eChapters

Frequency Distribution: A tabular presentation of the data in which the fre- quencies of values of a variable are given along with them is called a frequen- cy distribution. Two types of frequency distribution are available

1. Discrete Frequency Distribution or Ungrouped Frequency Distribution
2. Continuous Frequency Distribution or Grouped Frequency Distribution

Objective (a): Prepare a discrete frequency distribution from the following sentence in English: “Today there is hardly a phase of Endeavour which does not find statistical devices at least occasionally useful.”

Theory: This problem relates to discrete frequency distribution i. e. a frequency distribution which is formed by distinct values of a discrete or continuous variable.

Measures of Central Tendency

The term ‘Mean” or ‘average’ is something, we have been familiar with from a very early age when we start analyzing our marks on report card. We add together all of our test results and then divide it by the sum of the total number of marks there are. We often call it the average. However, statistically it’s the Mean!

The Median is the ‘middle value’. When the totals of the list are odd, the me- dian is the middle entry in the list after sorting the list into increasing order. When the totals of the list are even, the median is equal to the sum of the two middle (after sorting the list into increasing order) numbers divided by two. Thus, remember to line up values, the middle number is the median!

The Mode in a list of numbers refers to the list of numbers that occur most frequently. A trick to remember this one is to remember that mode starts with the same first two letters that most does. Most frequently - Mode.

MEAN DEVIATION

The mean deviation is the first measure of dispersion that we will use that ac- tually uses each data value in its computation. It is the mean of the distances between each value and the mean. It gives us an idea of how spread out from the center the set of values is.

The mean deviation is based on all the observations, a property which is not possessed by the range and the quartile deviation. The formula of the mean de- viation gives a mathematical impression that is a better way of measuring the variation in the data. Any suitable average among the mean, median or mode can be used in its calculation but the value of the mean deviation is minimum if the deviations are taken from the median.

MOMENTS

The term moment in mechanics refers to the measure of a force with reference to its tendency to produce rotation. The strength of this tendency is depen- dent upon the amount of the force and the distance from the origin at which the force is applied. If on both the sides of the origin the force are equal than there will be a balance, at a balanced position the positive product equals the negative product.

Moment is used in Statistics in a quite analogous sense. The class frequencies are looked upon as the forces and the deviations of the different values from the mean are taken as the distances. In other words, moment is the mean of the first, second, third, fourth, etc. powers of deviations of the different values from the arithmetic mean. The first moment about the mean is always zero and second moment about the mean is variance.

If the moment calculated from arithmetic mean are called central moments and denoted by μ with a subscript which indicate the order of the moment. Moments are the mean values of powers of the deviations in any frequency distribution taken about three points

SKEWNESS

Skewness means lack of symmetry. Skewness denotes the tendency of a distri- bution to depart from symmetry. A frequency distribution is said to be skewed if the frequencies decrease with markedly greater rapidity on one side of the central maximum than on the other side. This characteristic of a frequency distribution is known as skewness and the measures of asymmetry are usually called measures of skewness.

The main object of measuring skewness is to know the direction of the varia- tion from an average and to compare the frequency distribution and the shape of their curves.

There are two types of skewness

(i) Positive Skewness (ii) Negative Skewness

KURTOSIS

Kurtosis refers to the extent to which unimodal frequency curve is peaked. Kurtosis is a measure that refers to the peakedness of the top of the curve. Kurtosis gives the degree of flatness in the region about the mode of a frequency distribution.

Types of Kurtosis

There are three categories of kurtosis that can be displayed by a set of data. All measures of kurtosis are compared against a standard normal distribution, or bell curve.

The first category of kurtosis is a mesokurtic distribution. This type of kurtosis is the most similar to a standard normal distribution in that it also resembles a bell curve. However, a graph that is mesokurtic has fatter tails than a standard normal distribution and has a slightly lower peak. This type of kurtosis is considered normally distributed but is not a standard normal distribution.

The second category is a leptokurtic distribution. Any distribution that is leptokurtic displays greater kurtosis than a mesokurtic distribution. Characteristic of this type of distribution is one with extremely thick tails and a very thin and tall peak. The prefix of “lepto-” means “skinny,” making the shape of a leptokurtic distribution easier to remember. T-distributions are leptokurtic.

The final type of distribution is a platykurtic distribution. These types of distributions have slender tails and a peak that’s smaller than a mesokurtic distribution. The prefix of “platy-” means “broad,” and it is meant to describe a short and broad-looking peak. Uniform distributions are platykurtic.

CORRELATION

In case of bivariate or multivariate normal distributions, we may be interested in discovering and measuring the magnitude and direction of the relationship between two or more variables. For this purpose we use correlation. The sys- tematic interrelationship between the variables is termed as correlation. When only two variables are involved the correlation is known as simple correlation. If more than two variables are involved the correlation is known as multiple correlation. An increase in one variable may cause an increase in the other variable, or a decrease in one variable may cause a decrease in the other vari- able, then they are said to be positively correlated. If a decrease in one variable causes an increase in the other variable or vise versa, the variables are said to be negatively correlated.

REGRESSION

Regression means to revert or return back. The term was first introduced by Sir Francis Galton in1877. Regression technique is applicable in all those fields where two or more relative variables have the tendency to go back to the mean. Regression analysis refers to the methods by which estimates are made of the values of a variable from the knowledge of the values of one or more other variables and to the measurement of the errors involved in this estimation pro- cess.

