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 | Spearman's rho |
You cannot compare more than 3 methods |
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Independent variables | Variable 1 | Variable 1 | |
One or more categorical with independent groups, and one or more quantitative control variables of interval or ratio level (covariates) | One of ordinal level | One of ordinal level | |
Dependent variable | Variable 2 | Variable 2 | |
One quantitative of interval or ratio level | One of ordinal level | One of ordinal 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: $\rho_s = 0$
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. | |
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: $\rho_s \neq 0$ H1 right sided: $\rho_s > 0$ H1 left sided: $\rho_s < 0$ | |
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{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. | |
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 | Approximately the $t$ distribution with $N - 2$ degrees of freedom | |
n.a. | Significant? | Significant? | |
- | Two sided:
| Two sided:
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n.a. | Example context | Example context | |
- | Is there a monotonic relationship between physical health and mental health? | Is there a monotonic relationship between physical health and mental health? | |
n.a. | SPSS | SPSS | |
- | Analyze > Correlate > Bivariate...
| Analyze > Correlate > Bivariate...
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n.a. | Jamovi | Jamovi | |
- | Regression > Correlation Matrix
| Regression > Correlation Matrix
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Practice questions | Practice questions | Practice questions | |