This document provides an introduction to food analysis and basic statistical concepts relevant to food analysis. It discusses the importance of food analysis for quality control, new product development, regulatory enforcement, and problem solving. Various methods for presenting analytical data are described, including textual, tabular, and graphical formats. Measures of central tendency like the mean, median, and mode are explained. Accuracy refers to how close measurements are to the true value, while precision refers to the reproducibility of measurements. Understanding accuracy and precision is important for evaluating analytical results and making informed decisions based on food analysis data.

1. FOOD ANALYTICAL SCIENCE
(SBFT 06101)
DIPLOMA (Food SCi & Techn.) - NTA 6
FACILITATORS: DR MGINA, ZH

2. Lecture 1
INTRODUCTION TO FOOD
ANALYSIS

3. Introduction to food analysis.
 The growth and infrastructure of the model food
distribution system heavily relies on food analysis
(beyond simple characterization) as a tool for
 new product development
 quality control
 regulatory enforcement
 problem solving

4. Introduction to food analysis cont’d…
 All food products require analysis of various
characteristics to determine
 chemical composition, microbial content, physical
properties and sensory properties
 Food characteristics are part of the quality
management, from raw ingredients, through
processing, to the final product

5. Importance of food analysis
 Chemical composition and physical properties of food
use to determine;
-nutritive value
-functional characteristics
-acceptability of food
 Compositional data used by government agencies, food
industry, universities/ research institutions and
consumers

6. Importance of food analysis cont’d…
 GOVERNMENT AGENCIES
-Set policies and guidelines according to international
stipulations to ensure safety and quality of foods to be
marketed locally and internationally.
 FOOD INDUSTRY
-Competition in market determined by consumer
demands.
-Analysis NB in quality management systems.
-Critical to R&D process.

7. Importance of food analysis cont’d…
 CONSUMER
-Selective about choice of purchase;
-Demand variety, health claims, good value;
-Concerned about safety;
-Becoming more and more aware of what they eat.
 UNIVERSITIES/RESEARCH INSTITUTIONS.
-Design of experiments;
-Quality control;
-Repeatability of experiments by other researchers.

8. Importance of food analysis cont’d…
 In quality management, food analysis used as a tool to
address the following questions about different samples
analysed;
1. Raw materials;
-Do they meet company specification?
-Do they meet regulatory specifications?
-Do process parameters need to be adjusted to
accommodate deviation in quality.

9. Importance of food analysis cont’d…
2. Process control
-Do processing steps results in acceptable changes in
quality
-Do processing steps need to be modified to achieve
acceptable quality?
3. Finished product
-Does it meet regulatory requirements?
-What is the nutritive level and does it comply with
existing labels
-Does it meet product claims?
-Will it be acceptable to the consumer?
-Will it have appropriate shelf life?

10. Importance of food analysis cont’d…
4. Competitor product
-What are its composition and characteristics?
-How can information be used to develop new
products?
5. Complaint or returns
-How does returned sample compare to “ideal”
products?

11. Importance of food analysis cont’d…
 Properties analysed in foods;
i. Chemical composition;
ii. Physical properties ;
iii. Sensory properties .

12. Official methods
 Non-profit scientific organizations have developed and
published methods of analysis
 Standardized to make the choice of a method for a
specific characteristics or component to be analysed
easier.
 Allow for easy comparison of results between different
lobs following same procedure.

13. Official methods cont’d…
 Association of Official Analytical Chemists (AOAC)
INTERNATIONAL.
-Est. 1884 to serve analytical needs of government
regulatory and research agencies.
-Methods validated (with supporting data) and adopted
by AOAC published in journal of AOAC international.
-After rigorous testing and validation of methods, they
are compiled in books published and updates every 4-5
years with supplements published annually.

14. Official methods cont’d…
 American Association of Cereal Chemists (AACC)
-Approved laboratory methods applied primarily to
cereal products.
-Similar process of adopting methods to AOAC Int.
 American Oil Chemist Society (AOCS)
-Approved laboratory methods applied primarily to fat
and oil analysis (including edible fats and oils; oilseed
proteins, soaps and detergents, other lipid derivatives.

15. Official methods cont’d…
 Several other scientific organisation's with a specific
focus on specialized products including;
-American Public Health Association;
-Water Environment Federation ;
-International Organisation for Standards;
-British Standards Institute;
-National Academy of Science.

16. Official methods cont’d…
 South African Bureau of Standards.
-Est. In terms of Standards Act, 1945(Act No.24 of
1945). Operates under Act No. 29 of 2008)
-National institution promoting and maintaining
standards of quality.
-Food and Health Cluster provides accredited
conformity assessment to food industries as well as
other industries.

