Hypothesis Testing & ANOVA
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, th
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Hypothesis Testing & ANOVA
Keywords
α-Inflation • α error • Analysis of Variance (ANOVA) • β error • Bonferroni correction • Degrees of freedom • eta-squared • F-test • F-test of sample variance • Factor variable • Familywise error rate • Independent samples ttest • Interaction effect • Levene’s test • Mann-Whitney U test • Main effect • Nonparametric tests • Null and alternative hypothesis • Omega-squared • Onesample t-test • One-tailed test • One-way ANOVA • p-value • Paired samples ttest • Parametric test • Practical significance • Post hoc tests • Power of a test • Shapiro-Wilk test • Significance level • Sampling error • Statistical significance • t-test • Test statistic • Tukey’s honestly significant difference test • Two-sample t-test • Two-tailed test • Two-way ANOVA • Type I and type II error • Welch correction • Wilcoxon signed-rank test • z-test
Learning Objectives After reading this chapter, you should understand: – – – – – –
The logic of hypothesis testing. The steps involved in hypothesis testing. What a test statistic is. Types of error in hypothesis testing. Common types of t-tests, one-way, and two-way ANOVA. How to interpret Stata output.
6.1
Introduction
Do men or women spend more money on the Internet? Assume that the mean amount that a sample of men spends online is $200 per year against a women sample’s mean of $250. When we compare mean values such as these, we always # Springer Nature Singapore Pte Ltd. 2018 E. Mooi et al., Market Research, Springer Texts in Business and Economics, DOI 10.1007/978-981-10-5218-7_6
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6 Hypothesis Testing & ANOVA
expect some difference. But, how can we determine if such differences are statistically significant? Establishing statistical significance requires ascertaining whether such differences are attributable to chance or not. In this chapter, we will introduce hypothesis testing and how this helps determine statistical significance.
6.2
Understanding Hypothesis Testing
A hypothesis is a statement about a certain effect or parameter (such as a mean or correlation) that can be tested using a sample drawn from the population. A hypothesis may comprise a claim about the difference between two sample parameters (e.g., there is a difference between males’ and females’ mean spending). It can also be a test of a judgment (e.g., teenagers spend an average of 4 h per day on the Internet). Data from the sample are used to obtain evidence against, or in favor of, the statement. Hypothesis testing is performed to infer whether or not a certain effect is statistically significant. Statistical significance means that the effect is so large that it is unlikely to have occured by chance. Whether results are statistically significant depends on several factors, including the size of the effect, the variation in the sample data, and the sample size (Agresti and Finlay 2014). When drawing a sample from the population, there is always some probability that we might reach the wrong conclusion due to a sampling error, which is the difference between the sampl
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