instrumental or procedural flaw

• Reproducible

• Unidirectional

• Can be corrected

Example: System error from an uncalibrated burette

Causes of determinate errors?

1. Methodic - reflects the properties of the chemical system involved

2. Operative - faulty observation; mistake by the experimenter

3. Instrumental - miscalibration of apparatus

Random/Indeterminate Errors

• arises from uncontrolled variables during measurement

• cannot be corrected

example: electrical noise from an instrument

Identify the following as a Systematic/Determinate or Random/Indeterminate Error: A worker miscalculates the molecular weight of an analyte

Systematic/Determinate error

Identify the following as a Systematic/Determinate or Random/Indeterminate Error: A balance that is capable of measuring only to 0.0001 g cannot distinguish between 1.0151 g and 1.0149 g; in one case the measured mass is low and in the other case its high.

Random/Indeterminate error

Accuracy

a measure of how close a measurement comes to the actual or “true” value

How can you express accuracy?

with absolute error and relative error

*the smaller the error, the greater the accuracy!

Absolute Error

= |Accepted Value - Experimental Value|

Relative Error

= ( |Error| / Accepted Value ) x100

Precision

a measure of reproducibility, depending on replicate analyses

Accuracy vs. Precision

ACCURACY: correctness, checked by using a different method, and poor accuracy results from procedural or equipment flaws

PRECISION: reproducibility, checked by repeating measurements, and poor precision results from poor technique

Measurement Precision

EVERY measurement has an associated uncertainty (unless it’s an exact, counted integer; e.g. the number of trials conducted)

and EVERY calculated result also has an uncertainty related to the uncertainty in the measured data—this uncertainty can be reported as an explicit ± value or as an implicit uncertainty by using the appropriate number of sig figs

Rules for sig figs: Add/Subtract

LEAST # OF DECIMAL PLACES

Rules for sig figs: Multiply/Divide

LEAST # OF SIG FIGS

Absolute Uncertainty

refers to the actual uncertainty in a quantity

example: the average of three weightings is 6.3302 ± 0.0001 g, the absolute uncertainty is 0.0001 g

Relative Uncertainty

expresses the uncertainty as a fraction of the quantity of interest

Propagation of uncertainty from random error for addition/subtraction

use absolute uncertainty

Propagation of uncertainty from random error for multiplication/division

use percent relative uncertainty

Propagation of uncertainty from random error for mixed operations

1. work on the absolute uncertainties (addition/subtraction)

2. then convert to relative uncertainties

Propagation of uncertainty from random error for atomic mass (application)

Coefficient of Variation

the standard deviation expressed as a percentage of the mean value

Student’s t test

a statistical tool used most frequently to express confidence intervals, to evaluate the probability that a certain measurement will be found in a specified data range, and to compare results from different experiments

*note! the slides show many example problems asking your to do t tests—practice those!

Analysis of Variance (ANOVA)

“t-test beyond two means”; post hoc test to determine significance

Grubbs Test

used to identify outliers