eChapters

A probability distribution is a statistical function that describes all the possible values and likelihoods that a random variable can take within a given range. This range will be restricted between the minimum and maximum possible values.

The probability distribution shows how the set of all possible mutually exclusive events are distributed, and can be presented as an equation, a chart or a table.

A variable which can take different values with given probabilities is called a random variable.

There are numerous probability distributions which may be distinguished by whether the random variable is discrete, taking only a finite set of possible values, or continuous, taking an infinite set of possible values in a range of values.

A discrete random variable with only two possible values is called a binary variable, e.g. pregnant or not pregnant, diseased or healthy.

Probability distributions for discrete random variables The probability distribution for a discrete random variable y is the table, graph or formula that assigns the probability P(y) for each possible value of the variable y.

A. Definitions of probability

1. A probability relies on having an understanding of the theoretical model defining the set of all possible outcomes of a trial; we evaluate the probability solely on the basis of this model, without recourse to performing the experiment at all. It is often called an a priori probability. So, for example, we know that there are two equally likely outcomes when an unbiased coin is tossed: either a head or a tail. This is the model from which we can deduce that the probability of a defined event, obtaining a head, say, is 1/2 = 0.5.

2. The next approach to defining a probability, and the one commonly used in statistical inference, is to regard a probability as the proportion of times a particular outcome (the event) will occur in a very large number of ‘trials’ or ‘experiments’ performed under similar conditions.

The result of any one trial should be independent of the result of any other trial, so whether or not the event occurs in any one trial should not affect whether or not the event occurs in any other trial.

Correlation coefficient

We measure the degree of association between two variables by calculating Pearson’s product moment correlation coefficient, usually just called the correlation coefficient.

It was developed by Karl Pearson from a related idea introduced by Francis Galton in the 1880s, and for which the mathematical formula was derived and published by Auguste Bravais in 1844. In 1896, Karl Pearson published his first rigorous treatment of correlation and regression in the Philosophical Transactions of the Royal Society of London.

The linear correlation coefficient (sometimes called Pearson's Correlation Coefficient), commonly denoted, is a measure of the strength of the linear relationship between two variables.

• We say that we have perfect correlation if all the points lie on the line; in this case, the value of the correlation coefficient takes one of its extreme values, either +1 or −1 (Figure 7a and 7b).

• We have positive correlation if the sign of the correlation coefficient is positive; then there is a direct relationship between the two variables so that as one variable increases in value, the other variable increases (Figure 7a) or there is a tendency for it to do so.

• We have negative correlation if the sign of the correlation coefficient is negative; then there is an inverse relationship between the two variables so that as one variable increases in value, the other variable decreases (Figure 7b) or there is a tendency for it to do so.

• We have no linear association (i.e. the variables are uncorrelated) if the correlation coefficient is zero; then there is a random scatter of points with no indication of a linear relation between the variables (Figure 7c.). Note that a non-linear relationship between the variables can also give a correlation coefficient of zero.

Moments

In statistics, moments are measures of the shape and variability of a data set. They are used to describe the location and dispersion of the data. There are several types of moments that can be calculated, each providing different information about the data set.

Moments is a term which refers to a measure of force with respect to its tendency which provides rotation. The strength of the tendency depends upon the amount of force and distance from the point of origin where force is exerted.

So total moments of all the forces about origin, if total moment is divided by the total force, which is called moment actually arithmetic mean for frequency distribution.

Hence, arithmetic mean is called first moment about the origin

• Arithmetic mean of various powers expressed as deviation from mean in any distribution is called the moment of the distribution.

What is dispersion?

In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range. For instance, when the variance of data in a set is large, the data is widely scattered. On the other hand, when the variance is small, the data in the set is clustered.

Dispersion is contrasted with location or central tendency, and together they are the most used properties of distributions.

Measure of dispersion

(a) Range

The range is defined as the difference between the largest and smallest observations. Range(X)= Max(X)- Min (X)

Example

The range in statistics for a given data set is the difference between the highest and lowest values. For example, if the given data set is {2,5,8,10,3}, then the range will be 10 – 2 = 8. Thus, the range could also be defined as the difference between the highest observation and lowest observation.

