Chapter 2 Flashcards
Indeterminate error is
sufficient to explain any
difference in the values
being compared.
Null hypothesis (𝑯𝟎)
The difference between the
values is too great to be
explained by random error
and, therefore, must be real.
Alternative hypothesis (𝑯𝑨
the confidence level for retaining the null hypothesis (95%), or the
probability that the null hypothesis will be incorrectly rejected
Significance Level
The risk of falsely rejecting
the null hypothesis (𝛼)
▸ risk is always equivalent to α
Type I Error
The risk of falsely retaining
the null hypothesis (β)
Type II Error
comparing 𝑠
2
to 𝜎
2
▸ a test designed to indicate
whether there is a significant
difference between two
methods based on their
standard deviations.
F TEST
is defined in terms of the
variances of the two methods,
where the variance is the
square of the standard
deviation
F
There are two different degrees of freedom, 𝑣1and 𝑣2,
defined as N − 1 for each case.
If 𝑭𝒄𝒂𝒍𝒄 > 𝑭𝒕𝒂𝒃𝒍𝒆, then the
variances being compared are
SIGNIFICANTLY DIFFERENT
If 𝑭𝒄𝒂𝒍𝒄 < 𝑭𝒕𝒂𝒃𝒍𝒆, then the
variances being compared are
STATISTICALLY THE SAME
comparison is made between two
sets of replicate measurements
made by two different means
t-TEST
If 𝒕𝒄𝒂𝒍𝒄 > 𝒕𝒕𝒂𝒃𝒍𝒆, then the data
being compared have
SIGNIFICANT DIFFERENCE
If 𝒕𝒄𝒂𝒍𝒄 < 𝒕𝒕𝒂𝒃𝒍𝒆, then the data
being compared have
NO SIGNIFICANT DIFFERENCE
➢ used to obtain an improved estimate of the precision of a
method and for calculating the precision of the two sets of data
➢ provides a more reliable estimate of the precision of a method
than is obtained from a single set
➢ if random error is
assumed to be the same for each set, then
the data of the different sets can be pooled
Pooled Standard Deviation
Several ways and several situations in which t-test can be
used
▸ t- test when a reference value is known
▸ Comparison of the means of two methods
▸ Paired t-Test
▸ t-test to compare different samples
A statistical t value is calculated
and compared with a tabulated
value for the given number of
tests at the desired confidence
leve
t-calc
➢ two methods are used to make
single measurements on
several different samples.
➢ No measurement has been
duplicated
Paired t-Test
allows comparisons among more than
two population means
▸ use a single test to determine whether
there is or is not a difference among
the population means rather than
pairwise comparisons as is done with
the t test.
ANOVA
𝐻0: 𝜇1 = 𝜇2 = 𝜇3 = ⋯ = 𝜇𝑖
𝐻𝐴 : at least two of the 𝜇𝑖
’s are different
. Is there a difference in the results of five analysts determining calcium
by a volumetric method?
2. Will four different solvent compositions have differing influences on the
yield of a chemical synthesis?
3. Are the results of manganese determinations by three different
analytical methods different?
4. Is there any difference in the fluorescence of a complex ion at six
different values of pH?
to
compare the variations between the
factor levels (groups) to that within
factor levels
basic principle
