Spearman's rho - 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
Spearman's rho | Three or more way ANOVA |
|
---|---|---|
Variable 1 | Independent/grouping variables | |
One of ordinal level | Three or more categorical with independent groups | |
Variable 2 | Dependent variable | |
One of ordinal level | One quantitative of interval or ratio level | |
Null hypothesis | THIS TABLE IS YET TO BE COMPLETED | |
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. | - | |
Alternative hypothesis | n.a. | |
H1 two sided: $\rho_s \neq 0$ H1 right sided: $\rho_s > 0$ H1 left sided: $\rho_s < 0$ | - | |
Assumptions | n.a. | |
| - | |
Test statistic | n.a. | |
$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. | - | |
Sampling distribution of $t$ if H0 were true | n.a. | |
Approximately the $t$ distribution with $N - 2$ degrees of freedom | - | |
Significant? | n.a. | |
Two sided:
| - | |
Example context | n.a. | |
Is there a monotonic relationship between physical health and mental health? | - | |
SPSS | n.a. | |
Analyze > Correlate > Bivariate...
| - | |
Jamovi | n.a. | |
Regression > Correlation Matrix
| - | |
Practice questions | Practice questions | |