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We can categorize statistical theory into two general parts.

1. Firstly, there is descriptive statistics which uses the appropriate tools, typically tables, diagrams and/or numerical measures, to describe a data set and provide a summary of its distribution.

2. In addition, there is inferential statistics which is concerned with drawing conclusions about a population using information obtained from a representative sample selected from it.

(a) One aspect of statistical inference is the estimation of a population parameter by the appropriate sample statistic (e.g. the population mean by the sample mean).

(b) The second aspect of inferential statistics is hypothesis testing. In this case, we examine a hypothesis, framed in terms of the parameters in one or more populations.

Estimation is concerned with description whereas hypothesis testing is ultimately concerned with decision.

Basic concepts of hypothesis testing

Hypothesis testing is a process that is concerned with making conclusions about the population using the information obtained from its sample.

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.

To combat malnutrition and micronutrient deficiencies, nutrition-sensitive agriculture is a food-based strategy to agricultural development that emphasizes dietary diversity, fortification, and consumption of nutrient-rich foods. This strategy recognizes the importance of consuming a wide range of foods for optimal nutrition and acknowledges the social and economic significance of the food and agriculture industries in supporting rural livelihoods (WHO, 2014)

The overarching goal of nutrition-sensitive agriculture is to enhance the ability of the global food system to produce nutritious outcomes. An increasing number of governments, donor agencies, and development organizations are endorsing nutrition-sensitive agriculture as a means to achieve their developmental objectives. However, relying solely on nutrition-specific interventions falls short of meeting global targets for improving nutrition. Agriculture, with its significant potential to influence nutrition outcomes, must also play a role. 

Fisheries and aquaculture sector have been increasingly recognized for their essential contribution to global food security and nutrition. In 2020, total global catches in inland waters were 11.47 million tonnes and India stands top in the world with 1.8 million tonnes. India has witnessed remarkable growth in fish production in the last couple of years and stands second in world aquaculture production. The total fish production during 20-21 is estimated at 14.7 million metric tonnes (MMT) with a contribution of 11.25 MMT from inland sector and 3.48 MMT from marine sector. During FY 2020-21, export of marine products stood at 1.15 MMT and valued at Rs. 43,717.26 crores despite the market uncertainties raised by the Covid-19 pandemic outbreak. The inland open water resources of India are the life line of country?s vast population and provide nutritional and livelihood security besides other innumerable economic, social and ecological services. In addition to India, countries of Mekong cooperations including Myanmar, LaoPDR, Vietnam, Copyright: New India Publishing Agency, New Delhi, India. Commercial Use will call for Legal Action. Cambodia and Thailand contribute significantly to the Asian Fish production. As per FAO (2022) report, a number of Asian countries majorly contribute to the Inland capture fisheries production including India, Bangladesh, Myanmar and Cambodia have reported a steady or decline in fish catch, since the last few decades. Though there are several potential threats behind this declining fish production trend, major is linked to water availability, pollution, overfishing and climate change. 

India’s journey through the 75 years of independence and its splendid achievements are acclaimed by the Government of India through its initiative, Azadi Ka Amrit Mahotsav. Since independence, the nation has traversed a great distance and achieved feats in various spheres, such as agriculture, science, technology, art and culture, to name a few. Azadi Ka Amrit Mahotsav commemorates 75 glorious years of progressive India and its rich history, diverse population, magnificent culture and great achievements. The Hon’ble Prime Minister of India, Shri Narendra Modi’s, through this campaign, envisioned the foundation of a self-reliant India, and he said, “The Azadi Ka Amrit Mahotsav means elixir of energy of independence; elixir of inspirations of the warriors of freedom struggle; elixir of new ideas and pledges; and elixir of Aatmanir bharta. Therefore, this Mahotsav is a festival of awakening the nation a festival of fulfilling the dream of good governance, and a festival of global peace and development”

1 . The government of India, to celebrate the 75th anniversary of India’s independence, organised a series of events under the campaign Azadi Ka Amrit Mahotsav. 

In May 2020, The Government of India launched the flagship scheme called Pradhan Mantri Matsya Sampada Yojana (PMMSY), with an estimated investment of Rs. 20050 crores, comprising a Central share of Rs. 9407.00 crores, a state share of Rs 4880.00 crores, and a Beneficiary contribution of Rs. 5763.00 crores for its implementation during a period of 5 years from FY 2020-21 to FY 2024-25 in all States/Union Territories (Guidelines on Entrepreneurship Models in Fisheries and Aquaculture under PMMSY, 2020). The PMMSY will address critical gaps in fish production and productivity, quality, technology, traceability, post-harvest infrastructure, and management.

