eChapters

Molecular biology is a branch of science that deals with understanding the biological activities at the molecular level. Molecular biologists are involved in understanding the concepts behind various intra and intercellular interaction of molecules, contributing to the knowledge about interrelationship of DNA, RNA and protein synthesis, i.e., how genes are transcribed into RNAs and how RNA is translated into protein, the phenomenon which is commonly known as “Central Dogma”stated by Francis Crick in 1956.

“The central dogma of molecular biology deals with the detailed residue-by-residue transfer of sequential information. It states that such information cannot be transferred back from protein to either protein or nucleic acid”-Francis Crick.

The branch of statistics which describes the data is called descriptive statistics. After collection, the data are presented in form of tables, diagrams or graphs. This facilitates the further analysis of data. The most basic form of data analysis is descriptive analysis of data collected and presented for the study. The descriptive statistics summarises the data and helps to find the representative value of the entire data set and the variation of the other values in the data set around the representative value. The descriptive statistics includes the measures of central tendency or averages, measures of dispersion or scatteredness, measures of skewness and the measures of kurtosis. Before going to discuss the R codes for various measures of descriptive analysis, we would first discuss in brief about these measure. This will help in better understanding of the R codes.

Measures of central tendency or averages: They are the representative values of the data series. They give an idea about the concentration of the values in the central part of the distribution of the data. There are five types of averages. They are 1. Arithmetic Mean (A.M.) 2. Geometric mean (G.M.) 3. Harmonic Mean (H.M.) 4. Median 5. Mode.

Diagrams and graphs are the effective and attractive ways of presenting data. Widely used diagrams for data presentation are pi chart and bar diagrams. Bar diagrams are also of various types; (i) Simple bar diagram (ii) Component or sub-divided bar diagram (iii) Multiple bar diagram (iv) Percentage bar diagram. The widely used graphical presentation are histograms, frequency polygon and frequency curve.

There are numerous libraries to create charts and graphs in R programming language.

Pie-chart- A pie-chart is a representation of values of variable as sectors of a circle with different colours/shadings. The colours/shadings used for different sectors are indexed at the side of the graph. pie() function is used to create pie chrt in R.

Let us create an exel file names as ‘exp_sports’ which contains the expenditure made (in Rs.) under various sports in a sports club. The name of the sports are cricket, hockey, tennis and football. The names of sports are placed under the column head ‘sports’. The corresponding expenditure (in Rs.) are 7200, 3600, 1800, 1800 and they are placed under the column head ‘expenditure’.

The basic syntax for creating a pie-chart using the R is.

Frequency Distribution is the arrangement of various values of a variable in order of magnitude either individually or in groups alongwith their corresponding frequencies or class frequencies. Frequency distribution is necessary for data condensation and revealing pattern within the data. Frequency distribution can be (i) Ungrouped Frequency Distribution (ii) Grouped frequency distribution.

In case ofungrouped frequency distribution, the individual values ofthe variable are arranged in ascending order alongwith their frequencies. Frequency is the number of times a particular observation is repeated.

In case of grouped frequency distribution, the values of variable are grouped into classes alongwith their corresponding class frequencies. Class frequency of a class is the number of observations lying within the upper class limit (maximum value) and lower class limit (minimum value) of the class.

Let us first illustrate the preparation of ungrouped frequency distribution. Consider 50 petridishes each containing 6 no.s of seeds for germination. Let the variable x_i denote the no. of seeds germinated in a petridish.

Matrix is a rectangular array of numbers arranged in rows and columns. The order of a matrix is written as r x c, where r is the no. of rows and c is the no. of columns. The numbers included in a matrix are called elements of the matrix. The name of the matrix is denoted by an uppercase English alphabet.

The most important use of R programming lies in importing of data files which serves as input for the analysis work. After the analysis is over by using R codes, operators and functions, the output result must also be exported in form of files. The files are imported in form of csv files (comma separated variable), text files or excel files.

Before going to the actual content of the chapter we have to have an idea about csv files. CSV stands for Comma Separated value. It is used to store tabular data, such as a spreadsheet or database. CSV is delimited text file in which the values are separated by commas. CSV files occupy much less space than excel files and also gets imported in a program at a much faster rate than Excel files. CSV Files also does not manipulate data and stores as it is.

