Repeated measures ANCOVA - overview
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Repeated measures ANCOVA | $z$ test for a single proportion |
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Independent variable | Independent variable | |
One or more within subjects factors (related groups), one or more quantitative control variables of interval or ratio level (covariates), and possibly one or more between subjects factors (independent groups) | None | |
Dependent variables | Dependent variable | |
One quantitative of interval or ratio level | One categorical with 2 independent groups | |
THIS TABLE IS YET TO BE COMPLETED | Null hypothesis | |
- | H0: $\pi = \pi_0$
Here $\pi$ is the population proportion of 'successes', and $\pi_0$ is the population proportion of successes according to the null hypothesis. | |
n.a. | Alternative hypothesis | |
- | H1 two sided: $\pi \neq \pi_0$ H1 right sided: $\pi > \pi_0$ H1 left sided: $\pi < \pi_0$ | |
n.a. | Assumptions | |
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n.a. | Test statistic | |
- | $z = \dfrac{p - \pi_0}{\sqrt{\dfrac{\pi_0(1 - \pi_0)}{N}}}$
Here $p$ is the sample proportion of successes: $\dfrac{X}{N}$, $N$ is the sample size, and $\pi_0$ is the population proportion of successes according to the null hypothesis. | |
n.a. | Sampling distribution of $z$ if H0 were true | |
- | Approximately the standard normal distribution | |
n.a. | Significant? | |
- | Two sided:
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n.a. | Approximate $C\%$ confidence interval for $\pi$ | |
- | Regular (large sample):
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n.a. | Equivalent to | |
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n.a. | Example context | |
- | Is the proportion of smokers amongst office workers different from $\pi_0 = 0.2$? Use the normal approximation for the sampling distribution of the test statistic. | |
n.a. | SPSS | |
- | Analyze > Nonparametric Tests > Legacy Dialogs > Binomial...
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n.a. | Jamovi | |
- | Frequencies > 2 Outcomes - Binomial test
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Practice questions | Practice questions | |