**Statistics**

Statistics is defined as a body of methods for making reasonable and wise decisions in the face of uncertainty. These are used in the analysis of numerical data of various aspects including interpretation of data on the basis of certain statistical principles.

**Statistics** is a field of study concerned with techniques or methods of collection of data, classification, summarizing, interpretation, drawing, inferences, testing of hypothesis, making recommendations etc. only when a part of data is used.

**Biostatistics or Biometry**

**Biostatistics** is the term referred when tools of statistics are applied to the data that is derived from biological sciences. In other words when the principles of statistics are applied to study of organisms or living system, the study is called **biostatistics** or **biometry**.

It encompasses the design of biological experiments, especially in medicine, pharmacy, agriculture and fishery; the collection, summarization, and analysis of data from those experiments; and the interpretation of, and inference from the obtained results.

**Scope of Statistics**

1. In Physiology and Anatomy

- To define what is normal or healthy in a population and to find limits of normality in variables such as weight & pulse rate.
- To find the difference between means and proportions of normal at two places or in different periods. The mean height of Bangladeshi boys is less than the mean height of American boys . Whether this difference is due to chance or a natural variation or because of some other factors such as better nutrition playing a part, has to be decided.
- To find the correlation between two variables X and Y such as height & weight whether weight increases or decreases proportionately with height & if so by how much has to be found.

2. In Pharmacology

- To find the action of drug. For examples,a drug given to animals or humans to see whether the changes produced are due to drug or by chance
- To compare the action of two different drugs or two successive dosages of the same drug.
- To find the relative potency of a new drug with respect to a standard drug.

3. In Medicine

- To compare the efficacy of a particular drug, operation or line of treatment . For example, the percentage cured,relieved or died in the experiment & control groups is compared & difference due to chance or otherwise is found by applying statistical technique.
- To find an association between two attributes such as cancer & smoking -an appropriate test is applied for this purpose.
- To identify sign & symptoms of a disease or syndrome . Cough in typhoid is found by chance and fever is found in almost every case . The proportional incidence of one symptom or another indicates whether it is a characteristic feature of the disease or not.

4. In Community Medicine & Public Health

- To test usefulness of vaccines in the field – percentage of attacks or deaths among the vaccinated subjects is compared with that among the non-vaccinated ones to find whether the difference observed as statistically significant .
- In epidemiological studies – the role of causative factors is statistically tested . Deficiency of iodine as an important cause of goitre in a community is confirmed only after comparing the incidence of goitre cases before and after giving iodised salt.

**Reference:**

1. Mahajan BK 2002 (Methods in Biostatistics) (6th edition)

2. Zaman SM, HK Rahim and M Howlader 1982. (Simple Lessons from Biometry), BRRI

3. Class Note.

**Variable**

In statistical language any character, characteristic or quality that varies is called **variable**.

A characteristic that takes on different values in different persons, places or things such as height, weight, blood pressure, age etc is variable. It is denoted usually as “x”.

**Characteristics**

- Variable is usually represented by x. Such as x
_{1 }x_{2 }x_{3 ……… }x_{n }, where number of variable is n and individual variable is x. - Variation is created due to genetic recombination.
- Variation can be caused by both artificial and natural mutation.

**Random variable**

**Random variable** is a variable whose value is a numerical outcome of a random phenomenon. For example: Flip three coins and let x represent the number of heads. Here, x is a **random variable**.

**Random variable** is not a probability. Its value doesn’t need to be positive or between 0 and 1 as in the case of probability.

Variables can be of two types:

**Qualitative or Discrete Data or, Variable
**

**Quantitative or Continuous Data or, Variable**

**Qualitative or Discrete Data or, Variable**

**Qualitative Data** are classified by counting the individuals or things having the same characteristic or attribute; and not by measurement. Examples:

- The number of cars in a parking lot,
- Number of quarters in a purse, jar, or bank,
- Ages on birthday cards (always in discrete number like 21 years old) etc.

Individuals with the same characteristic are counted to form specific groups or classes.

**Qualitative data** are discrete in nature, such as, number of deaths in different years, population of different towns, persons with different blood groups in a population.

**Characteristics**

- Discrete variables have no continuity. So, they are also called qualitative variables.

**Quantitative or Continuous Data or, Variable**

A continuous variable is a variable that has an infinite number of possible values. In other words, any value is possible for the variable.