Let us consider that an excel file named as ‘plant’ which stores three variables, named as ph, pd and yield is created inside the folder named as ‘My Data’ which is placed in the desktop. Thus the path of the file is “C:\\Desktop\\My Data\\plant”

To import excel file the package will be readxl and the command will be library(readxl)

In R there is facility of reshaping the data. Reshaping of data includes joining of two or more vectors to create a data frame. Also two or more data frames can be merged. Appropriate functions are available for these jobs. While merging the data frames, we can join columns or rows.

Illustration of joining two vectors by using cbind() function.

R packages include functions, codes and sample data. The functions used in R are contained in packages. A package in R contains several functions which are related to some particular type of job. A package conatins at least one function and there is no maximum limit to the no. of functions in a package. The set of packages in R which are set by default in the software is called base package. It contains a lot of commonly used functions. The packages in R are stored under a directory called “library” in the R environment. The packages get installed by default while installing R in the computer. Also more packages can be added later on after installation, when required for some specific purposes. The base packages are available by default when we start using R. But the other packages which are already installed while installing R have to be loaded while using R. These packages can be viewed in the package window by clicking on package. To install the package we have to click on install menu in the package window and then write the name of the package.

The packages can also be installed by using the function install.packages(“abc”) where abc is the name of the package to be installed.

Once a package is installed, it remains in the hard disk of the PC/laptop. But the package will have to be called for use in the current R session. The package once installed can be loaded for use in the current R session by checking the box near the name of the package displayed after clicking on the install menu in the Files/ Plots/Packages/Help window. The package can also be loaded by using library() function. The command will be library(“abc”) where abc is the name of the package. The loaded package remains in the memory for the current R session. Once we quit the R session, the installed package has to loaded again if needed.

This chapter deals with the objects used in R which contains the data in various formats. The data types used in R has also been mentioned in this chapter. The chapter also includes the functions used in R as the codes for accomplishing several jobs related to data analysis.

Unlike C language and Java, the variables in R are not declared as some data type. The variables are assigned with R object and the data type of R object becomes the data type of the variable. The commonly used R objects in R are vectors, lists, matrices, arrays, factors and data frames. The vector object is the simplest one and other R-objects are built upon the vectors. The different data types of these vectors are logical, numeric, integer, complex, character and raw. The objects in R are stored by the name of a variable and the data type of the object is determined by its content. To know the data type of a variable the class() function is used. The various data types are described as below:

R software is a programming language used for statistical analysis, graphical representation and reporting, and is currently developed by the R Development Core Team. R software is available freely under the GNU General Public License, and the binary versions are provided for the Windows, Linux and Mac operating systems. To develop R, effort from all over the world is made in a collaborative manner.

What is GNU?

GNU stands for GNU’s Not Unix. It is a Unix like computer operating system, but different from Unix. GNU consists of GNU packages which are program specific and released by GNU project. Free software means that the users of the software have freedom to run and use the software and also can copy, change, improve and distribute the software freely.

Development of R

R software was initially written by Robert Gentleman and Ross Ihaka also known as “R & R” of the statistics department of the University of Auckland, New Zealand. R appeared first in 1993. Since then various contribution to R has been made by a large group of talented individuals by sending code and bug reports. A core group, known as the “R Core Team” modify the R source code archive since 1997. Thus R is a collaborative project with many contributors.

Introduction

Natural evolution gifted the biological world a treasure of diverse bio-molecules that take part in various cellular activities. Proteins, one of the vital molecules of biological function are wisely folded polymers comprising 20 different aminoacids. Function of each protein is encoded in its aminoacid sequence. Aminoacid residues can indulge in bonded or non-bonded interactions depending on the environment. These inter residue interactions with in a polypeptide drive its folding in to a compact conformation from a linear molecule. Biochemical properties as well as the linear arrangement of the aminoacids determines the three dimensional structure of a protein. These determinants of defined structure directly or indirectly dictates functional fate of the folded protein also.

