Today, we are living in the Information Age. We make many of our decisions, whether we intend to go out to sea to fish, buy a new computer, invest in projects, built a new resort, or even go to war, based on information that we gather. The more information we obtain, how fast we get them and how relevant they are will affect our decisions. However, more important than speed or amount of information is whether the information we got is real or reflects the truth or has been interpreted correctly. Unfortunatley, for various reasons, there are many information out there that is false, half-truths, misinterpreted or just made up, either intentionally or unintentionally. So how do we know that a certain information that we obtain is the truth? Is it the truth because Mr. X said so? Can we trust his words? Who is this Mr. X? Can we believe him just because he is the Prime Minister or President of the United States? How did he obtain this information in the first place? Has he got any ulterior motive feeding you with this information? So we start to doubt. But if we are going to doubt every information that comes, then we will have a serious problem making our day to day decisions.

## Science

There is a need for some mechanism where information generated from that mechanism has the highest probability of being true. This mechanism is called Science. Science comes from the Latin word “scientia” which means “knowledge”. So science is a system or mechanism of aquiring knowledge and is aimed at finding the truth. Scientists are in the business of generating new knowledge and it is important that the new knowledge refect what is true. That is why the scientific community demands that all scientists must possess a high level of integrity and honestly so that results from their research reflects the truth based on the facts gathered. If false information were allowed to be diseminated, in time, nobody will believe in information generated by the scientific community and that will be the end of science. To prevent this from happening, a set of guidelines were put in place to be followed by scientists in their acquisition of knowledge. It is thus very important for for young scientists to follow the Scientific Method in their research investigations.

As scientists, we also need to think scientifically. Our powers of reasoning must lead successfully to the most logical answers and reach reliable conclusions. Scientific thinking is based on three things i.e. the use of empirical evidence, practice logical reasoning and possessing a skeptical attitude. Empirical evidence is evidence that one can see, hear, touch, taste, or smell. It is evidence that others, besides yourself, can experience, and it is repeatable. Empirical evidence is the only type of evidence used by scientists to make decisions and reach sound conclusions. Logic is not an ability that we are born with. It is a skill or discipline that must be learned. Emotional, hopeful, and wishful thinking is more common than logical thinking because they are easier and more cogenial to human nature. Most individuals would rather believe something is true because they feel, hope, or wish it were true, rather than deny their emotions and accept that their beliefs are false. Possessing a Skeptical Attitude is to constantly question your beliefs and conclusions. Good scientists constantly examine the evidence, arguments and reasons for their beliefs. A skeptic holds beliefs only tentatively, and will willingly discard them if new evidence can prove otherwise. We must have an open mind.

## Scientific Method

Science is about discovering reliable knowledge about nature. Reliable knowledge is knowledge that has a high probability of being true because its veracity has been justified by a reliable method. The Scientific Method is a Process for evaluating knowledge to explain observable events in nature by natural causes without assuming the existence of the supernatural. Scientists use observations and reasoning to propose tentative explanations for natural phenomena, termed hypotheses. Predictions from these hypotheses are then tested by experiments, which should be reproducible. An important aspect of a hypothesis is that it must be falsifiable, i.e. it must be conceivable to prove the hypothesis to be false. Once a hypothesis is repeatedly verified through experiment, it is considered to be a theory and new predictions are based upon it. Scientific methods are means used by scientific communities for building supportable, evidence-based understandings of our natural world.

There are four essential elements within a scientific method :

Characterizations (quantifications, observations and measurements)

Hypotheses (theoretical, hypothetical explanations of observations and measurements)

Predictions (reasoning including logical deduction from hypotheses and theories)

Experiments (tests of all of the above)

A pragmatic scheme of the four above points is sometimes offered as a guideline for proceeding:

Define the question

Gather literature, information and resources

Form your hypothesis

Plan the experiment

Do the experiment and collect data

Analyze the observed data

Interpret data and draw conclusions that serve as a starting point for new hypotheses

Communicate your results

## Statistical Analysis

A very important component of the Scientific Method is the statistical analysis of your collected data or observations. How you analyse the data, whether done correctly or incorrectly, will ultimately determine the conclusions from your research. Any body who has to collect data, prepare reports, read reports and draw intelligent conclusions from them must have a good understanding of statistics. There is universal acceptance of statistics as an essential tool for all types of research. This has also resulted in an increase in the number and diversity of statistical procedures. Although this diversity indicates the availability of appropriate statistical techniques for most research problems, it also indicates the difficulty of matching the best technique to a specific experiment. Choosing the correct statistical procedure for a given experiment must be based on expertise in statistics and in the subject matter under study. Statistics, like any useful tool, can be misused either deliberately or by well-meaning researchers who know too little about research or statistical concepts and procedures.