The central tendency measure is defined as the number used to represent the center or middle of a set of data values. The three commonly used measures of central tendency are the mean, median, and mode.

Measures of location (averages)

The term average refers to any one of several measures of the central tendency of a data set.

• The mean has the disadvantage that its value is influenced by outliers. An outlier is an observation whose value is highly inconsistent with the main body of the data. An outlier with an excessively large value will tend to increase the mean unduly, whilst a particularly small value will decrease it.

• The mean is an appropriate measure of central tendency if the distribution of the data is symmetrical.

The mean will be ‘pulled’ to the right (increased in value) if the distribution is skewed to the right, and ‘pulled’ to the left (decreased in value) if the distribution is skewed to the left.

2.1 What is a frequency distribution?

A frequency distribution shows the frequencies of occurrence of the observations in a data set. Often the distribution of the observed data is called an empirical frequency distribution, in contrast to the theoretical probability distribution determined from a mathematical model.

The class interval is a term used in statistics when we are given a continuous series. Class means a group of numbers in which items are placed such as 0-10, 10-20, 20-30, etc. Class interval refers to the numerical width of any class in a particular distribution.

2.2 Relative frequency distributions

Although creating a frequency distribution is a useful way of describing a set of observations, it is difficult to compare two or more frequency distributions if the total number of observations in each distribution is different. A way of overcoming this difficulty is to calculate the proportion or percentage of observations in each class or category. These are called relative frequencies and each is obtained by dividing the frequency for that category by the total number of observations (column 3 of Table 2.1). The sum of the relative frequencies of all the categories is unity (or 100%) apart from rounding errors.

Statistics

It is a branch of mathematics, which comprises several areas like Algebra, Trigonometry, Calculus, Geometry, Statistics and Probability etc.

Biostatistics is a mathematical science which analyses numerical facts or biometric data of biological events following certain rules like design of experiments, analysis of data, presentation of data with tables, figures hypothesis testing, making a probability prediction and conclusion etc.

or it is an art of analysis and presentation of data following certain rules and international norms accepted by international journals for pharmacology experiments, animal farm data, human and animal medicines data, epidemiology data, non-parametric data etc.

What is statistics?

The number of introductory or elementary texts on the subject of statistics indicates how important the subject has become for everyone in the biological sciences. However, the fact that there are many texts might also suggest that we have yet to discover a fool proof method of presenting what is required. The problem confronted in biological statistics is as follows:

When there is a need to make a set of numerical observations in biology, it has been observed that the values are scattered. Then questions arise to know whether these values differ because of factors e.g. treatments or these are part of a ‘background’ i.e., natural variation. You need to evaluate what the numbers actually mean, and to represent them in a way that readily communicates their meaning to others.

Packaging is an essential tool to make products stand out from the competition. Beyond the shelf appeal, packaging also provides protection to the contents from physical, chemical and microbiological hazards. However, a lesser known fact is that the same packaging material could also be a source of chemical contaminants, and hence, may impact food safety as well as food quality. Among the different components of packaging material, packaging inks play a critical role as they might hamper product and consumer safety.

Each packaging ink is a mixture of different chemicals and some of these chemicals might be harmful with the potential to migrate to the foodstuff. In terms of risk, the chemicals could be toxic, carcinogenic, mutagenic, repro-toxic and even endocrine disruptors. The chemical contaminants from the packaging inks can get transferred to the foodstuff by a process called migration.

Over the last two decades, a number of scientific papers have been published, revealing the migration potential of substances from the printed matter. However, the first big scandal that brought the subject alive was about the f indings of isopropyl thioxanthone (ITX, a low molecular photo initiator used in UV inks) in baby milk and other liquid foodstuffs all over Europe, resulting in a product recall in the year 2005. The food scandal alerted the packaging chain about the linkage between packaging inks and food safety. Consequently, the authorities issued strict regulations for the application of printing inks as well as general food control measures.

