Monday, April 26, 2010


By Siddharth Kalla (2009)

n statistics, confidence interval refers to the amount of error that is allowed in the statistical data and analysis.

Since statistics uses a sample space and predicts the trends for the whole population, it is quite natural to expect a certain degree of error and uncertainty. This is captured through the confidence interval.

You will frequently encounter this concept while looking at survey results, which take the data of a few people and extend it to the whole group.

Suppose the survey shows that 34% of the people vote for Candidate A. The confidence that these results are accurate for the whole group can never be 100%; for this the survey would need to be taken for the entire group.

Therefore if you are looking at say a 95% confidence interval in the results, it could mean that the final result would be 30-38%. If you want a higher confidence interval, say 99%, then the uncertainty in the result would increase; say to 28-40%.

The confidence interval depends on a variety of parameters, like the number of people taking the survey and the way they represent the whole group.

For most practical surveys, the results are reported based on a 95% confidence interval. The inverse relationship between the confidence interval width and the certainty of prediction should be noted.

In normal statistical analysis, the confidence interval tells us the reliability of the sample mean as compared to the whole mean.

For example, in order to find out the average time spent by students of a university surfing the internet, one might take a sample student group of say 100, out of over 10,000 university students.

From this sample mean, you can get the average time spent by that particular group. In order to be able to generalize this to the whole university group, you will need a confidence interval that reflects the applicability of this result for the given sample of students to the whole university.

The size of this interval naturally depends on the type of data and its distribution.

For sufficiently large values of sample size, it can be mathematically shown through the central limit theorem that the distribution is approximately normal distribution. In such a case, the 95% confidence level occurs at an interval of 1.96 times the standard deviation.



by Martyn Shuttleworth (2009)

Often, one of the trickiest parts of designing and writing up any research paper is how to write a hypothesis.

The entire experiment and research revolves around the research hypothesis (H1) and the null hypothesis (H0), so making a mistake here could ruin the whole design.

Needless to say, it can all be a little intimidating, and many students find this to be the most difficult stage of the scientific method.

In fact, it is not as difficult as it looks, and if you have followed the steps of the scientific process and found an area of research and potential research problem, then you may already have a few ideas.

It is just about making sure that you are asking the right questions and wording your hypothesis statements correctly.


Often, it is still quite difficult to isolate a testable hypothesis after all of the research and study. The best way is to adopt a three-step hypothesis; this will help you to narrow things down, and is the most foolproof guide to how to write a hypothesis.

Step one is to think of a general hypothesis, including everything that you have observed and reviewed during the information gathering stage of any research design. This stage is often called developing the research problem.


A worker on a fish-farm notices that his trout seem have more fish lice in the summer, when the water levels are low, and wants to find out why. His research leads him to believe that the amount of oxygen is the reason – fish that are oxygen stressed tend to be more susceptible to disease and parasites.

He proposes a general hypothesis.

“Water levels affect the amount of lice suffered by rainbow trout.”

This is a good general hypothesis, but it gives no guide to how to design the research or experiment. The hypothesis must be refined to give a little direction.

“Rainbow trout suffer more lice when water levels are low.”

Now there is some directionality, but the hypothesis is not really testable, so the final stage is to design an experiment around which research can be designed, a testable hypothesis.

“Rainbow trout suffer more lice in low water conditions because there is less oxygen in the water.”

This is a testable hypothesis – he has established variables, and by measuring the amount of oxygen in the water, eliminating other controlled variables, such as temperature, he can see if there is a correlation against the number of lice on the fish.

This is an example of how a gradual focusing of research helps to define how to write a hypothesis.


Once you have your hypothesis, the next stage is to design the experiment, allowing a statistical analysis of data, and allowing you to test your hypothesis.

The statistical analysis will allow you to reject either the null or the alternative hypothesis. If the alternative is rejected, then you need to go back and refine the initial hypothesis or design a completely new research program.

This is part of the scientific process, striving for greater accuracy and developing ever more refined hypotheses.



by Martyn Shuttleworth (2008)

The null hypothesis, H0, is an essential part of any research design, and is always tested, even indirectly.

