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Statistical Hypothetical Testing

The statistical hypothetical testing is used for making decisions by using data which can be from a controlled experiment or from an observational study. The result is statistically significant when its occurrence does not depend solely on chance as per the predetermined threshold probability. The phrase of test of significance was initially coined by Ronald Fisher. Confirmatory data analysis is the other name given to hypothesis testing. Hypothesis testing is also used to decide that whether the experimental results obtained contains enough information for casting doubt on conventional wisdom or not. When the result found is statistically significant, it is called positive result and when the result does no fall under the null hypothesis, it is termed as a negative result.

The process of hypothetical testing

1. The research hypothesis is started where the truth in not yet known.

2. In the first step, the null and alternative hypotheses are clearly stated. The stage is very important as mis-starting will lead to muddying of the whole process.

3. During the second step we consider the statistical assumptions about the samples for doing various tests. For example, the assumption can be regarding the statistical assumption or about the form in which the observations are distributed. It is very important as invalid assumptions means that the results are also invalid.

4. After deciding which test is appropriate, we start the relevant test statistics.

5. Next stage involves the deriving of the test static distribution form the assumptions, under the null hypotheses.

6. Then the test statistic partitions area distributed with the possible of T is amalgamated into those for whom the null hypotheses has been rejected and for those for whom it is not.

7. The observed value or the tobs, is then computed from the observations which are having the test statistic T.

8. As per the decision rule, the null hypothesis H0 is rejected if the observed value of tobs lies in the critical region, and if it does not, then to ‘fail to reject’ or to ‘accept’ the other thesis, otherwise, is the other option.

Some example of the hypothesis are-

1. Courtroom trial- this statistical test procedure is very similar to a courtroom trial where the defendant is considered not guilty until his guilt is proven. The prosecutor tries to prove the hit of the defendant who is convicted when there is enough charging evidence. This procedure proceeds with two hypothesis,

Namely H0 when defendant is not guilty (null hypotheis) and H1 when the defendant is guilty (alternative hypothesis). The hypothesis one tries to prove is the alternative one.

2. The clairvoyant card game- here the person or subject is tested for clairvoyance. He is shown the reverse of card which are randomly chosen 25 times and then asked the four suits it belongs to. The number of correct answers or hits given is termed as X. the null hypotheses describes the person as not being clairvoyant and the alternative hypothesis describes him as more being more or less clairvoyant.

3. The radioactive suitcase- it is similar to determining whether a suitcase contains some radioactive element or not. Let’s assume it produces 10 counts per minute when placed under a Geiger counter. Here the null describes the suitcase as not being radioactive and all counts are measured because of harmless objects and the surrounding air. When there is an average count of 9 per minute with a standard deviation 1 count per minute, the suitcase is in compatibility with the null hypothesis. When the count is 3 per minute and the standard deviation is 1 count per minute, then the suitcase in not said to be compatible with null hypothesis and other factors contribute to the measurements.

4. A lady testing tea-this experiment module was given by fisher and dependent on lady’s ability to test the tea preparation by taste.

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