Ssck 1203 Data Analysis 090214 Students 02

8/13/2019 Ssck 1203 Data Analysis 090214 Students 02

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STATISTICS IN DATA EVALUATION Defining confidence limits

Estimating the different of two means

(t test)

Estimating the precision of data from twoexperiments (F test)

Deciding to accept or reject outliers (Q test)

Calibration graphs

Methods of validation


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CONFIDENCE LIMITS ANDCONFIDENCE INTERVAL

Confidence- assert a certain probability thatthe confidence interval does include the true

value. The greater the certainty, the greater the

interval required.


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CONFIDENCE LIMITS (CL) OF MEAN Since the exact value of population mean,

cannot be determined, one must usestatistical theory to set limits around themeasured mean, , that probably contain .

CL only have meaning with the measuredstandard deviation, s, is a good

approximation of the population standarddeviation, , and there is no bias in themeasurement.

x


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0 2 4-2-4 -3 -1 1 3

dN/N

80%

+1.29-1.29

CONFIDENCE LIMITS (CL)

In the absence of any systematic errors, the limits withinwhich the population mean () is expected to lie with a

given degree of probability.

0 2 4-2-4 -3 -1 1 3

dN/N

50%

+0.67-0.67

0 2 4-2-4 -3 -1 1 3

dN/N

95%

-1.96 +1.96


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CONFIDENCE INTERVAL (CI)

CI when is known (Population)

N = Number of measurements

N

zx =

forCI


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VALUES FOR z AT VARIOUSCONFIDENCE LEVELS

Confidence Level, % z

50 0.67

68 1.080 1.2990 1.6495 1.9696 2.00

99 2.5899.7 3.0099.9 3.29


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CI For Small Data Set (N < 20)Not Known

Values of t depend on degree of freedom,

(N - 1) and confidence level (from Table t).

t also known as students t and will be used in

hypothesis test.

Example 2

N

tsx =forCI
http://sscc%202243%20space/SSC%202243%20201112%20I/CHAPTER_2/Example2.pdfhttp://sscc%202243%20space/SSC%202243%20201112%20I/CHAPTER_2/Example2.pdf


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VALUES OF t AT VARIOUSCONFIDENCE LEVEL

Degrees of Freedom 80% 90% 95% 99%(N-1)

1 3.08 6.31 12.7 63.7

2 1.89 2.92 4.30 9.923 1.64 2.35 3.18 5.844 1.53 2.13 2.78 4.605 1.48 2.02 2.57 4.036 1.44 1.94 2.45 3.717 1.42 1.90 2.36 3.508 1.40 1.86 2.31 3.369 1.38 1.83 2.26 3.25

19 1.33 1.73 2.10 2.8859 1.30 1.67 2.00 2.66 1.29 1.64 1.96 2.58


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OTHER USAGE OF CONFIDENCEINTERVAL

To determine number of replicates neededfor the mean to be within the confidenceinterval.

To determine systematic error.
http://sscc%202243%20space/SSC%202243%20201112%20I/CHAPTER_2/replicate.pdfhttp://sscc%202243%20space/SSC%202243%20201112%20I/CHAPTER_2/systematic_error.pdfhttp://sscc%202243%20space/SSC%202243%20201112%20I/CHAPTER_2/systematic_error.pdfhttp://sscc%202243%20space/SSC%202243%20201112%20I/CHAPTER_2/replicate.pdf


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SIGNIFICANT TESTS

Approach tests whether the differencebetween the two resultsis significant (due to

systematic error) or notsignificant(merely

due to random error).


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NULL HYPOTHESIS, Ho The values of two measured quantities do not differ

(significantly)UNLESS we can prove it that the two

values are significantly different.

Innocent until proven guilty

The calculated valueof a parameter from theequation is compared to the parameter value from

the table.

If the calculated value is smallerthan the table value,the hypothesis is acceptedand vice-versa.


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NULL HYPOTHESIS, Ho

Can be used to compare:

and and s and s1and s2

2x

x

1x


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APPLICATION OF t-TEST

A t-test is used to compareone set of

measurement with another to decide

whether or not they are significantlydifferent.


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t TEST

1. Comparison between experimental mean

and true mean (and )

To check the presence of systematic error.

Stepsfor t test.

