Hypothesis and its testing

Hypothesis(from Greek):
It consists either of a suggested explanation for a fact or of a reasoned proposal suggesting a possible correlation between multiple facts. Scientists generally base such assumption or hypotheses on prior readings or on outcome of scientific theories. Even though the words "hypothesis" and "theory" are often used synonymously, a scientific hypothesis is not the same as a scientific theory. A hypothesis requires either a confirmation or disproval by researchers. In due course, a confirmed hypothesis may become part of a theory or can grow to become a theory itself. Now-a-days, scientific hypotheses have the form of a mathematical model.

Types:

1. If and then in case of dependent variables.
2. Statistical
   Null Hypothesis- H0: coin-tossing operates "fairly" (equally likely to fall "Heads" or "Tails")
   Alternate Hypothesis- H1: coin-tossing operates in a biased manner to give a 90% probability of falling "Heads"

Testing:
The purpose of hypothesis testing is to test the viability of the null hypothesis in the light of experimental data. Depending on the data, the null hypothesis either will or will not be rejected as a viable possibility. The null hypothesis is often the reverse of what the experimenter actually believes; it is put forward to allow the data to contradict it.

However, various statistical approaches (such as Bayesian statistics and classical statistics (i.e. t-tests)) can quantify the strong intuition that H1 appears much less likely than H0 let us suppose that if, in 1,000 tosses, 495 came out "Heads" — and much more likely if 895 came out "Heads". Researchers generally evaluate experiments statistically.

1. After specifying the H0, the next step is to select a significance level(it is the criterion used for rejecting the null hypothesis). The level of significance is chosen as 0.05 level(also referred as 5%) or 0.01 level(also referred as 1%).


2. Then the difference between the results of the experiment and the null hypothesis is determined.


3. Next, assuming the null hypothesis is true, the probability of a difference that large or larger is computed .


4. Finally, this probability is compared to the significance level. If the probability is less than or equal to the significance level, then the null hypothesis is rejected and the outcome is said to be statistically significant.

For further understanding pls. pay a visit to http://statpages.org/