17. Official methods cont’d…
 NB Standards differ from country to country.
 Development of foods and analytical methods to be
marketed internationally need to comply with standards
set by international bodies.
 Codex Alimenntarius Commission.
 International Organisation for Standards.

18. Requirements and choice of analytical
methods
 Several methods available to assay samples for specific
characteristics
 Choice of method dependant on a number of factors.
 Eventual choice of methods will depend on which factor
is most critical
 To meet legislative requirements, use of officially
approved methods is critical

19. Factor determining choice of method
1. Precision:
-Ability method to reproduce an answer by same or
different investigator in same lab using same
procedure and instruments.
2. Reproducibility:
-Similar to precision.
-Ability of methods/ procedure to reproduce an answer
by different investigator and/lab using the same
procedure.
3. Accuracy:
-Ability to measure what is intended to be measured
(e.g Measurement of protein and not all N-containing
substances).

20. Factor determining choice of method cont’d…
4. Simplicity of operation:
-Measure of ease with which analysis may be carried
out by relatively unskilled workers.
5. Economy:
-Cost involved in terms of reagents, instrumentation,
time.
6. Speed:
-Time taken to complete analysis.
7. Sensitivity:
-Capacity of method to detect and quantify
components at very low concentrations.

21. Factor determining choice of method cont’d…
8. Specificity:
-Ability to detect and quantify specific constituents even
in the presence of similar compounds.
9. Detection limits:
-The lowest possible increment that can be detected by
a methods.
10. Safety:
-Considers hazard nature of certain reagents used (e.g.
Corrosiveness of acids or bases, flammability of solvents).
11. Official approval:
-Nationally or internationally approved official methods.

22. Lecture 2
Presentation of data

23. Introduction to Presentation of data
 Whether analytical data are collected in a research
laboratory or in the food industry
 The important decisions are made based on the data
 Appropriate data collection and analysis help avoid bad
decisions being made based on the data

24. Presentation of data cont’d…
 Having a good understanding of the data and how to
interpret the data (e.g., what numbers are statistically
the same) are critical to good decision making
 Talking with a statistician before designing
experiments or testing products produced can help to
ensure appropriate data collection and analysis, for
better decision making

25. Presentation of Data cont’d…
 Data
 Information in raw or unorganized form (such as
alphabets, numbers, or symbols) that refer to, or
represent, conditions, ideas, or objects
 should be presented in the simplest but most
informative formative form to enable quick and easy
reading and interpretation

26. Methods of Data Presentation
 This refers to the organization of data into tables,
graphs or charts, so that logical and statistical
conclusions can be derived from the collected
measurements.
 Data may be presented in(3 Methods): -
 Textual,
 Tabular or
 Graphical.

27. Textual Presentation
 The data gathered are presented in paragraph form
 Data are written and read
 It is a combination of texts and figures

28. Textual Presentation
 Example
 Of the 150 sample interviewed, the following
complaints were noted: 27 for lack of books in the
library, 25 for a dirty playground, 20 for lack of
laboratory equipment, 17 for a not well maintained
university buildings

29. Tabular Presentation
 Method of presenting data using the statistical table
 A systematic organization of data in columns and rows.
 i.e
 Columns – Vertical lines
 Rows – Horizontal lines

30. Tabular Presentation cont’d…
 Parts of a statistical table
 Table heading – consists of table number and title
 Stubs – classifications or categories which are found
at the left side of the body of the table
 Box head – the top of the column
 Body – main part of the table
 Footnotes – any statement or note inserted
 Source Note – source of the statistics

31. Tabular presentation - Illustration

32. Example of Tabular presentation

33. Graphical Presentation
 Kinds Of Graphs or Diagrams
 BAR GRAPH
 used to show relationships/ comparison between
groups
 PIE OR CIRCLE GRAPH
 shows percentages effectively
 LINE GRAPH
 most useful in displaying data that changes
continuously over time
 PICTOGRAPH – or pictogram
 It uses small identical or figures of objects called
isotopes in making comparisons
 Each picture represents a definite quantity

34. Graphical Presentation – Bar Graph

35. Graphical Presentation – Pie or Circle Graph

36. Graphical Presentation - Line Graph

37. Graphical Presentation - Pictograph or Pictogram

38. Data Presentation cont’d…
 Presentation of figures is effective in tables and even
more effective in certain types of graphs.
 Graphs most effective way to indicate any trends.
 When preparing graphs note that:-
 Simple numbers should be used on axes. i.e 10,20,
30,…Rather than 0.001, 0.002, 0.003….
 When dealing with small numbers, labels on axes
should be modified to indicate multiplication factor
used, e.g x 103