Example 4.

x
http://sscc%202243%20space/SSC%202243%20201112%20I/CHAPTER_2/steps_t.pdfhttp://sscc%202243%20space/SSC%202243%20201112%20I/CHAPTER_2/Example4.pdfhttp://sscc%202243%20space/SSC%202243%20201112%20I/CHAPTER_2/Example4.pdfhttp://sscc%202243%20space/SSC%202243%20201112%20I/CHAPTER_2/steps_t.pdf


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t TEST

2. Compare and from two sets of data

Normally used to determine whether the twosamples are identical or not.

The difference in the mean of two sets of thesame analysis will provide information onthe similarity of the sample or the existence

of random error.

Steps Example 5

1x 2x
http://sscc%202243%20space/SSC%202243%20201112%20I/CHAPTER_2/steps_t2.pdfhttp://sscc%202243%20space/SSC%202243%20201112%20I/CHAPTER_2/Example5.pdfhttp://sscc%202243%20space/SSC%202243%20201112%20I/CHAPTER_2/Example5.pdfhttp://sscc%202243%20space/SSC%202243%20201112%20I/CHAPTER_2/steps_t2.pdf


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Comparing the precisionof twomeasurements

Is Method A more precise than Method B?

Is there any significant difference betweenboth methods?

F TEST


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DIXONS TEST OR Q TEST

A way of detectingoutlier, a data which isstatistically does not belong to the set.

Data:10.05, 10.10, 10.15, 10.05, 10.45, 10.10

By inspection, 10.45 seems to be out of thedata normal range.

Should this data be eliminated? Example 7 Table Q
http://sscc%202243%20space/SSC%202243%20201112%20I/CHAPTER_2/Example7.pdfhttp://sscc%202243%20space/SSC%202243%20201112%20I/CHAPTER_2/TableQ.pdfhttp://sscc%202243%20space/SSC%202243%20201112%20I/CHAPTER_2/TableQ.pdfhttp://sscc%202243%20space/SSC%202243%20201112%20I/CHAPTER_2/Example7.pdf


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CALIBRATION GRAPHS Commonly used in analytical chemistry to find the

quantitative relationbetween two variables (e.g.

response and concentration).

The calibration curves are normally linear, howevernot all the points are located on the drawn straightline (random error).

Regression analysiscan be done on the data to see

how good the linearityof the data is.(Method of least squares)


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METHOD OF LEAST SQUARES

Linear relationship between analytical signal (y)andconcentration (x).

Calculate best straight line through data points, eachof which is subject to experimental errors.


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CALIBRATION CURVES

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Concentration (X)

Respons

e(Y) y = mx c

m = slope

c = intercept


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CALIBRATION METHODS Standard Calibration Method Standard Addition Method


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STANDARD CALIBRATION METHOD

1 ppm 2 ppm 3 ppm 4 ppm 5 ppm

SampleBlank


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Calibration Plot for Absorbance versus Concentration

0.000.05

0.10

0.15

0.20

0.25

0.30

0.35

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Concentration

Absorbance

STANDARD CALIBRATION METHOD

y = 0.06x 0.0067


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STANDARD ADDITION METHOD

(x + 0) ppm (x + 10) ppm (x + 20) ppm ( x + 50) ppm

(x + 100) ppm Blank


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Concentration (ppm) Signal

(x + 0.00) 5.0

(x + 10.00) 11.0

(x + 20.00) 17.0

(x + 50.00) 28.0

(x + 100.00) 55.0


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0

10

20

30

40

50

60

-20 -10 0 10 20 30 40 50 60 70 80 90 100 110 120

Concentration

Abs


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The closer the R value to 1 (or 1), the betterthe correlation between y and x.

R = +1: perfect positive correlation with all

points lying on a straight line withpositive slope.

R = 1: perfect negative correlation.

Correlation coefficient, R2of > 0.999:evidence of acceptable fitof the data to theregression line.


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METHOD VALIDATIONDEFINITION

Method validation is the process to confirmthat the analytical procedureemployed for aspecific testis suitable for its intended use.

The process of verifyingthat a procedure or

methodyields acceptable results.


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PURPOSE OF VALIDATION

To defend validity of the resultand

demonstrate method is fit for the intended

purpose.

Responsibility of the laboratories.

Based on evaluation of the method

performanceand the estimated uncertainty

on the result.


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VALIDATION OF ANALYTICAL METHOD

(METHOD VALIDATION) Analysis of Standard Samples (SRM) Analysis by Other Methods

Standard Addition to the Sample

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Ssck 1203 Data Analysis 090214 Students 02