# Statistical Tests

Posted June 29, 2009

Statistical tests are of various types, depending upon the nature of the study. Statistical tests provide a method for making quantitative decisions about a particular sample. Statistical tests mainly test the hypothesis that is made about the significance of an observed sample.

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There are some key concepts of statistical tests that can help in understanding statistical tests.

Type I error: Type I error in a statistical test is usually committed when a correct sample is rejected.

Type II error: Type II error in a statistical test is usually committed when a false sample is accepted.

We can say that statistical testsare generally categorized into various types depending upon the type of field. Statistical tests are carried out extensively in psychology, medicine, nursing and business.

In the field of psychology, statistical tests of significances like t-test, z test, f test, chi square test, etc., are carried out to test the significance between the observed samples and the hypothetical or expected samples. For example, if a researcher wants to conduct a statistical test upon the significant difference between the IQ levels of two college students, then the researcher can perform the t statistical test for the difference of the two samples. If one wants to test the goodness of fit of a particular assumed model, then one can use the chi square test of goodness of fit. This is the only statistical test (among other statistical tests), that helps in testing the goodness of fit of an assumed model.

In the field of business, statistical tests are used for conducting Analysis of variance (ANOVA). Analysis of variance (ANOVA) is basically used for examining the differences in the mean values of the dependent variables associated with the effect of the controlled independent variables, after taking into account the influence of the uncontrolled independent variables. Thus, in Analysis of variance (ANOVA), f statistical test calculates the significance of the samples.

Statistical tests are directly correlated to statistical inference. Statistical inference involves tests of hypothesis, where statistical tests play a crucial role. In the field of medicine and nursing, tests of hypotheses are conducted using various statistical tests. If the researcher makes mistakes in calculation while performing the statistical tests, then the researcher might end up committing a type II error. In other words, if the researcher makes a mistake in calculation, then the statistical tests will conclude that a false drug sample is a correct drug sample. Further, the researcher might end up tagging a false drug sample as a correct drug sample. Thus, the researcher should be cautious while performing statistical tests. In the field of medicine and nursing, errors in statistical tests can result in huge problems in people’s lives, as it affects their drugs and dosages etc.

Statistical tests can be performed in software such as SPSS. Statistical tests in SPSS can be performed with the help of the “analysis” menu. For every statistical test, there are different sample sizes. In the t test, for example, we should have a sample size less than 30. Similarly, for a statistical z test, we should have a sample size more than 30. Statistical tests come with some general assumptions like the assumption that samples should be drawn from the population in a random manner. The observations in statistical tests must be independent. The observations in statistical tests must have the same underlying distribution. Especially, in the chi sq statistical test, observations must be grouped in different categories. Normal distribution of deviations is assumed in statistical tests.

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