Madhya Pradesh has the highest population of Schedule tribes in India. With a population of 15,316,784, they occupy 21.1% of the state’s total population and 14.7% of the total tribal population of India. About 61% of the rural tribal population in Madhya Pradesh is living below the poverty line and is primarily relying on agriculture and allied industries for their livelihood (Planning Commission Report, 2010). But since the majority of them rely on unscientific subsistence farming, the income earned from such practices is very low. Apart from the higher poverty level, the nutrition levels in Madhya Pradesh also signify a grave situation. The state has one of the highest levels of anaemic children and women in India, and this incidence is highest in tribal regions of the state. The tribal regions of Madhya Pradesh have one of the highest percentages of malnourished children in India (UNICEF, 2019). The undernutrition and anaemia in tribes are primarily due to the lack of access to quality food. 

Ornamental fish breeding and culture: an innovative scheme for the development of rural women.” Funded by the Department of Biotechnology, Ministry of Science & Technology Govt. of India, New Delhi.

Selection of members and group formation

The location was selected to impart the training on ornamental fish culture, based on the PRA, group discussions, and meetings with NGOs, village panchayat authorities, and members of the area. Raichak, Kamar Pool, and Diamond Harbour Road were the working locations. Groups formed by identifying the interested women from the selected location. In each group, there are 25 women registered for the training. The selected members were introduced to the ornamental fish farms located at Amtala to appraise the working possibilities and viability of the activities.

Ornamental fish trade is a part of the culture of fisheries in India and is an important sector for livelihood and income generation, especially for women. Recent trends in production and demand share assume that during the next five years, domestic trade will double from the present. The growth of any business depends on technology, management, market, and infrastructure. The ornamental fish industry includes breeding of exotic live-bearer and egg layer fish, captive breeding of indigenous ornamental fish, the development of small-scale enterprises, backyard fish breeding and culture activities in rural areas, and ancillary units with high potential for large- scale exports as part of the multibillion-dollar global trade of the ornamental fish sector. Women are sensible and caring enough to take care of and nurture the small, tiny, colourful fish in their backyard units of ornamental fish. One of the important sectors of the ornamental fish industry is aquarium making and decoration, which is not only women friendly but also ensures earnings. 

The SCSP training programme on biofloc-based fish farming in Manipur aimed to promote entrepreneurship in fish farming by providing training on modern and innovative techniques. The training programme was sponsored by MANAGE, Hyderabad, and was conducted by two organisations in Manipur: AOC Manipur and Green Biotech Ecosolutions Pvt. Ltd. The programme was held over a period of three days at Khurkhul Village, Imphal West, Manipur. The programme focused on biofloc-based fish farming, which is an innovative and sustainable method of fish farming that uses microbial flocs as a source of nutrition for fish.

There are various training programmes being conducted in Tamil Nadu to promote seaweed cultivation and its various applications. The one-day SCSP training programme organised by ICAR-RVS KVK, Tiruneveli, Tamil Nadu, and the three-day SCSP training programme on seaweed for food and industrial application by Jehovah Shamma Aqua One Centre, both sponsored by MANAGE, Hyderabad, seem to have been well received by the coastal population of Tamil Nadu. The training programmes covered topics such as the status and distribution of seaweeds on the Indian coast, by-products from marine seaweeds, and nutraceutical products from marine seaweeds. These are important areas of knowledge that can help the coastal population explore the various opportunities available in seaweed cultivation and to utilise the seaweed species to their full potential.

A one -day SCSP training program was organised by Mitraniketan Krishi Vigyan Kendra (ICAR), Kerala on 17 December 2021. The training theme was “Market opportunities for value-added Fish Products.” 4 male and 46 female participants participated in the training program. The training was taken at KVK, Mitaraniketan, Kerala.

The sessions were oriented towards theory and practice. The training modules and session topics delivered on various value-added fishery products were arranged for the beneficiaries to transfer their expertise in fishery products and equip them to establish entrepreneurship in fish and fishery products and market the fishery products. In addition to providing financial support for women, the programme would also help pregnant women and adolescent girls with their nutritional needs