A continuous variable doesn’t have to have every possible number (like -infinity to +infinity), it can also be continuous between two numbers, like 1 and 2. For example, data of a discrete variable could be 1, 2 while the continuous variables could be 1, 2 and also everything or anything in between: 1.00, 1.01, 1.001, 1.0001…

Examples

- Time it takes a computer to complete a task,
- A person’s weight,
- Age etc.

The weight of students from 2nd year are (in kg) 40.9, 45, 55, 50.1, 53, 54, 54, 48, 48.5, 46, 70, 85, 82, 83.1, 62.5 etc.(See how the number varies within a range)

In case of quantitative/continuous data there are two variables- the characteristics such as height & the frequency. We find the characteristic as well as the frequency both vary from person to person as well as from group to group.

The quantitative data obtained from characteristic variable (e.g. height of individuals in 2nd year) are called continuous data because each individual has one measurement from a continuous spectrum or range.

Some of the statistical methods employed in analysis of quantitative data are mean, range, standard deviation, coefficient of variation etc.

Discrete Variable or, Data | Continuous Variable or,Data |

A variable that can take only certain values. | A variable which can take any value in a particular limit. |

Deals with descriptions. | Deals with numbers. |

Data can be observed but not measured. | Data which can be measured. |

Leaf color, blood group, inherited diseases due to single mutation etc. Example: The blood group for students of 2nd year in Department of Botany is - 25 has O group.
- 20 has A group.
- 10 has B group.
- 3 has AB group of blood.
| Length, width, area, volume, weight, speed, time, temperature, humidity, sound levels, cost, numbers, ages etc. Example: The weight of students from 2nd year are (in kg) 40.9, 45, 55, 50.1, 53, 54, 54, 48, 48.5, 46, 70, 85, 82, 83.1, 62.5 etc. (See how the number varies within a range) |

Qualitative-Quality | Quantitative-Quantity |

**References**

Mahajan BK 2002. (Methods in Biostatistics) (6th Edition)

**Variation **

- Morphological variation
- Genetic variation

Based on continuity of traits in genetics, variation can be two types:

- Qualitative variation
- Quantitative variation

**Qualitative variation/traits**

A qualitative trait is expressed qualitatively, which means that the phenotype falls into different categories. E.g. If a species of plant had either red leaves or yellow leaves, and nothing in between, this would be a discrete trait, ABO blood group, Inherited diseases caused by single mutation etc.

- These categories do not necessarily have a certain order.
- Qualitative characters have limited variation.
- “Yes or no” traits, traits where an organism either has the trait or doesn’t, also fit into this category
- Usually, a single gene (monogene) or small group of genes (oligogene) control qualitative traits E.g. height, intelligence, skin color, shape, scent etc.
- Mode of inheritance is simple Mendelian (monogenic usually).
- The environment has very little influence on the phenotype of these traits.

**Quantitative variation/traits**

- Quantitative traits occur as a continuous range of variation. This means that these traits occur over a range.
- Generally, a larger group of genes control qualitative traits. So, also called polygenic traits.
- Unlike qualitative traits, these traits cannot be distinctly classified.
- g. animal’s metabolism, milk yield, growth rate, nutrient factors etc.
- Mode of inheritance is complex (polygenic).
- Environment affects quantitative traits largely.
- The phenotype values for a population will typically have a normal distribution.
- One and a few crosses don’t change the quantitative traits as they are controlled by many genes.
- Additive effect or cumulative effect is observable here.
- The variation among the individuals in a population is present in small fragments.

**Some Random Things (Good to know)**

- F2 progenies are highly segregated.
- F2 progenies have all parental characters.
- Causes of segregation or variation in progeny are meiosis, crossing over and recombination.
- In
**linkage or linked genes**, no crossing over takes place. So, generation after generation, the characters are conserved. - Example: Tallness and red colored genes have linkage.
- Phenotype = Genotype + Environment i.e. P = G + E
- Amount of variation is variance.
- Variance is never negative but it can be zero.
- Phenotypic variance = Genotypic variance + Environmental variance i.e. V
_{p }= V_{G}**+**V

V_{G} more, V_{E} less

V_{G} less, V_{E} more.

This is a very important concept especially in breeding science which asks how much genotypically developed a hybrid is.

- The hybrid must be developed genotypically (V
_{G}more). - Cross pollination is a kind of hybridization.

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