39. Data Presentation cont’d…
 When preparing graphs note that:-
 Symbols used to indicate data point on graphs should
be clear. E.g. Use of different shapes opposed to
small dots
 Points on graphs should be separated by equal
spacing's
 For graphs conforming to equation of a straights line,
line of best fit should be drawn
 Error of each value should be indicated by the use of
vertical error bars

40. Data quality and Improvement
 Data is obtained via experimental means.
 NB to ensure all apparatus and reagents are optimal in
order to improve the reliability of data produced.
 The following measures may be taken to ensure quality
and reliability of data:
-Glassware quality.
-Handling and cleanliness of equipment.
-blank analysis.

41. Data quality and Improvement cont’d…
-Replication (the same sample for accuracy and
precision)
-Recovery experiments (spiking and recovery).
-Reference samples.
-Collaborative tests.
-Confirmatory analysis.

42. LECTURE 3
OVERVIEW OF BASIC STATISTICAL
CONCEPTS

43. Introduction to basic statistics concept
 All experimental data requires processing in order for us
to make sense out of it.
 Several mathematical treatments available to the food
analyst to give an indication of how well an analysis has
been performed (accuracy and precision) and how
reliable subsequent data is.
 Software is available to make life much easier.

44. basic statistical concepts cont’d…
 In order to evaluate the food product parameters, the
analysis of a sample is usually performed (repeated)
several times
 At least three assays are typically performed, though
often the number can be much higher
 To ensure which value is closest to the true value,
 Carry out the measures of central tendency using all
the values obtained to report the results

45. Measures of Central Tendency
 Measures of central tendency are statistics or numbers
expressing (numerically) the most typical or average
scores in a distribution
 The word average denotes a representative of a whole
set of observations.
 It is a single figure which describes the entire series of
observations with their varying sizes
 It is a typical value occupying a central position where
some observations are larger and some others are
smaller than it

46. Measures of Central Tendency cont’d…
 Average is a general term which describes the centre of
a series
 It is a central part of the distribution and therefore called
the measures of central tendency
 The most common measures of central tendency are
 Mean (Arithmetic mean)
 Median
 Mode

47. Measures of Central Tendency cont’d…
 For Example, given the set of observations of analyzed
moisture content of certain cereal product
 50.0; 53.0; 52.5; 51.8; and 52.5.
 Which value is closest to the true value?
 To increase accuracy and precision experiments are
repeated.
 Then, the average of several (at least 3) replicates is
taken because we are unsure of true value of
component present is sample.

48. Mean (Arithmetic mean)
 Is defined as the sum of all the observations divided by
the number of observations
 The mean is the arithmetic average for a distribution.
 gives no indication about its accuracy or precision.
 Some values may be closer to the true value than
others.
 Often not enough for scientific reporting

49. Mean cont’d…
 Where:
 = mean
 X1, X2, X3 etc. = individually measured values (Xi)
 n = number of measurements

50. Mean cont’d…
 For example, suppose we measured a sample of
uncooked hamburger for percent moisture content four
times and obtained the following results: 64.53 %, 64.45
%, 65.10 %, and 64.78 %
 = 64.53 + 64.45 + 65.10 + 64.78
4
= 64.72%

51. Accuracy and Precision
 If we look at hamburger experiments,
 The first data obtained are the individual results
 Second is a mean value
 The next questions should be:
 “How close were our individual measurements?”
 “How close were they to the true value?”
 Both questions involve accuracy and precision

52. Accuracy
 Refers to how close a particular measure is to the true
or correct value
 Recall the moisture analysis for hamburger mean of
64.72 %
 Assume the true moisture value was actually 65.05 %.
 Comparing these two numbers,
 could probably make a guess that your results were
fairly accurate because they were close to the
correct value

53. Accuracy cont’d…
 The problem in determining accuracy is that most of the
time we are not sure what the true value is
 For certain types of materials, we can purchase
known samples from for example, the National
Institute of Standards and Technology and check our
assays against these samples
 compare our results with those of other labs to
determine how well they agree, assuming the other
labs are accurate

54. Precision
 A measure of how reproducible or how close replicate
measurements become.
 If repetitive testing yields similar results, then we
would say the precision of that test was good.
 From a true statistical view
 the precision often is called error, when we are
actually looking at experimental variation
 So, the concepts of precision, error, and variation are
closely related

