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Hypothesis Testing

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Applied Statistics and Multivariate Data Analysis for Business and Economics

Abstract

Among the most important techniques in statistics is hypothesis testing. A hypothesis is a supposition about a certain state of affairs. It does not spring from a sudden epiphany or a long-standing conviction; rather, it offers a testable explanation of a specific phenomenon. A hypothesis is something that we can accept (verify) or reject (falsify) based on empirical data.

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Notes

  1. 1.

    In Excel 2010, this can be reached by clicking File → Options → Add-ins → Go.

  2. 2.

    For a very good explanation of how to perform this test in SPSS, see https://www.youtube.com/watch?v=MJGk2sg4EZU on the how2stats YouTube channel.

  3. 3.

    For a very good explanation of how to perform this test in Stata, see https://www.youtube.com/watch?v=ajzMeANAMzI on the Stata Learner YouTube channel.

  4. 4.

    For a very good explanation of how to perform this test in Excel, see https://www.youtube.com/watch?v=wy8GVt7Ityk on the YouTube channel of https://alphabench.com

  5. 5.

    Most statistical software packages perform this step automatically.

  6. 6.

    For a very good explanation of how to do this in SPSS, see https://www.youtube.com/watch?v=dkobjvhxTro on the YouTube channel of Dr. Todd Grande.

  7. 7.

    For a very good explanation of how to do this in Stata, see https://www.youtube.com/watch?v=2oJxerMCwIE and https://www.youtube.com/watch?v=NIwtaZqNFs8 on the Stata Learner YouTube channel.

  8. 8.

    For a very good explanation of how to do this in Excel, see https://www.youtube.com/watch?v=xlgeta9FivI on the YouTube channel of Matthias Kullowatz and https://www.youtube.com/watch?v=mJtbhGETU88 on the YouTube channel of Dr. Todd Grande.

  9. 9.

    Based on the results of the Kolmogorov–Smirnov test and the Shapiro–Wilk test (see Sect. 9.6.2), we must reject the hypothesis of a normal distribution.

  10. 10.

    Based on the results of the Kolmogorov–Smirnov test and the Shapiro–Wilk test (see Sect. 9.6.2), we must reject the hypothesis of a normal distribution.

  11. 11.

    In Excel 2010 this can be reached by clicking File → Options → Add-ins → Go.

  12. 12.

    For a very good explanation of how to perform these steps using Excel, see https://www.youtube.com/watch?v=BlS11D2VL_U on the YouTube channel of Jim Grange or https://www.youtube.com/watch?v=X14z9r8FUKY on the YouTube channel of Dr. James Clark from the Kings College London (Essential Life Science Tutorials).

  13. 13.

    See Conover (1980). For more information on accurately calculating the approximated U test, see Bortz et al. (2000, p. 200).

  14. 14.

    Based on the results of the Kolmogorov–Smirnov test and the Shapiro–Wilk test, we must reject the hypothesis of a normal distribution.

  15. 15.

    See the file Chocopraline_colour_name_price.sav for SPSS and Chocopraline_colour_name_price.dta for Stata.

  16. 16.

    The result of a single-factor univariate ANOVA for a factor with two traits is the same as that of a t-test for independent samples.

  17. 17.

    Traditionally, the F-test (or its application to groups, Bartlett’s test) is used to measure equal variance. But these tests react very sensitively to deviations from the normal distribution, which is why the more robust Levene’s test is preferred. SPSS automatically performs Levene’s test for equal variance when performing ANOVA (choose Options → Homogeneity tests). Stata uses the one-way ANOVA to determine Bartlett’s test for equal variances. The Levene’s test calculation (w_0) is located under the heading Hypothesis Tests.

  18. 18.

    Strictly speaking, all the measures of regression diagnostics (heteroskedasticity, autocorrelation, multicollinearity, etc.) should be performed when carrying out an ANCOVA (see Sect. 10.10).

  19. 19.

    When using Excel 2010, select File → Options → Add-ins → GO instead.

  20. 20.

    For a very good explanation of ANOVA in Excel, see https://www.youtube.com/watch?v=tPGPV_XPw-o on the YouTube channel of Dr. James Clark from the Kings College London (Essential Life Science Tutorials) and https://www.youtube.com/watch?v=JfUf5DR2Azs on the YouTube channel of StatisticsHowTo.com

  21. 21.

    ti represents the respective number of rank scores for the value i. In our example, we have 4 rank scores of 2.5 for value 1, 3 rank scores of 6 for value 2, 8 rank scores of 11.5 for value 3, and 9 rank scores of 20 for value 4.

  22. 22.

    The data in titanic.sav (SPSS), titanic.dta (Stata), and titanic.xls (Excel) contain figures on the number of persons on board and the number of victims. The data is taken from the British Board of Trade Inquiry Report (1990), Report on the Loss of the Titanic′ (S.S.), Gloucester (reprint).

  23. 23.

    For a very good explanation of how to calculate the chi-square test of Independence using SPSS, see https://www.youtube.com/watch?v=wfIfEWMJY3s on the YouTube channel of ASK Brunel.

  24. 24.

    Syntax command: tabulate class survived, cchi2 cell chi2 clrchi2 column expected row V.

  25. 25.

    For a very good explanation of how to calculate the chi-square test of independence using Stata, see: https://www.youtube.com/watch?v=GZIi9zAlzIA on the StataCorp LLC YouTube channel.

  26. 26.

    For a very good explanation of how to calculate the chi-square test of independence using Excel, see https://www.youtube.com/watch?v=ODxEoDyF6RI on the YouTube channel of Ken Blake.

  27. 27.

    For a very good explanation of how to test for normal distribution using SPSS, see https://www.youtube.com/watch?v=dK-JNR3g_LU on the Dragonfly Statistics YouTube channel and https://www.youtube.com/watch?v=sQkB-AlJgPI on the HowToStats.com YouTube channel.

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Authors and Affiliations

  1. Pforzheim Business School, Pforzheim University of Applied Sciences, Pforzheim, Baden-Württemberg, Germany

    Thomas Cleff

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Cleff, T. (2019). Hypothesis Testing. In: Applied Statistics and Multivariate Data Analysis for Business and Economics. Springer, Cham. https://doi.org/10.1007/978-3-030-17767-6_9

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