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 Stata. 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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Notes
- 1.
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.
- 2.
Stata does not directly support Welch’s correction for an ANOVA, but a user-written package called wtest is readily available and can be installed (see Chap. 5 on how to install user-written packages in Stata). This allows you to perform a test similar to the standard ANOVA test with Welch’s correction. For more information see Stata’s help file: http://www.ats.ucla.edu/stat/stata/ado/analysis/wtest.hlp
- 3.
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.
- 4.
To obtain the critical value, write display invt(9,1–0.05/2) in the command window.
- 5.
Unfortunately, there is some confusion about the difference between the α and p-value. See Hubbard and Bayarri (2003) for a discussion.
- 6.
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.
- 7.
Note that this doesn’t apply, for instance, to exact tests for probabilities.
- 8.
We don’t have to conduct manual calculations and tables when working with Stata. However, we can easily compute the p-value ourselves by 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., http://graphpad.com/quickcalcs/pvalue1.cfm) that calculate p-values and test statistic values.
- 9.
The number of pairwise comparisons is calculated as follows: k·(k − 1)/2, with k the number of groups to compare.
- 10.
Mitchell (2015) provides a detailed introduction to other ANOVA types, such as the analysis of covariance (ANCOVA).
- 11.
In fact, these two assumptions are interrelated, since unequal group sample sizes result in a greater probability that we will violate the homogeneity assumption.
- 12.
SS is an abbreviation of “sum of squares,” because the variation is calculated using the squared differences between different types of values.
- 13.
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.
- 14.
The Stata help contrast function provides an overview and references.
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Mooi, E., Sarstedt, M., Mooi-Reci, I. (2018). Hypothesis Testing & ANOVA. In: Market Research. Springer Texts in Business and Economics. Springer, Singapore. https://doi.org/10.1007/978-981-10-5218-7_6
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