Introduction

Nanotechnology is a rapidly expanding branch of science that has a critical role to play in raising the standard of living for people in the modern world. The global market for nanotechnology in food packaging is valued at 20 billion in 2023 and is expected to grow to 46.50 billion by 2031, with a compound annual growth rate (CAGR) of 11.32% from 2024 to 2031 (InsightAce Analytic, 2023). The rapid expansion of nanotechnology has paved the way for number of industrial areas, including food processing, food contact materials, and agricultural output (Mohammadi & Jafari, 2021). Nanotechnology is the fastest-growing field of science that significantly enhances the quality of life in today's world. This rapid advancement has opened up numerous industrial sectors, such as food processing, food contact materials, and agricultural production. A natural advancement is the integration of nanotechnology into food packaging. This includes enhanced packaging, active packaging, and a new category known as smart or intelligent packaging. Food contact materials, such as antimicrobial metals and oxides, biodegradable nanocomposites, and nanosensors, are utilized to create active and intelligent packaging. These materials enhance thermal and mechanical durability, increase safety and extend the shelf life of food, and facilitate the monitoring of packaged food (Kah et al., 2013). At the nanoscale, material properties change significantly, making it challenging to predict, identify, evaluate, and manage the health, safety, and environmental risks associated with nanomaterials. For example, nanoparticles (NPs) of 50 nm can enter cells, those of 70 nm can penetrate the lungs, and 30 nm NPs can cross blood-brain barriers.

Introduction

The landscape of the Indian food industry has undergone a dramatic transformation in recent years. Rising disposable incomes, coupled with the rapid pace of urbanization, have fuelled a surge in demand for convenient and processed food options. Consumers, increasingly pressed for time, are turning towards ready-to-eat meals, packaged snacks, and a wider variety of processed food products. While this trend signifies a growing economy and changing lifestyles, it has also brought to light a critical concern: ensuring food safety and empowering consumers with clear and accessible information. In order to empower consumers to make educated food choices and build trust between brands and consumers, food label transparency is crucial. Transparent labelling is essential for improving public health because it gives precise and unambiguous information about ingredients, nutritional value, and possible allergies. This information helps prevent diseases linked to a certain lifestyle, such diabetes, heart disease, and obesity. Additionally, it guarantees that customers are not misled about the quality or provenance of their food, shielding them from dishonest business tactics. Transparency also promotes market justice by levelling the playing field, making product integrity apparent, and fostering creativity and brand loyalty. Transparent labelling promotes ethical and sustainable consumption while also facilitating international trade by adhering to regulatory norms in many countries.

Recognizing this need for a more transparent and consumer-centric food ecosystem, the Food Safety and Standards Authority of India (FSSAI) introduced the FSS Labelling and Display (L & D) Regulations in 2020 under the Food Safety and Standards Act, 2006 (FSS Act). This landmark legislation marked a significant shift in the way food is labelled and marketed in India. By establishing stricter regulations and mandating the inclusion of comprehensive information on food packaging, the FSSAI aimed to empower consumers to make informed choices while also promoting fair competition within the food industry. This comprehensive review delves into the intricacies of the FSS Labelling and Display Regulations 2020. It explores the key provisions of the regulations, analyzes their impact on various stakeholders, and examines the challenges and opportunities associated with their implementation. By providing an in-depth analysis, this chapter aims to shed light on the significance of these regulations in shaping a more responsible and transparent food industry landscape in India.

Introduction

Food packaging materials development has been driven by the need to protect food products throughout distribution and storage. Nanotechnology offers opportunities to improve technical packaging features and develop sustainable smart packaging and sensors for monitoring product quality over time. However, the inherent permeability of conventional packaging materials to atmospheric gases and water vapour poses challenges in maintaining optimal conditions for food. The integration of nanotechnology into food packaging has emerged as a promising solution to address these challenges. Nanocomposite materials, composed of a polymer matrix and nanoscale fillers, offer a novel approach to enhancing packaging performance while addressing issues related to food spoilage, degradation, and safety.