55. How the Precision Differ from Accuracy
 Imagine shooting a rifle at a target that represents
experimental values
 The bull’s eye would be the true value, and
 where the bullets hit would represent the individual
experimental values
 If the values can be tightly spaced (good precision) and
close to the bull’s eye (good accuracy)
 There can be also situations with good precision but
poor accuracy

56. Comparison of accuracy and precision
(a) good
accuracy and
good precision
(b) good
precision and
poor accuracy
a b

57. How the Precision Differ from Accuracy
cont’d…
 The worst situation is when both the accuracy and
precision are poor
 In this case, because of errors or variation in the
determination, interpretation of the results becomes very
difficult

58. Comparison of accuracy and precision cont’d…
(c) good
accuracy and
poor precision
(d) poor
accuracy and
poor precision
c d

59. The MEDIAN
 It is the middle, most point or central value in a set of the
observations
 When observations are arranged either in ascending or
descending order of their magnitudes.
 Median is the value of that item in a series which divides
the series into two equal parts
 One part consists of all values less and the other all
values greater than it.

60. The Median cont’d…
 To calculation of Median
 Simple series (ungrouped data)
 use the formula (n + 1)/2.
 Where ‘n’ = total number of observations in a sample
 Procedure:
 Arrange the data in (either ascending or descending)
order of magnitude
 If the number of observation be odd, the value of the
middle – the most item is the median.
 However, if the number be even, the arithmetic mean
of the two middle most items is taken as median

61. The Median cont’d…
 NB:
 When ‘n’ is odd; take n+1/2th as a median
 M = n+1/2th term
 when ‘n’ is even; there are two middle terms. n/2th and
(n/2+1)th.
 The median is the average of these two terms
 M = n/2+(n/2+1)/2.
 Example
 Find the median of the following observations
a) 64.53; 64.45; 65.10; and 64.78;
b) 50.0; 53.0; 52.5; 0;51.8. and 52.5.

62. The Median cont’d…
 Solution
 Let us arrange the data in order
a) 64.45, 64.53, 64.78, 65.10.
 In this data the number of item is n = 4 (even)
 Median = average of n/2th+(n/2+1)th terms
 Average (4/2)th and 4/2 +1)th terms
= Average 2th and 3th
M = 64.53 + 64.78 /2
=129.31/2 = 64.66
Median is 64.66

63. The Median cont’d…
 Solution
b) 50.0; 53.0; 52.7; 51.8. and 52.5.
 let us arrange the data in order
 50.0, 51.8, 52.5, 52.7, 53.0
 In this data the number of items is n = 5 (odd)
 Median = M = (n+1/2)
 (5+1/2)th item = 3th item
 Now the 3th value in the data is 52.5
 Median is 52.5

64. The Median cont’d…
 To calculation of Median
 Discrete series (grouped data)
 Procedure;
 Arrange the data in either ascending or descending
order of magnitude
 A table is prepared showing the corresponding
frequencies and cumulative frequencies

65. The Median cont’d…
 Now calculate the median by the following formula
 M = (n+1/2)th; N = ∑f
 Where
 ‘n’ = total number of observations in a sample
 ‘N’ = total number of frequencies
 ‘f’ = number of samples

66. The Median cont’d…
 Example:
 Calculate the median for the following data
Number of Samples 6 16 7 4 2 8
Observations 20 25 50 9 80 40

67. The Median cont’d…
 Solution
 Let us arrange the data in ascending order and then
form cumulative frequencies
observations No. of Samples (f) Cumulative frequency (cf)
9 4 4
20 6 10
25 16 26
40 8 34
50 7 41
80 2 43

68. The Median cont’d…
 From the table above
 ∑f = n = 43
 Median (M) is = n+1/2
 = 43+1/2
 = 22th
 The table shows that all items from 11 to 26 have their
values 25
 Since 22 and items lies in this interval, therefore it value
is 25

69. The Median cont’d…
 To calculation of Median
 Continuous series
 Procedure;
 Here data is given in the form of a frequency table with
class interval
 Cumulative frequencies are found out for each value
 Median class is then calculated ( where cumulative
frequency N/2 lies is called median class)

70. The Median cont’d…
 Now median is calculated by applying the following formula
 M = L + N/2 – C / fm x I
 Where
 L = lower limit of the class in which median lies
 N = total number of frequencies
 fm = frequency of the class in which median lies
 C = Cumulative frequency of the class preceding
the median class
 i = width of the class interval in which the median
lies

71. The Median cont’d…
 Example
 Find the median and median class of the data given
below
Class boundaries 15-25 25-35 35-45 45-55 55-65 65-75
Frequency 4 11 19 14 0 2