## Why do we need Statistics?

Diversity is an intricate property of nature. It is with diversity that life on earth can continue to exist as it allows evolution and adaptation to the ever changing environment on earth. With diversity, there exist variation. Variation occurs everywhere and in almost everything. There is variation in height, weight, colour, smell, etc. Thus for every population, there is variation in physical, chemical and biological properties. As such, before we can say that there is a difference in a particular parameter between two population, we have to take into consideration this variation. We have to show prove that even with the variation that exist within each population for the parameter in question, it is still highly probable that differences exist between the two populations. Statistical procedures were developed to do just that. To take into account the variations before deciding whether we can safely say that the two populations are different. If there is no variation, there will be no need for statistics.

## Types of Statistics in Marine Science Research

There are basically two types of statistics

## a) Descriptive statistics.

Reduction of large masses of raw data to a manageable form – e.g. graphs, tables, measures of central tendency and measures of dispersion.

## b) Predictive statistics.

The data we collect is almost always a sample of all the data we could have collected, and we want to use it to draw conclusions about the whole population. The ability to make such generalised conclusions, inferring characteristics of the whole from characteristics of the sample lies within the realm of inferential or predictive statistics.

In Predictive Statistics, statistical analysis are usually conducted on the sampled evidence or data from which conclusions about the population is drawn. The statistical analysis usually starts with a hypothesis and based on the evidence in the data, the probability of a certain outcome of the hypothesis is determined.

## Hypothesis Testing

Hypothesis Testing is a means by which will help us make decisions concerning differences. It is a process of infering from a sample or samples whether or not to accept a certain statement about the population. The statement itself is called the hypothesis. The hypothesis is tested on the basis of evidence contained in the sample or samples. The hypothesis should be the simplest one possible with the least number of unknown factors. It is a prerequisite to the application of a statistical test.

## General procedure in statistical hypothesis testing.

## a) Specify a nul hypothesis (H0).

The hypothesis of no difference. The hypothesis that nothing out of the ordinary has happened or what is expected to happen according to some standard theory.

## b) Specify the alternate hypothesis (H1).

Example:

H0: There is no difference in growth of fishes fed with diet A and diet B.

H1: There is a difference in growth of fishes fed with diet A and diet B.

H0: The population sampled conforms to the Normal Distribution.

H1: The population sampled does not conform to the Normal Distribution.

H0: The two samples belong to the same population.

H1: The two samples come from different populations.

## c) Check data.

From the data, see which of H0 or H1 is correct.

The answer will either be

i) Not obvious

ii) Obvious

iii) Very obvious

Only in case i) do you go to do a statistical test. It is neither necessary or useful to do a lot of arithmetic to show something that was obvious before you started. Statistics is not a substitute for common sense.

## d) Specify the level of significance, .

Specify the critical probability level below which H0 will be rejected. It is conventionally taken to be 0.05 or 5% level of significance (or 95% confidence limits) in biological statistics.

In statistics, we are testing for differences. We first assume that there is no difference, H0. Then we test for difference, H1.

Hence, the level of significance is the maximum probability of rejecting a true null hypothesis ( 5% level of rejecting H0 ) when it is actually correct.

= probability of committing a Type I error (i.e. probability of rejecting H0 when it is actually correct).

= probability of committing a Type II error (i.e. probability of accepting H0 when it is actually not correct).

Null Hypothesis (H0)

## TRUE

## FALSE

## REJECT

Type I Error

Correct

## ACCEPT

Correct

Type II Error

It is better to commit a Type II error than a Type I error.

We will never know if we have committed a Type I error but then the probability of committing it is specified as < 5% (using a =0.05) or < 1% (using a = 0.01).

or,

What is the probability, p, of making the error of rejecting Ho when Ho is actually true ?

If p is very low then we reject Ho.

