Formulating and Testing Hypotheses
The term hypothesis has been mentioned several times in the preceding chapters. The definition that will be used here is that a hypothesis is a proposition set forth as explanation for the occurrence of a specified phenomenon. The basis of scientific investigation is the collection of information that is used either to formulate or to test hypotheses. One assesses the important variables and tries to build a model or hypothesis that explains the observed phenomenon. In general, a hypothesis is formulated by rephrasing the objective of a study as a statement, e.g., if the objective of an investigation is to determine if a pesticide is safe, the resulting hypothesis might be “the pesticide is not safe”, or alternatively that “the pesticide is safe”. A hypothesis is a statistical hypothesis only if it is stated in terms related to the distribution of populations. The general hypothesis above might be refined to: “this pesticide, when used as directed, has no effect on the average number of robins in an area”, which is a testable hypothesis. The hypothesis to be tested is called the null hypothesis (H0). The alternative hypothesis (H1) for the above example would be “this pesticide, when used as directed, has an effect on the average number of robins in an area”. In testing a hypothesis, H0 is considered to be true, unless the sample data indicate otherwise, (i.e., that the pesticide is innocent, unless proven guilty). Testing cannot prove H0 to be true but the results can cause it to be rejected. In accepting or rejecting H0, two types of error may be made. If H0 is rejected when, in fact, it is true a type 1 error has been committed. If Ho is not true and the test fails to reject it, a type 2 error has been made.
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