Nanocomposite materials encompass a range of nanomaterials, including inorganic (i.e., metals and metal oxides), nanoclay, organic nanomaterials, and nanoemulsions (Huang et al., 2018; Jamaleddin et al., 2019; P. Kumar et al., 2020). NMs are used for three types of packaging: improved packaging, active packaging and intelligent packaging, Nanotechnology facilitates the development of improved bio-based packaging, enhancing mechanical strength and barrier performance while maintaining stability under varying environmental conditions (S. Kumar et al., 2020; Zhang et al., 2020). Active packaging harnesses nanostructures to encapsulate bioactive compounds, encompassing antimicrobials, antioxidants, and oxygen scavengers, which can interact with food and extend its shelf life (Motelica et al., 2020). Intelligent packaging releases active compounds in response to environmental triggers such as temperature or pH changes, transforming packaging into an intelligent, actively responsive material (Jamróz et al., 2019).

Introduction

A biopolymer is defined as a polymeric substance obtained from any living organism (plant or animal) [1]. These polymers are organic compounds where simpler molecules are covalently bonded with each other [2]. Although biopolymers are strictly synthesized naturally by living cells but some of them are also synthesized from non-biomaterial as well. Natural biopolymers are of different types based on their chemical nature like carbohydrate based, protein based or lipid based. Biopolymers can be broken down by the action of naturally-occurring organisms which leaves organic non-harming by-products like water and carbon dioxide in the environment[3].

Bio polymers are gaining importance in the field of food packaging, medical application, commodity packaging etc. because of their have specific physical, chemical, biological, biomechanical and degradation properties. Wide ranges of natural or synthetic biopolymers capable of undergoing degradation hydrolytically or enzymatically are being investigated for many applications[1]. Bio polymers are mainly based on two properties: a) Biological origin b) Biodegradability.

Earlier natural biopolymers such as cellulose, protein, starch have been used extensively for food applications. Recently, synthetic biopolymers such as polylactic acid (PLA), polycaprolactone (PCL), polyglycolic acid (PGA), polyvinyl alcohol (PVOH), and polybutylene succinate (PBS) are gaining more attention[4] for various applications. Natural biopolymers are more stereospecific and mostly hydrophilic having complex 3D structures as compared to the synthetic polymers[2]. Among the synthetic biopolymers some are microbiologically degradable in the environment whereas some are recyclable[1].

Introduction

The purpose of this e-book is to outline the main hazards in food production and processing that could influence the safety of foods and thus the health and wellbeing of consumers. The suggestive actions to restrain the formation of compounds or organisms that may threaten the safety of a food will be discussed along with the legal and regulatory framework.

“Safe Food Now for a Healthy Tomorrow”

Food is the third most basic human need, after air and water. Only when food is safe can it contribute to our food security and health. When food is not safe, people cannot thrive, hunger and poverty cannot be alleviated, and a healthy life is not possible. Food safety has a significant impact on human health, and food, which is essential for human survival, comes from plants and animals. Food safety is a core tenet of One Health.

This chapter gives an overview of the main hazards such as physical hazards, chemical hazards, biological hazards, and adulterants in different types of foods and how the hazards influence the safety of the food along with health and well-being of the consumers. The effective way of management of these hazards and different hazard limits set by the regulators such as FSSAI, USFDA, EU AND CODEX along with labelling requirements for the hazards has been discussed in this chapter.

Introduction

Packaging is an integral and pervasive part of contemporary world. Packaging makes material handling convenient, economical and effortless and modern consumer marketing will seem virtually impossible without packaging. For an engineer or food scientist, packaging is specialized arrangement of matrices fabricated for the delivery of safe food products with maintaining high quality and food safety, at every step of distribution chain including procurement of raw material to manufacturing of finished product; packaging of product; storage; transportation and distribution to wholesaler, retailer and consumer and even for recycling operations [17].

Packaging of food is imperative in a world dominated by marketing-based economy The fact that 73% of purchase decisions are made at point of sale highlighted the importance of a good package design in marketing. During scanning of food package, consumer made quick and rapid perception about the inclusion of a particular food based on the various verbal and nonverbal attributes embodied on food package [25]. Designing is an indispensable are of food packaging. It is medium to attract potential buyers and distinguished the product from the competitors. The presence of visual attributes on package design will not only ameliorates the food product and glamorizes the packets but also defines its authenticity and peculiarity. Therefore, a quality package design is characterized as communication channel between the manufacture and consumer, and unless performed correctly the market image of the brand and product suffers and influence consumer’s perception.

