Spearman's rho - overview
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Spearman's rho |
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Independent variable | |
One of ordinal level | |
Dependent variable | |
One of ordinal level | |
Null hypothesis | |
$\rho_s = 0$
$\rho_s$ is the unknown Spearman correlation in the population. In words: there is no monotonic relationship between the two variables in the population | |
Alternative hypothesis | |
Two sided: $\rho_s \neq 0$ Right sided: $\rho_s > 0$ Left sided: $\rho_s < 0$ | |
Assumptions | |
Sample of pairs is a simple random sample from the population of pairs. That is, pairs are independent of one another
Note: this assumption is only important for the significance test, not for the correlation coefficient itself. The correlation coefficient itself just measures the strength of the monotonic relationship between two variables. | |
Test statistic | |
$t = \dfrac{r_s \times \sqrt{N - 2}}{\sqrt{1 - r_s^2}} $ where $r_s$ 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 | |
Approximately a $t$ distribution with $N - 2$ degrees of freedom | |
Significant? | |
Two sided:
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Example context | |
Is there a monotonic relationship between physical health and mental health? | |
SPSS | |
Analyze > Correlate > Bivariate...
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Jamovi | |
Regression > Correlation Matrix
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Practice questions | |