The hypothesis tests presented in the previous sections are good for analyzing means between two populations. But what if there are more than two populations? Consider an example of testing the impact of nutrition and exercise on 60 candidates between age 18 and 50. The candidates are randomly split into six groups, each assigned with a different weight loss strategy, and the goal is todetermine which strategy is the most effective.
Group 1 only eats junk food.
Group 2 only eats healthy food
Group 3 eats junk food and does cardio exercise every other day.
Group 4 eats healthy food and does cardio exercise every other day
Group 5 eats junk food and does both cardio and strength training every other day
Group 6 eats healthy food and does both cardio and strength training every other day.
Multiple t-tests could be applied to each pair of weight loss strategies. In this example, the weight loss of Group 1 is compared with the weight loss of Group 2, 3, 4, 5, or 6. Similarly, the weight lossof Group 2 is compared with that of the next 4 groups. Therefore, a total of 15 t-tests would beperformed.
However, multiple t-tests may not perform well on several populations for two reasons. First, because the number of t-tests increases as the number of groups increases, analysis using the multiple t-tests becomes cognitively more difficult. Second, by doing a greater number of analyses, the probability of committing at least one type I error somewhere in the analysis greatly increases.
Analysis of Variance (ANOVA) is designed to address these issues. ANOVA is a
generalization of the hypothesis testing of the difference of two population means. ANOVA tests if any of the population means differ from the other population means. The null hypothesis of ANOVA is that all the population means are equal. The alternative hypothesis is that at least one pair of thepopulation means is not equal. In other words,
Consider an example that every customer who visits a retail website gets one of two promotionaloffers or gets no promotion at all. The goal is to see if making the promotional offers makes a difference. ANOVA could be used, and the null hypothesis is that neither promotion makes a difference. The code that follows randomly generates a total of 500 observations of purchase sizeson three different offer options.
Because only the influence of one factor (offers) was executed, the presented ANOVA is known asone-way ANOVA. If the goal is to analyze two factors, such as offers and day of week, that would be a two-way ANOVA [16]. If the goal is to model more than one outcome variable, then multivariateANOVA (or MANOVA) could be used.
The hypothesis tests presented in the previous sections are good for analyzing means between two populations. But what if there are more than two populations? Consider an example of testing the impact of nutrition and exercise on 60 candidates between age 18 and 50. The candidates are randomly split into six groups, each assigned with a different weight loss strategy, and the goal is todetermine which strategy is the most effective.
Group 1 only eats junk food.
Group 2 only eats healthy food
Group 3 eats junk food and does cardio exercise every other day.
Group 4 eats healthy food and does cardio exercise every other day
Group 5 eats junk food and does both cardio and strength training every other day
Group 6 eats healthy food and does both cardio and strength training every other day.
Multiple t-tests could be applied to each pair of weight loss strategies. In this example, the weight loss of Group 1 is compared with the weight loss of Group 2, 3, 4, 5, or 6. Similarly, the weight lossof Group 2 is compared with that of the next 4 groups. Therefore, a total of 15 t-tests would beperformed.
However, multiple t-tests may not perform well on several populations for two reasons. First, because the number of t-tests increases as the number of groups increases, analysis using the multiple t-tests becomes cognitively more difficult. Second, by doing a greater number of analyses, the probability of committing at least one type I error somewhere in the analysis greatly increases.
Analysis of Variance (ANOVA) is designed to address these issues. ANOVA is a
generalization of the hypothesis testing of the difference of two population means. ANOVA tests if any of the population means differ from the other population means. The null hypothesis of ANOVA is that all the population means are equal. The alternative hypothesis is that at least one pair of thepopulation means is not equal. In other words,
Consider an example that every customer who visits a retail website gets one of two promotionaloffers or gets no promotion at all. The goal is to see if making the promotional offers makes a difference. ANOVA could be used, and the null hypothesis is that neither promotion makes a difference. The code that follows randomly generates a total of 500 observations of purchase sizeson three different offer options.
Because only the influence of one factor (offers) was executed, the presented ANOVA is known asone-way ANOVA. If the goal is to analyze two factors, such as offers and day of week, that would be a two-way ANOVA [16]. If the goal is to model more than one outcome variable, then multivariateANOVA (or MANOVA) could be used.