The simplistic definition of the null is as the opposite of the alternative hypothesis, H1, although the principle is a little more complex than that.

The null hypothesis is a hypothesis which the researcher tries to disprove, reject or nullify.

The 'null' often refers to the common view of something, while the alternative hypothesis is what the researcher really think is the cause of a phenomenon.

An experiment conclusion always refers to the null, rejecting or accepting H0 rather than H1.

Despite this, many researchers neglect the null hypothesis when testing hypotheses, which is poor practice and can have adverse effects.


A researcher may postulate a hypothesis:

H1: Tomato plants exhibit a higher rate of growth when planted in compost rather than in soil.

And a null hypothesis:

H0: Tomato plants do not exhibit a higher rate of growth when planted in compost rather than soil.

It is important to carefully select the wording of the null, and ensure that it is as specific as possible. For example, the researcher might postulate a null hypothesis:

H0: Tomato plants show no difference in growth rates when planted in compost rather than soil.

There is a major flaw with this null hypothesis. If the plants actually grow more slowly in compost than in soil, an impasse is reached. H1 is not supported, but neither is H0, because there is a difference in growth rates.

If the null is rejected, with no alternative, the experiment may be invalid. This is the reason why science uses a battery of deductive and inductive processes to ensure that there are no flaws in the hypotheses.

Many scientists neglect the null, assuming that it is merely the opposite of the alternative, but it is good practice to spend a little time creating a sound hypothesis. It is not possible to change any hypothesis retrospectively, including H0.


If significance tests generate 95% or 99% likelihood that the results do not fit the null hypothesis, then it is rejected, in favor of the alternative.

Otherwise, the null is accepted. These are the only correct assumptions, and it is incorrect to reject, or accept, H1.

Accepting the null hypothesis does not mean that it is true. It is still a hypothesis, and must conform to the principle of falsifiability, in the same way that rejecting the null does not prove the alternative.


The major problem with the null hypothesis is that many researchers, and reviewers, see accepting the null as a failure of the experiment. This is very poor science, as accepting or rejecting any hypothesis is a positive result.

Even if the null is not refuted, the world of science has learned something new. Strictly speaking, the term ‘failure’, should only apply to errors in the experimental design, or incorrect initial assumptions.


Up until the 1500's most people thought that the world was flat (At the time: The null hypothesis). Columbus challenged this idea with the alternative hypothesis: The world is round. Then most people thought that the earth was the center of the universe (The 'new' null hypothesis).

Copernicus had an alternative research hypothesis that the world actually circled around the sun, thus being the center of the universe. Eventually, people got convinced and accepted it as the null.

Later someone proposed an alternative hypothesis that the sun itself also circled around the something within the galaxy. This is how research works - the null hypothesis get's closer to the reality each time, even if it isn't correct, it is better than the last null hypothesis.



Shuttleworth, Martyn (2008). Null Hypothesis. Retrieved [Date of Retrieval] from Experiment Resources:

What is a Research Hypothesis

by Martyn Shuttleworth (2008)

A research hypothesis is the statement created by a researcher when they speculate upon the outcome of a research or experiment.

Every true experimental design must have this statement at the core of its structure, as the ultimate aim of any experiment.

The hypothesis is generated via a number of means, but is usually the result of a process of inductive reasoning where observations lead to the formation of a theory. Scientists then use a large battery of deductive methods to arrive at a hypothesis that is testable, falsifiable and realistic.

The precursor to a hypothesis is a research problem, usually framed as a question. It might ask what, or why, something is happening.

For example, to use a topical subject, we might wonder why the stocks of cod in the North Atlantic are declining. The problem question might be ‘Why are the numbers of Cod in the North Atlantic declining?’

This is too broad a statement and is not testable by any reasonable scientific means. It is merely a tentative question arising from literature reviews and intuition. Many people would think that instinct and intuition are unscientific, but many of the greatest scientific leaps were a result of ‘hunches’.

The research hypothesis is a paring down of the problem into something testable and falsifiable. In the aforementioned example, a researcher might speculate that the decline in the fish stocks is due to prolonged over fishing. They must generate a realistic and testable hypothesis around which they can build the experiment.

