Three or more way MANOVA - overview
This page offers structured overviews of one or more selected methods. Add additional methods for comparisons (max. of 3) by clicking on the dropdown button in the right-hand column. To practice with a specific method click the button at the bottom row of the table
Three or more way MANOVA | One sample $z$ test for the mean |
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Independent/grouping variables | Independent variable | |
Three or more categorical with independent groups | None | |
Dependent variables | Dependent variable | |
Two or more quantitative of interval or ratio level | One quantitative of interval or ratio level | |
THIS TABLE IS YET TO BE COMPLETED | Null hypothesis | |
- | H0: $\mu = \mu_0$
Here $\mu$ is the population mean, and $\mu_0$ is the population mean according to the null hypothesis. | |
n.a. | Alternative hypothesis | |
- | H1 two sided: $\mu \neq \mu_0$ H1 right sided: $\mu > \mu_0$ H1 left sided: $\mu < \mu_0$ | |
n.a. | Assumptions | |
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n.a. | Test statistic | |
- | $z = \dfrac{\bar{y} - \mu_0}{\sigma / \sqrt{N}}$
Here $\bar{y}$ is the sample mean, $\mu_0$ is the population mean according to the null hypothesis, $\sigma$ is the population standard deviation, and $N$ is the sample size. The denominator $\sigma / \sqrt{N}$ is the standard deviation of the sampling distribution of $\bar{y}$. The $z$ value indicates how many of these standard deviations $\bar{y}$ is removed from $\mu_0$. | |
n.a. | Sampling distribution of $z$ if H0 were true | |
- | Standard normal distribution | |
n.a. | Significant? | |
- | Two sided:
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n.a. | $C\%$ confidence interval for $\mu$ | |
- | $\bar{y} \pm z^* \times \dfrac{\sigma}{\sqrt{N}}$
where the critical value $z^*$ is the value under the normal curve with the area $C / 100$ between $-z^*$ and $z^*$ (e.g. $z^*$ = 1.96 for a 95% confidence interval). The confidence interval for $\mu$ can also be used as significance test. | |
n.a. | Effect size | |
- | Cohen's $d$: Standardized difference between the sample mean and $\mu_0$: $$d = \frac{\bar{y} - \mu_0}{\sigma}$$ Cohen's $d$ indicates how many standard deviations $\sigma$ the sample mean $\bar{y}$ is removed from $\mu_0.$ | |
n.a. | Visual representation | |
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n.a. | Example context | |
- | Is the average mental health score of office workers different from $\mu_0 = 50$? Assume that the standard deviation of the mental health scores in the population is $\sigma = 3.$ | |
Practice questions | Practice questions | |