72. The Median cont’d…
 Solution
Class boundary Midvalue (m) Frequency (f) Cumulative
frequency (cf)
15 - 25 20 4 4
25 - 35 30 11 15
35 - 45 40 19 34
45 - 55 50 14 48
55 - 65 60 0 48
65 - 75 70 2 50

73. The Median cont’d…
 From the table above
 N/2 = 50/2 = 25; L = 35; fm = 19; C = 15 and i =
10
 It is more than cumulative frequency 15, but is less than
the cf = 34. Hence the median class interval is 35-45.
 M= 35 + 25 -15/19 x 10
= 35 + 10/19 x 10
= 35 + 5.263 = 40.263
Median class = 35 – 45.

74. MODE
 Is considered as the value in a series which occurs most
frequently, i.e. has the maximum frequency
 The mode of a distribution is a value at the point around
which the items tend to be most heavily concentrated
 Regarded as most the most typical value

75. Calculation of mode
 Simple Series ( Ungrouped Data)
 Procedure
 Mode can be determined by locating that value which
occurs the maximum number of times
 It can be determined by inspection only
 It is that value of the variable which corresponds to
the largest frequency.

76. Calculation of mode cont’d…
 Example
 Find the mode of the data given below:
 1, 3, 1, 3, 3, 5, 3, 3, 1, 5, 3, 3, 4, 2, 3, 2, 3, 2, 3, 7, 6,
3, 2, 5, 2, 3, 3, 2, 6, 2, 3, 2, 3, 2, 4, 2, 3.
 Solution:
 Prepare the table showing the frequency

77. Calculation of mode cont’d…
Value Number of items (f)
1 3
2 8
3 14
4 3
5 4
6 2
7 1

78. Calculation of mode cont’d…
 From the table above;
 3 repeats 14 times and is most frequent hence is the
mode

79. INDICATORS OF PRECISION
 Several tests are commonly used to give some
appreciation of how much the experimental values would
vary if the test is repeated
 An easy way to look at the variation or scattering is to
report the range and Standard Deviation of the
experimental values as an indicators of precision

80. Range
 Simply the difference between the largest and smallest
observation
 this measurement is not very useful
 is seldom used in evaluating data
 For example, Consider the values obtained from
measured sample of uncooked hamburger for percent
moisture content, 64.53 %, 64.45 %, 65.10 %, and 64.78
%
 Range = 65.10 – 64.45
= 0.65%

81. Standard Deviation (𝜎)
 The best and most commonly used statistical evaluation
of the precision of analytical data
 Measures spread of a series of observations.
-Gives indication of precision between replicate
measurements (how close the values are to each
other)
-Based on assumption of normal distribution curve for
populations

82. Standard Deviation (𝜎) cont’d…
-If number of replicates < 30, n is replaced by n-1
-Calculation of standard deviation is made easier by
using function on a scientific calculator or any statistical
software

83. Coefficient of variation (CV)
 Once we have a mean and standard deviation, we must
next determine how to interpret these numbers
 One easy way to get a feel for the standard deviation is
to calculate what is called the coefficient of variation
(CV)
 also known as the relative standard deviation.
 Expressed as a percentage of the mean.
 Should ideally be < 5% to reveal good precision

84. Coefficient of variation (CV) cont’d…
 In a population with a normal distribution,
 68 % of those values would be within ±1 standard
deviation from the mean,
 95 % would be within ± 2 standard deviations, and
 99.7 % would be within ± 3 standard deviations.
 In other words, there is a probability of less than 1 %
that a sample in a population would fall outside ± 3
standard deviations from the mean value

85. Coefficient of variation (CV) cont’d…
 Often mean, standard deviation and coefficient of
variation are sufficient to show precision of analysis
 Other statistical tools are available to provide an
indication of experimental precision ( Refer to your
statistics and biometric notes)

86. SOURCES OF ERROR/VARIATION
 Error is inevitable in any analytical work
 Goal is to achieve lowest possible minimum
1. Systematic/Determinate Error
 Results constantly deviate from expected value
 May result in good precision but poor accuracy
 Often result of poor apparatus, impure reagents or
wrong choice of method
 Generally rectified by proper instrument calibration,
blank determinations, changing analytical method

87. SOURCES OF ERROR/VARIATION Cont’d…
2. Random/Indeterminate Errors
 Always present in all analytical measurements.
 Result of natural human error and background
instrument “noise”
3. Blunders.
 Easily eliminated.
 Experimental data usually obviously scattered.
 Often result of using wrong reagents, sloppy or
incorrect technique.
 Easy to identify and correct/eliminate.