ANCOVA - 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
ANCOVA | Spearman's rho | One sample $t$ test for the mean |
You cannot compare more than 3 methods |
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Independent variables | Variable 1 | Independent variable | |
One or more categorical with independent groups, and one or more quantitative control variables of interval or ratio level (covariates) | One of ordinal level | None | |
Dependent variable | Variable 2 | Dependent variable | |
One quantitative of interval or ratio level | One of ordinal level | One quantitative of interval or ratio level | |
THIS TABLE IS YET TO BE COMPLETED | Null hypothesis | Null hypothesis | |
- | H0: $\rho_s = 0$
Here $\rho_s$ is the Spearman correlation in the population. The Spearman correlation is a measure for the strength and direction of the monotonic relationship between two variables of at least ordinal measurement level. In words, the null hypothesis would be: H0: there is no monotonic relationship between the two variables in the population. | 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 | Alternative hypothesis | |
- | H1 two sided: $\rho_s \neq 0$ H1 right sided: $\rho_s > 0$ H1 left sided: $\rho_s < 0$ | H1 two sided: $\mu \neq \mu_0$ H1 right sided: $\mu > \mu_0$ H1 left sided: $\mu < \mu_0$ | |
n.a. | Assumptions | Assumptions | |
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n.a. | Test statistic | Test statistic | |
- | $t = \dfrac{r_s \times \sqrt{N - 2}}{\sqrt{1 - r_s^2}} $ Here $r_s$ is the sample Spearman correlation and $N$ is the sample size. The sample Spearman correlation $r_s$ is equal to the Pearson correlation applied to the rank scores. | $t = \dfrac{\bar{y} - \mu_0}{s / \sqrt{N}}$
Here $\bar{y}$ is the sample mean, $\mu_0$ is the population mean according to the null hypothesis, $s$ is the sample standard deviation, and $N$ is the sample size. The denominator $s / \sqrt{N}$ is the standard error of the sampling distribution of $\bar{y}$. The $t$ value indicates how many standard errors $\bar{y}$ is removed from $\mu_0$. | |
n.a. | Sampling distribution of $t$ if H0 were true | Sampling distribution of $t$ if H0 were true | |
- | Approximately the $t$ distribution with $N - 2$ degrees of freedom | $t$ distribution with $N - 1$ degrees of freedom | |
n.a. | Significant? | Significant? | |
- | Two sided:
| Two sided:
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n.a. | n.a. | $C\%$ confidence interval for $\mu$ | |
- | - | $\bar{y} \pm t^* \times \dfrac{s}{\sqrt{N}}$
where the critical value $t^*$ is the value under the $t_{N-1}$ distribution with the area $C / 100$ between $-t^*$ and $t^*$ (e.g. $t^*$ = 2.086 for a 95% confidence interval when df = 20). The confidence interval for $\mu$ can also be used as significance test. | |
n.a. | n.a. | Effect size | |
- | - | Cohen's $d$: Standardized difference between the sample mean and $\mu_0$: $$d = \frac{\bar{y} - \mu_0}{s}$$ Cohen's $d$ indicates how many standard deviations $s$ the sample mean $\bar{y}$ is removed from $\mu_0.$ | |
n.a. | n.a. | Visual representation | |
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n.a. | Example context | Example context | |
- | Is there a monotonic relationship between physical health and mental health? | Is the average mental health score of office workers different from $\mu_0 = 50$? | |
n.a. | SPSS | SPSS | |
- | Analyze > Correlate > Bivariate...
| Analyze > Compare Means > One-Sample T Test...
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n.a. | Jamovi | Jamovi | |
- | Regression > Correlation Matrix
| T-Tests > One Sample T-Test
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Practice questions | Practice questions | Practice questions | |