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1 Handout OMGT 6123 Hypothesis Testing I Several considerations factor into the determination of the appropriate statistical technique to use when conducting a hypothesis test. However, the two most important ones are: (1)the type of data being measured and (2)the purpose or objective of the statistical inference. Concerning the former, data are measured by four types of scales: Nominal, Ordinal, Interval, and Ratio. Nominal scales are ones whose data fall into distinct descriptive categories: i.e. gender (male, female). Ordinal scales are ones whose values represent ranked responses, i. e. class rank of students listed from high to low. Interval and ratio scales are ones whose values are quantitative real numbers and the differences between these numbers or values are meaningful such that means and variances can be computed, i. e. per capita income. The latter two types of scales allow for hypotheses to be tested using parametric techniques, whereas the former two scales require the use of nonparametric statistical methods. The purpose or objective of the statistical inference can include any of the following: (1)description of one population, (2)comparison of two populations, (3)comparison of more than two populations, and (4)analyzing the relationship between variables. Once the type of data being measured and the purpose of the statistical inference is known, other relevant criteria concern the assumptions underlying the test, as well as the sample size(s). For example, when comparing the means of two independent groups when both samples are under 30, the appropriate statistical test chosen is usually the t test. However, this test assumes that the underlying populations from which the data was drawn were normally distributed with equal variances. If these assumptions are not true or if they are suspected to not be true, the more appropriate test would be a nonparametric test. Nonparametric tests are distribution free, that is they are not bound by restrictive assumptions in order to be valid. II The five step approach to hypothesis testing (1)Stating the null hypothesis (Ho)- This statement involves setting the population parameter equal to a value believed to exist in the underlying population. (2)Stating the alternative hypothesis (Ha)- This statement is the antithesis to the null hypothesis. In other words, if the researcher has enough statistical evidence based on the sample data to disprove the null hypothesis, he will conclude that the alternative situation (Ha) exists. of (3)Calculation a test statistic- The test statistic is computed from the data in a sample drawn from the original population of values. It transforms the data, which is measured in original units, into a standard distance from the center of the underlying distribution of values. Commonly used test statistics include the t and the z . Generally the z test statistic is used to test hypotheses based on large samples of 30 or more observations, whereas a t statistic is appropriate for small samples of less than 30 observations. Hypotheses testing a population mean or difference in means use either the z or t statistic; hypotheses testing a proportion or difference in proportions use a z statistic since they must have sample sizes of at least 100 to be valid. If variances are compared, a different test statistic, known as the F test score is used. (4)Creation of decision criteria- This step involves choosing a critical value of the test statistic used in step 3. These critical table values incorporate the concept of probability into the decision making process. Note: If running the test on the computer, the alpha level, p value, is computed for you. The p value, or significance level, is the smallest value of alpha at which the calculated test statistic in step 3 will still fall in the rejection region. It is based on a two-tailed test. (5)Stating a conclusion- This step involves two parts. First, the researcher will either reject or fail to reject the null hypothesis. Second, a practical interpretation concerning the results is given. III Choosing Between a One-tailed or Two-Tailed Hypothesis Generally speaking, a two-tailed hypothesis is appropriate when the researcher is unsure as to the direction of the results. For example, suppose we are hypothesizing that the average scores of ECU students SATs are equal to the average scores of UNC Wilmington students SATs in the null hypothesis. The alternative hypothesis allows for a significant difference to occur, meaning ECU students could have higher OR lower SATs than UNC Wilmington students. If, however, the researcher is trying to prove a specific direction, indicated by such words as greater than, less than, at most, at least, etc., then a one-tailed ( one direction ) test is appropriate. Theory helps the researcher decide if a one direction test is called for. In the case of a one-tailed hypothesis, the p value on the printout should be divided in half in order to interpret the results.

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