Errors, Random Errors, and Statistical Data in Chemical Analyses Part 2 [Sir Jameson PPT] Flashcards
The random, or indeterminate, errors in the results of an analysis can be evaluated by the __________.
methods of statistics.
Ordinarily, statistical analysis of analytical data is based on the assumption that ________ follow a Gaussian, or normal, distribution
random errors
Sometimes analytical data depart seriously from Gaussian behavior, but the ____________ is the most common.
normal distribution
a finite number of experimental observations
sample of data
Statisticians call the theoretical infinite number of data
population
must be modified substantially when applied to
a small sample because a few data points may not be representative of the population.
Statistical laws
The equation contains just two parameters
the population mean μ
population standard deviation σ
is a measure of the precision or scatter of a population of data, which is given by the equation
The Population Standard Deviation (σ)
The square of the standard deviation σ2.
Variance
A normal error curve has several general properties:
1) the mean occurs at the central point of maximum frequency;
2) there is a symmetrical distribution of positive and negative deviations about
the maximum;
3) there is an exponential decrease in frequency as the magnitude of the
deviations increases.
The quantity N — 1 is
the number of degrees of freedom.
Another term to describe the precision of a set of replicate results
Spread or Range (w)
– It is the difference between the largest value in the set and the
smallest
Spread or Range (w)
One of the best ways of indicating reliability is to give a ___________ at the 90% or 95% confidence level.
confidence interval
define a numerical interval around that
contains μ with a certain probability.
Confidence limits
