# hypothesis testing

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## hypothesis testing

the development and use of statistical criteria to aid in taking decisions about the validity of a HYPOTHESIS in uncertain conditions. In any decision about the validity of a hypothesis, there is a chance of making a correct choice and a risk of making a wrong choice. Hypothesis testing is concerned with evaluating these chances and providing criteria that minimize the likelihood of making wrong decisions.For example, suppose we wanted to decide whether or not company size determines management remuneration and formulated the hypothesis that average management remuneration is larger in bigger firms, this hypothesis can be either true or false and will be either accepted or rejected; these options are shown in the matrix below:

Hypothesis | Hypothesis | |

is true | is false | |

Accept | correct | error |

hypothesis | decision | (type 2) |

Reject | error | correct |

hypothesis | (type 1) | decision |

If the hypothesis is true and we accept it, and if the hypothesis is false and we reject it, our decision will be correct. On the other hand, we could reject the hypothesis when it should be accepted (a *type 1 error), * or we could accept a hypothesis that should be rejected (a *type 2 error). * The risk of making such errors in testing a hypothesis using available sample data can be minimized. To avoid the risk of making a type 2 error and to establish clear probabilities for the risk of committing a type 1 error, careful formulation of the hypothesis is necessary Often this involves formulating a *null hypothesis, * which assumes the exact opposite of what we want to prove. For example, in place of the earlier hypothesis that average management remuneration is larger in bigger firms, we would formulate the null hypothesis that average management remuneration is the same in large and small companies. Rejection of this null hypothesis is equivalent to acceptance of the original hypothesis. This null hypothesis can then be tested against sample data.

If repeated samples are taken from the population of firms, then these samples can be used to assess the PROBABILITY of making a type 1 error. This probability of making a type 1 error is called the *level of significance, * at which a test of the significance of the null hypothesis will be conducted (customarily 0.01,0.05 or 0.10). This level of significance is always specified before any test is made.

The final step involves the test of significance: average management remuner- ation is calculated from sample data for small and large firms and compared with expected management remuneration, which, according to our null hypothesis, should be the same in both small and big companies. If the difference between what we expect to find (average remuneration the same) and what we get is so large that it cannot reasonably be attributed to chance, we reject the null hypothesis on which our expectation is based. On the other hand, if the difference between what we expect (average remuneration the same) and what we get is so small that it reasonably may be attributed to chance, the results are not statistically significant. In the former case we would reject the null hypothesis and accept its mirror image, namely that management remuneration is larger in bigger firms. In the latter case we would reserve judgement on the issue of company size and management remuneration since no clear link is either proved or disproved.

The statistical techniques of hypothesis testing are widely employed in empirical economic research.