Transcript t - UniMAP Portal

TESTS OF SIGNIFICANCE
It is a test to compare the results of
the method with those accepted
method.
HOW TO INDICATE THAT WHETHER
THERE IS A SIGNIFICANT
DIFFERENCE??
By using:
The T test
The T test
• Is used to determine if 2 sets of
measurements are statistically different.
• The comparison between 2 set of
measurements which made by 2 method, one
will be test method and the other one will be
accepted method.
• By using T test, we can determine whether
these two method are significant difference.
A statistical T value is calculated and compared
with the tabulated T value.
If
the calculated T value > the tabulated T
value
Then there is a significant difference
between the results by the two
methods at that confidence level.
• There are 3 ways can be used in a T test.
• If accepted value of μ is available, the result is
statistically equal to μ at a given confidence
level.
• If accepted value of μ is not available, then we
need to replicated analyses on a single sample
by 2 method, or a series of analyses on a
different sample by 2 method but one of the
method should be accepted method.
1. T Test when an Accepted Value is
Known
Calculated T value = 2.9
Tabulated T value = 2.776
calculated T value > tabulated T
value
There is a significant difference between
the reference value and the measured
value.
Comparison of the Means of Two
Samples
When t test is applied to two sets of data,µ is replaced by the
mean of the second set.
Reciprocal of the standard deviation of the mean( √N/s) replace
by the difference between the two.
Sp is pooled standard deviation of the individual measurements
of two sets:
• The pooled standard deviation sometimes
used to obtain an improved estimate of the
precision of the method .
• Calculating the precision of the two sets of
data in a paired t test.
• Preferable to perform several sets of analyses
examples on different samples with slightly
different compositions.
• If indeterminate error is assumed to be the
same for each set, then the data of the
different set can be pooled.
The pooled standard deviation, sp is
given by:
x => values in each set
N => num. of measurements
x =>means of each of k sets of analyses
N – k => degree of freedom from (N1-1) + (N2-2) + … +
(Nk-1)
• EXAMPLE :
A new gravimetric method is developed for
iron (III) in which the iron is precipitated in
crystalline form with organocarbon “cage”
compound.
The accuracy of the method is checked by
analyzing the iron in an ore sample and
comparing with the results using the standard
precipitation with ammonia and weighing of
Fe2O3.
The results, reported as % Fe for each analysis,
were as follows
Test Method
Reference Method
20.20%
18.89%
20.50
19.20
18.65
19.00
19.25
19.70
19.40
19.40
X₁=19.65%
X₂=19.24%
Is there a significant difference between the two
methods?
Solution
Paired t Test
 t value is calculated in a slightly different form
 difference between each of the paired
measurements on each sample is computed
• Average difference D is calculated and
individual deviations of each from D are used
to compute a standard deviation, sd
• t value is calculated from :
Example
• You are developing a new analytical method
for the determination of blood urea nitrogen
(BUN). You want to determine whether you
method differs significantly from a standard
one for analyzing a range of sample
concentrations expected to be found in the
routine laboratory. It has been ascertained
that the two methods have comparable
precisions. Following are two sets of results
for a number of individual samples.
• 95% confidence level is considered significant
• 99% level is highly significant
• Smaller the calculated t value, more confident
that there is no significant difference between
the two method
• Too low confidence level (e.g. 80%), likely to
conclude erroneously that there is a
significant difference between two methods
(type I error)
• On the other hand, too high confidence level
will require too large a difference to detect
(type II error)
• If a calculated t value is near tabular value at
the 95% confidence level, more tests should
be run to ascertain definitely whether the two
methods are significantly different
Thank you