Food Contact Materials (FCM)

Before food consumption, during production, processing, preparation, packaging, packing, transportation, storage, serving etc. food comes in contact o many materials, all these materials are called food contact materials (FCM). FCM may be containers used for transportation for example milk container, machineries for its production or processing, packaging materials for its packaging like cans of soft drinks, kitchenware used for its cooking, serving, heating, washing. The selection of FCM requires intense care because FCM can affect human health and also the quality of food. During contact with food, molecules can migrate from FCM to food. Hence, FCM should have the following common attributes:

1. FCM should be compatible with the materials used for production, processing, transport, storage, serving etc.

2. FCM should be inert and non-reactive.

3. FCM should withstand the chemical, Mechanical and Thermal variations.

4. FCM should be clean, hygienic and tamper proof.

5. FCM should not have blisters, cracks, sharp edges and visible defects. 6. FCM should be free from rust.

Introduction

Packaging of food material is an essential component of food industry since packaging provides protection, physical tampering resistance and unique appearance to the food products which attracts the customers (Robertson, 2006). The handling of food products would be inefficient and costly if they are not packed properly (Robertson, 2006). The style and design of packaging influence their sale as well as demand. The main aim of packaging is to corroborate the safety and quality of food by preventing microbial contamination (Lee K.M, 2010). Plastics, papers, glass and metals are the common materials used for packaging of food products (Arvanitoyannis and Bosnea, 2004). Among these plastics are most commonly used packaging material because of their low cost, light weight, design freedom and high durability (British Plastic Federation). Various additives are added to the plastics to achieve desired physical and chemical properties. These additives are stabilizers, plasticisers, lubricants and f lame retardants. These additives have potential to transfer from the packaging materials to the food stuffs(K Bunia et al., 2013).

The efficient food packaging solutions are the need of the hour for the Earth. The food losses including the production, post harvest, processing stages of the supply chain and food wastage includes loss of edible food occurring at the f inal stages of food chain that is during retail supply or ultimate consumption. The food born illnesses cannot be ignored which are a consequence of the contamination of food by bacteria, viruses, parasites, new chemical entities or toxicants. We need to optimise the food supply chain, increase food shelf life and consciousness amidst food producers to food consumers. The active and intelligent packaging may help the globe through sufficient food for the increasing population. Scavengers/ absorbers are important solutions which may absorb substances from the packaging inner atmosphere (ethylene absorbers, oxygen scavengers; emitters and antioxidants).

Introduction

Food packaging is one of the most dynamic and fast-growing industries in the current scenario of increasing industrialization. With the constant upsurge in the food wastage at different stages of processing (suchas harvest, storage, processing, transportation, and distribution) leads to more than 15% of food produced ending up in the dumping grounds due to food spoilage caused by climatic conditions andmicroorganisms.Ever-increasing demands of consumers for convenient food makes packaging technology a need of the hour in order to keep the food safe, wholesome and of high quality at the same time.

So appropriate packaging has the potential of not only preventing spoilage but also taking care of healthand well-being of the individuals.Therefore, packaging plays the most important role in the overall safety of the food product.This makes packaging as the ever-evolving field since new requirements need new materials which demands new approaches and technology for better quality products.

By definition, Food packaging is a well-organized system of protecting the food product from any kind of physical, chemical, and biological damage in order to ensure that food reaches the consumer in its most safe condition at minimum applicable cost. It is bridge between production and consumption (Paine, 1992).

• General Consideration

• Post-mortem examination of large animals

• Post-mortem examination of poultry

• Steps in post-mortem examination

• Writing of post-mortem report

• Collection, preservation and dispatch of specimens for laboratory diagnosis

General Consideration

Necropsy is examination of animal after death also known as post mortem examination. It helps in diagnosis of diseases and their control. It is said that “Necropsy is a message of wisdom from dead to living”. Necropsy include systemic examination of dead animal, recording of pathological lesions, their interpretation to make diagnosis of disease. Sometimes it is difficult to arrive any conclusion merely based on gross examination of dead animal. Then one should seek the help of laboratory examinations such as Histopathology, Microbiology, Immunology and Toxicology for confirmation.