Introduction
Recently, there is a great need to analyze and exploit the huge amount of biological data information generated through high throughput modern technologies like phenotyping, allelic variation, gene expression, chromatography, DArT, molecular marker etc. Principal component analysis (PCA) has stronghold on modern data analysis - A black box that is widely used but poorly understood. The goal of this article is to dispel the magic behind this black box and to focus on building a solid intuition for how and why principal component analysis works in huge numbers of high throughput biological data set. It is a versatile and easy-to-use multivariate mathematical statistical method (Jolliffe et al, 2003) developed to extract maximal information from large data matrices containing numerous columns and rows. It also makes possible the elucidation of the relationship between the columns and rows of any data matrix without being one of the dependent variable. So the PCA is a projection method representing the original data in smaller dimensions.

A microarray, as the name suggests, is a two dimensional array of microscopic probes which captures certain molecules in an environment by a process known as hybridization, and are used to detect quantities of these molecules in the environment. The probes can vary according to requirement of experiment, and so can the environment, which in technical terms is an extract of tissue under study.

A simple random sample (SRS) of size n consists of n individuals from the population chosen in such a way that every set of n individuals has an equal chance to be the sample actually selected.

A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen. An example of a simple random sample would be the names of 25 employees being chosen out of a hat from a company of 250 employees. In this case, the population is all 250 employees, and the sample is random because each employee has an equal chance of being chosen.

The two-way ANOVA compares the mean differences between groups that have been split on two independent variables (called factors). The primary purpose of a two-way ANOVA is to understand if there is an interaction be- tween the two independent variables on the dependent variable. For example, you could use a two-way ANOVA to understand whether there is an interac- tion between gender and educational level on test anxiety amongst university students, where gender (males/females) and education level (undergraduate/ postgraduate) are your independent variables, and test anxiety is your depen- dent variable. Alternately, you may want to determine whether there is an in- teraction between physical activity level and gender on blood cholesterol con- centration in children, where physical activity (low/moderate/high) and gender (male/female) are your independent variables, and cholesterol concentration is your dependent variable.

The interaction term in a two-way ANOVA informs you whether the effect of one of your independent variables on the dependent variable is the same for all values of your other independent variable (and vice versa). For example, is the effect of gender (male/female) on test anxiety influenced by educational level (undergraduate/postgraduate)? Additionally, if a statistically significant interaction is found, you need to determine whether there are any “simple main effects”, and if there are, what these effects are (we discuss this later in our guide).

ANALYSIS OF VARIANCE

Analysis of Variance (ANOVA) is a hypothesis-testing technique used to test the equality of two or more population (or treatment) means by examining the variances of samples that are taken. ANOVA allows one to determine whether the differences between the samples are simply due to random error (sampling errors) or whether there are systematic treatment effects that cause the mean in one group to differ from the mean in another.

Most of the time ANOVA is used to compare the equality of three or more means, however when the means from two samples are compared using ANOVA it is equivalent to using a t-test to compare the means of independent samples.

ANOVA is based on comparing the variance (or variation) between the data samples to variation within each particular sample. If the between variation is much larger than the within variation, the means of different samples will not be equal. If the between and within variations are approximately the same size, then there will be no significant difference between sample means.

The chi square is a continuous distribution based on the assumption that the ul- timate class frequency is not less than 5 otherwise the value of χ₂ will be over- estimated and may cause too many rejections of null hypothesis. Therefore, to maintain the continuity of χ₂ and to draw the correct inference in 2×2 we apply a correction which is known as Yates’s correction for continuity.

CHI- SQUARE TEST (χ₂ TEST)

The chi square test is used to determine if the two attributes are independent of each other. Chi square is a measure to evaluate the difference between observed frequencies and expected frequencies to examine whether the difference so obtained is due to a chance factor or due to sampling error.

In a contingency table if each attribute is divided into two classes it is known as 2×2 contingency table. When one attribute is divided into two classes and another into r or c resultant contingency table is known as r×2 or 2×c contingency table. Here, r denotes the number of rows and c the number of columns. For such data, the statistical hypothesis under test is that the two attribute are independent of one another. To test this hypothesis we use the test statistic

STANDARD NORMAL DISTRIBUTION

If μ = 0 and σ = 1, the distribution is called the standard normal distribution or the unit normal distribution, and a random variable with that distribution is a standard normal deviate. The approximate test is given by