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2019 | OriginalPaper | Buchkapitel

6. Hypothesis Testing and ANOVA

verfasst von : Marko Sarstedt, Erik Mooi

Erschienen in: A Concise Guide to Market Research

Verlag: Springer Berlin Heidelberg

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Abstract

We first describe the essentials of hypothesis testing and how testing helps make critical business decisions of statistical and practical significance. Without using difficult mathematical formulas, we discuss the steps involved in hypothesis testing, the types of errors that may occur, and provide strategies on how to best deal with these errors. We also discuss common types of test statistics and explain how to determine which type you should use in which specific situation. We explain that the test selection depends on the testing situation, the nature of the samples, the choice of test, and the region of rejection. Drawing on a case study, we show how to link hypothesis testing logic to empirics in SPSS. The case study touches upon different test situations and helps you interpret the tables and graphics in a quick and meaningful way.

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Vorheriges Kapitel Descriptive Statistics

Nächstes Kapitel Regression Analysis

In experimental studies, if respondents were paired with others (as in a matched case control sample), each person would be sampled once, but it still would be a paired sample.

The exact calculation of this test is shown on https://www.ibm.com/support/knowledgecenter/en/SSLVMB_20.0.0/com.ibm.spss.statistics.help/alg_npar_tests_mannwhitney.htm

The fundamental difference between the z- and t-distributions is that the t-distribution is dependent on sample size n (which the z-distribution is not). The distributions become more similar with larger values of n.

To obtain the critical value, you can also use the TINV function provided in Microsoft Excel, whose general form is “TINV(α, df).” Here, α represents the desired Type I error rate and df the degrees of freedom. To carry out this computation, open a new Excel spreadsheet and type in “ = TINV(2*0.025,9).” Note that we have to specify “2*0.025” (or, directly 0.05) under α, because we are applying a two-tailed instead of a one-tailed test.

Unfortunately, there is some confusion about the difference between the α and p-value. See Hubbard and Bayarri (2003) for a discussion.

Note that this is convention and most textbooks discuss hypothesis testing in this way. Originally, two testing procedures were developed, one by Neyman and Pearson and another by Fisher (for more details, see Lehmann 1993). Agresti and Finlay (2014) explain the differences between the convention and the two original procedures.

Note that this rule doesn't always apply such as for exact tests of probabilities.

We don’t have to conduct manual calculations and tables when working with SPSS. However, we can calculate the p-value using the TDIST function in Microsoft Excel. The function has the general form “TDIST(t, df, tails)”, where t describes the test value, df the degrees of freedom, and tails specifies whether it’s a one-tailed test (tails = 1) or two-tailed test (tails = 2). Just open a new spreadsheet for our example and type in “ = TDIST(2.274,9,1)”. Likewise, there are several webpages with Java-based modules (e.g., https://graphpad.com/quickcalcs/pvalue1.cfm) that calculate p-values and test statistic values.

The number of pairwise comparisons is calculated as follows: k·(k − 1)/2, with k the number of groups to compare.

In fact, these two assumptions are interrelated, since unequal group sample sizes result in a greater probability that we will violate the homogeneity assumption.

SS is an abbreviation of “sum of squares,” because the variation is calculated using the squared differences between different types of values.

Note that the group-specific sample size in this example is too small to draw conclusions and is only used to show the calculation of the statistics.

Note that when initiating the analysis by going to ► Analyze ► General Linear Model ► Univariate, we can request these statistics under Options (Estimates of effect size).

Agresti, A., & Finlay, B. (2014). Statistical methods for the social sciences (4th ed.). London: Pearson.

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Hubbard, R., & Bayarri, M. J. (2003). Confusion over measure of evidence (p’s) versus errors (α’s) in classical statistical testing. The American Statistician, 57(3), 171–178.CrossRef

Kimmel, H. D. (1957). Three criteria for the use of one-tailed tests. Psychological Bulletin, 54(4), 351–353.CrossRef

Lehmann, E. L. (1993). The Fischer, Neyman-Pearson theories of testing hypotheses: One theory or two? Journal of the American Statistical Association, 88(424), 1242–1249.CrossRef

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Titel: Hypothesis Testing and ANOVA
verfasst von: Marko Sarstedt
Erik Mooi
Verlag: Springer Berlin Heidelberg
Buch: A Concise Guide to Market Research
Print ISBN: 978-3-662-56706-7

Electronic ISBN: 978-3-662-56707-4

Copyright-Jahr: 2019
DOI: https://doi.org/10.1007/978-3-662-56707-4_6