திங்கள், 2 நவம்பர், 2015

NET PAPER 1:Hypothesis

Answer: A tentative proposal made to explain certain observations or facts that requires further investigation to be verified. A hypothesis is a formulation of a question that lends itself to a prediction. This prediction can be verified or falsified. A question can only be use as scientific hypothesis, if their is an experimental approach or observational study that can be designed to check the outcome of a prediction.

Nature of hypothesis

N the various discussions of the hypothesis which have appeared in works on inductive logic and in writings on scientific method, its structure and function have received considerable attention, while its origin has been comparatively neglected. The hypothesis has generally been treated as that part of scientific procedure which marks the stage where a definite plan or method is proposed for dealing with new or unexplained facts. It is regarded as an invention for the purpose of explaining the given, as a definite conjecture which is to be tested by an appeal to experience to see whether deductions made in accordance with it will be found true in fact. The function of the hypothesis is to unify, to furnish a method of dealing with things, and its structure must be suitable to this end. It must be so formed that it will be likely to prove valid, and writers have formulated various rules to be followed in the formation of hypotheses. These rules state the main requirements of a good hypothesis, and are intended to aid in a general way by pointing out certain limits within which it must fall.

In respect to the origin of the hypothesis, writers have usually contented themselves with pointing out the kind of situations in which hypotheses are likely to appear. But after this has been done, after favorable external conditions have been given, the rest must be left to "genius," for hypotheses arise as "happy guesses," for which no rule or law can be given. In fact, the genius differs from the ordinary plodding mortal in just this ability to form fruitful

Hypotheses in the midst of the same facts which to other less gifted individuals remain only so many disconnected experiences. Hypothesis is to determine its nature a little more precisely through an investigation of its rather obscure origin, and to call attention to certain features of its function which have not generally been accorded their due significance.

The scope hypothesis

We should be surprised that language is as complicated as it is. That is to say, there is no reasonable doubt that a language with a context-free grammar, together with a transparent inductive characterization of the semantics, would have all of the expressive power of historically given natural languages, but none of the quirks or other puzzling features that we actually find when we study them. This circumstance suggests that the relations between apparent syntactic structure on the one hand and interpretation on the other the interface conditions, in popular terminology should be seen through the perspective of an underlying regularity of structure and interpretation that can be revealed only through extended inquiry, taking into consideration especially comparative data. Indeed, advances made especially during the past twenty-five years or so indicate that, at least over a broad domain, structures either generated from what is (more or less) apparent, or else underlying those apparent structures, display the kind of regularity in their interface conditions that is familiar to us from the formalized languages. The elements that I concentrate upon here are two: The triggering of relative scope (from the interpretive point of view), and the distinction between those elements that contribute to meaning through their contribution to reference and truth conditions, on the one hand, and those that do so through the information that they provide about the intentional states of the speaker or those the speaker is talking about, on the other. As will be seen, I will in part support Jaakko Hintikka's view that the latter distinction involves scope too, but in a more derivative fashion than he has explicitly envisaged.

Testing Of Hypothesis

Hypothesis testing refers to the process of using statistical analysis to determine if the observed differences between two or more samples are due to random chance (as stated in the null hypothesis) or to true differences in the samples (as stated in the alternate hypothesis). A null hypothesis (H0) is a stated assumption that there is no difference in parameters (mean, variance, DPMO) for two or more populations. The alternate hypothesis (Ha) is a statement that the observed difference or relationship between two populations is real and not the result of chance or an error in sampling. Hypothesis testing is the process of using a variety of statistical tools to analyze data and, ultimately, to fail to reject or reject the null hypothesis. From a practical point of view, finding statistical evidence that the null hypothesis is false allows you to reject the null hypothesis and accept the alternate hypothesis. Hypothesis testing is the use of statistics to determine the probability that a given hypothesis is true. The usual process of hypothesis testing consists of four steps.

  1. Formulate the null hypothesis (commonly, that the observations are the result of pure chance) and the alternative hypothesis (commonly, that the observations show a real effect combined with a component of chance variation).

  2. Identify a test statistic that can be used to assess the truth of the null hypothesis.

  3. Compute the P-value, which is the probability that a test statistic at least as significant as the one observed would be obtained assuming that the null hypothesis were true. The smaller the-value, the stronger the evidence against the null hypothesis.

  4. Compare the-value to an acceptable significance value (sometimes called an alpha value). If, that the observed effect is statistically significant, the null hypothesis is ruled out, and the alternative hypothesis is valid.

Flow Diagram

1 Identify the null hypothesis H0 and the alternate hypothesis HA.

2 Choose? The value should be small, usually less than 10%. It is important to consider the consequences of both types of errors.

3 Select the test statistic and determine its value from the sample data. This value is called the observed value of the test statistic. Remember that a t statistic is usually appropriate for a small number of samples; for larger number of samples, a z statistic can work well if data are normally distributed.

4 Compare the observed value of the statistic to the critical value obtained for the chosen?

5 Make a decision.

If the test statistic falls in the critical region:

Reject H0 in favour of HA. If the test statistic does not fall in the critical region:

Conclude that there is not enough evidence to reject H0.

Practical Example

One tailed Test

An aquaculture farm takes water from a stream and returns it after it has circulated through the fish tanks. The owner thinks that, since the water circulates rather quickly through the tanks, there is little organic matter in the effluent. To find out if this is true, he takes some samples of the water at the intake and other samples downstream the outlet, and tests for Biochemical Oxygen Demand (BOD). If BOD increases, it can be said that the effluent contains more organic matter than the stream can handle. The data for BOD (One tailed t-test) in the stream are given in the following table:

Upstream

Downstream

6.782

9.063

5.809

8.381

6.849

8.660

6.879

8.405

7.014

9.248

7.321

8.735

5.986

9.772

6.628

8.545

6.822

8.063

6.448

8.001

  1. A is the set of samples taken at the intake; and B is the set of samples taken downstream. Then verify the validity of following hypothesis

    1. H0: B < A

    2. H1: B > A

  2. Let us use 5% for this example.

  3. The observed t value is calculated

  4. The critical t value is obtained according to the degrees of freedom

Result

The resulting t test values are shown in this table of t-Test: Two-Sample Assuming Equal Variances

Input

Upstream

Downstream

Mean

6.6539

8.6874

Variance

0.2124

0.2988

Observations

10.0

10.0

Pooled Variance

0.2556

NA

Hypothesized Mean Difference

0.0

0.0

Degrees of freedom

18.0

NA

t-stat

-8.9941

NA

The numerical value of the calculated for t-statistic is higher than the critical-t value. We therefore reject H0 and conclude that the effluent is polluting the stream.