If p is high then we had better accept Ho.

How low should p be before we reject Ho ? is determined by the level of significance, a, set by us (usually 0.05).

## e) Calculate the probability, p.

Assuming that Ho is correct, calculate the probability, p, (using appropriate statistics) of obtaining results as extreme, or more extreme, than those observed.

There are several statistical tests available. In order to select, we consider several properties of the various tests e.g.

i) Are the assumptions of these tests valid assumptions in my experiment ? Criticisms on an experiment is often highest due to lack of consideration of the assumptions.

ii) The test should be unbiased and consistent.

iii) The test should be more efficient in some sense than the other tests.

## f) Comment.

We rarely have enough training or knowledge to thoroughly understand all the possible violations of assumptions inherent in the design and analysis of their research, although they are most surely aware of the hypothesis they are trying to test.

## Types of Statistical Tests

Various types of statistical tests are available. However, we can generally divide them into Parametric and Non-parametric tests.

## a) Parametric test

For making inferences about population parameters by examining sample statistics. Assumes that the variable in question follows (at least approximates) the normal distribution. For interval and ratio scale data.

## b) Data transformation

Generally to normalise data which do not satisfy the above assumption so that they may be analysed using parametric methods.

## c) Nonparametric test

To draw inferences about population, not parameters. Do not require knowlegde about population distribution (distribution free statistics). Fast with less arithmetic but less powerful than parametric tests. For norminal and ordinal scale data. Note that interval and ratio scale data can be converted to ordinal data by ranking.

## Examples of parametric tests

## a) Testing differences between two means.

## 1) Z-test

Where population variance, S, is known.

## 2) Student’s t-test (One and two samples)

Where the estimate s must be used.

## 3) Paired sample t-test

For paired samples.

## b) Testing differences between a set of sample means.

## 1) One-way ANOVA.

## 2) Two-way ANOVA with and without replications.

## 3) Multi-way ANOVA.

## 4) Latin-Square.

## 5) Multiple comparisons.

## a. Least Significant difference, LSD.

## b. Tukey Test.

## c. Student-Newman-Keuls Test.

## d. New Duncan’s Multiple Range Test.

## e. Trend comparisons

## c) Testing differences between variances.

## 1) F-test

## 2) Bartlett’s test

## d) Correlation and regression analysis

## Examples of Non-parametric tests

## a) Runs test

Test for randomness in a linear sequence of nominal data.

## b) Chi-square Goodness-of-fit test

Test or compare observed frequency distribution with predicted/theoretical frequency distribution.

## c) Homogeneity Chi-square test and Contingency tables

Test or compare 2 observed frequency distributions.

## d) Kolmogorov-Smirnov test

Goodness-of-fit test for ordinal scale data. Uses cumulative frequency data rather than Chi-square. Powerful where n is small, Fi is small.

## e) Mann-Whitney U-test

Nonparametric procedure anologous to 2 sample students t-test.

## f) Wilcoxon’s paired sample test

Nonparametric procedure anologous to paired sample t-test.

## g) McNemar’s test

Paired sample testing of nominal data.

## h) Kruskal-Wallis test

Nonparametric One-way ANOVA by ranks.

## i) Freidman’s test

Nonparametric randomised block design by ranks.

## j) Spearman’s Rank Correlation

Nonparametric correlation on ordinal data.

## Multivariate Statistics

Most of the Statistical methods mentioned above are termed as Univariate statistics because they examine only one variable while the other are treated as treatment groups of factors. However, there is an increasing use of Multivariate Analysis where the procedure will examine a number of variables at once largely to detect patterns, relationships and interactions between them. Some of the most commonly used multivariate procedures include:

a) Multiple regression and correlation.

Where one wishes to establish maximal linear relationships among three or more sets of variables.

b) Principal Component Analysis.

To reduce the dimensionality of the original data while minimizing loss of information and determining those that account for most of the variation in the population.

c) Factor Analysis.

Resolve the intercorrelations among variables into their underlying causes.

d) Multivariate analysis of variance.

To determine if the samples could have been drawn from a single statistical population.

e) Discrimant Analysis.

To sort the objects into their appropriate populations with minimal error.

f) Cluster analysis.

To sort previously unpartitioned heterogeneous collection of objects into a series of sets and determine the relation ships between the sets.