In statistical modeling, regression analysis is a statistical process for estimat- ing the relationships among variables. It includes many techniques for mod- eling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. Regres- sion analysis helps one understand how the typical value of the dependent variable (or ‘criterion variable’) changes when any one of the independent variables is varied, while the other independent variables are held fixed. Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables – that is, the average value of the dependent variable when the independent variables are fixed.

t TEST FOR SINGLE MEAN

A t-test is any statistical hypothesis test in which the test statistic follows a Student’s t distribution if the null hypothesis is supported. It can be used to determine if two sets of data are significantly different from each other, and is most commonly applied when the test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known. When the scaling term is unknown and is replaced by an estimate based on the data, the test statistic (under certain conditions) follows a Student’s t distribution.

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

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 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).

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.

In any organism and biomolecules (enzyme, proteins, etc.), most biological activities could be seen only within a narrow environmental conditions. Therefore in order to carry out a successful experiment, from cell culturing to DNA sequencing or assessing an enzyme’s activity, one has to pay utmost attention in calculating correct reaction components.

A solution is defined as a homogenous mixture of solute and solvent. In this case the amount solute is less as compared to the solvent. It is not always necessary that solvent is liquid and solute is solid. There are several examples where solute and solvents are found in other physical states such as gas or solids. For example, carbonated water CO₂ is solute and water is solvent; and smoke is solution of different smoke particles (solute) in air (solvent). The concentration of solution is described as amount of solute in a given volume of solvent. Several ways are there to express the concentration of a solution, such as molarity, normality, molality, and ppm. In this chapter we would discuss the general terms used in making solutions and a brief introduction about buffer solutions.

Molecular diagnostic laboratory set-up has basic requirements of space, laboratory benches and equipments. In terms of laboratory space, minimum four chambers, one each for sample preparation and nucleic acid extraction, PCR reaction mixture preparation, thermal cycling and gel analysis are required. In addition there should be sufficient space for storage of consumables and laboratory wares. In addition, there are some laboratory equipments which are needed in a molecular diagnostic laboratory. In the following section the equipments of a molecular diagnostic laboratory are discussed. The pictures are taken from the instruments present in the laboratory of the author. The purpose of this chapter is to introduce the reader to a molecular diagnostic laboratory. None of the pictures below are meant for promotion of any particular brand or manufacturer.

3.1 UV-VIS spectrophotometer

A spectrophotometer is required for determining the quality and quantity of nucleic acids extracted from a sample. Photometric research applications such as DNA, RNA and protein analysis can be carried out in a UV-Vis Spectrophotometer. There are various units that feature a broad wavelength range (including UV area), path length correction and a fast reading speed. Various instruments also provide an interface that allows quick measurements directly from the instrument or comprehensive easy-to use software for demanding assays.

Nucleic acid extraction from clinical samples is the first step to be followed in molecular detection of cancer. Nucleic acids are the starting material for all downstream molecular diagnostic tools. Quality of test results largely depends upon the quality of starting material. Thus utmost importance should be given to the extraction protocols to isolate good quantity and good quality nucleic acids from patient samples.

Basic principle: The basic principle of nucleic acid extraction is to disrupt cell membrane and nuclear membrane to release and precipitate nucleic acid in the solution. Following precipitation,removal of other cellular contaminates such as protein, lipids, polysaccharides etc is performed to obtain a good quantity and quality of nucleic acid.

5.1 Purpose

To employ a standard protocol to perform agarose gel electrophoresis.

5.2 Principle

Agarose gel electrophoresis is the most effective way of separating DNA fragments of varying sizes ranging from 100 bp to 25 kb. Migration rate of DNA molecule depends on various factors like 1) size of DNA molecule; 2) agarose concentration; 3) DNA conformation 4) voltage applied, 5) presence of ethidium bromide, 6) type of agarose and 7) electrophoresis buffer. After separation, the DNA molecules can be visualized under UV light.

6.1 Designing primers

Designing correct primers are very important to get the expected result in PCR experiment. There are two primers (Forward & Reverse) required for the amplification of the desired DNA fragment. One primer should anneal to the sense strand (oriented to the 5'→3' direction) and another primer should complement the antisense strand (oriented in the 5'→3' direction).

There are various characteristics to be considered to design a good primer including Tm, length, GC content, secondary structure and specificity.

There are commercially available softwares besides free online tools at NCBI (primer blast) for designing PCR primers. In addition, primer sequences published in peer reviewed literature can also be used.

7.1 Basic concept

What is DNA sequencing?

The genome of any biological organism is a sequence of nucleotides arranged in a specific manner. The nucleotides are chemically a base which usually exists in 4 different forms; Purine – Adenine (A) and Guanine (G) and Pyramidine – Cytosine (C) and Thymine (T). These four nucleotides make up an entire sequence of Deoxyribose Nucleic Acid (DNA) which is encodes the information of any cell in the form of a gene. The genome, therefore, is the complete set of all genes that is required to build and maintain that organism. DNA sequencing is the process wherein the precise order of these nucleotides along the gene is detected and analysed which includes any method or technology that assists in determining the sequence.

For RT-PCR, the extracted total RNA is first reverse transcribed to cDNA using reverse transcriptase enzyme. Following are the protocols for cDNA sysnthesis and RT-PCR.

Note: cDNA synthesis and RT-PCR can be performed according to the manufacturer protocol from where the specific reagents for the above methodologies are purchased.

8.1 Purpose

To lay down a uniform protocol for the synthesis of c-DNA from total RNA

8.2 Scope

The scope of this Standard Operating Procedure is to lay down a standard procedure for the synthesis of c-DNA from total RNA