This might be a question, a statement or an ‘If/Or’ statement. Some examples could be:

* Is over-fishing causing a decline in the stocks of Cod in the North Atlantic?
* Over-fishing affects the stocks of cod.
* If over-fishing is causing a decline in the numbers of Cod, reducing the amount of trawlers will increase cod stocks.

These are all acceptable statements and they all give the researcher a focus for constructing a research experiment. Science tends to formalize things and use the ‘If’ statement, measuring the effect that manipulating one variable has upon another, but the other forms are perfectly acceptable. An ideal research hypothesis should contain a prediction, which is why the more formal ones are favored.

A scientist who becomes fixated on proving a research hypothesis loses their impartiality and credibility. Statistical tests often uncover trends, but rarely give a clear-cut answer, with other factors often affecting the outcome and influencing the results.

Whilst gut instinct and logic tells us that fish stocks are affected by over fishing, it is not necessarily true and the researcher must consider that outcome. Perhaps environmental factors or pollution are causal effects influencing fish stocks.

A hypothesis must be testable, taking into account current knowledge and techniques, and be realistic. If the researcher does not have a multi-million dollar budget then there is no point in generating complicated hypotheses. A hypothesis must be verifiable by statistical and analytical means, to allow a verification or falsification.

In fact, a hypothesis is never proved, and it is better practice to use the terms ‘supported’ or ‘verified’. This means that the research showed that the evidence supported the hypothesis and further research is built upon that.

A research hypothesis, which stands the test of time, eventually becomes a theory, Source:

Friday, April 16, 2010

Thesis examinations

April 16 2010

One of the requirements for certain advanced degrees is often an oral examination. This examination normally occurs after the dissertation is finished but before it is submitted to the university, and may comprise a presentation by the student and questions posed by an examining committee or jury. In North America, this examination is known as a thesis or dissertation defense, while in the UK and other English-speaking countries it is called a viva voce.
[edit] Examination results

The result of the examination may be given immediately following deliberation by the examiners (in which case the candidate may immediately be considered to have received his or her degree), or at a later date, in which case the examiners may prepare a defense report that is forwarded to a Board or Committee of Postgraduate Studies, which then officially recommends the candidate for the degree.

Potential decisions (or "verdicts") include:

* Accepted / pass with no corrections.

The thesis is accepted as presented. A grade may be awarded, though in many countries PhDs are not graded at all, and in others only one of the theoretically possible grades (the highest) is ever used in practice.[citation needed]

* The thesis must be revised.

Revisions (for example, correction of numerous grammatical or spelling errors; clarification of concepts or methodology; addition of sections) are required. One or more members of the jury and/or the thesis supervisor will make the decision on the acceptability of revisions and provide written confirmation that they have been satisfactorily completed. If, as is often the case, the needed revisions are relatively modest the examiners may all sign the thesis with the verbal understanding that the candidate will review the revised thesis with his or her supervisor before submitting the completed dissertation.

* Extensive revision required.

The thesis must be revised extensively and undergo the evaluation and defense process again from the beginning with the same examiners. Problems may include theoretical or methodological issues. A candidate who is not recommended for the degree after the second defense must normally withdraw from the program.

* Unacceptable

The thesis is unacceptable and the candidate must withdraw from the program.
This verdict is given only when the thesis requires major revisions and when the examination makes it clear that the candidate is incapable of making such revisions.

At most North American institutions the latter two verdicts are extremely rare, for two reasons. First, to obtain the status of doctoral candidates, graduate students typically write a qualifying examination or comprehensive examination, which often includes an oral defense. Students who pass the qualifying examination are deemed capable of completing scholarly work independently and are allowed to proceed with working on a dissertation. Second, since the thesis supervisor (and the other members of the advisory committee) will normally have reviewed the thesis extensively before recommending the student proceed to the defense, such an outcome would be regarded as a major failure not only on the part of the candidate but also by the candidate's supervisor (who should have recognized the substandard quality of the dissertation long before the defense was allowed to take place). It is also fairly rare for a thesis to be accepted without any revisions; the most common outcome of a defense is for the examiners to specify minor revisions (which the candidate typically completes in a few days or weeks).