ANCOVA - overview
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ANCOVA | Spearman's rho | Logistic regression |
You cannot compare more than 3 methods |
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Independent variables | Variable 1 | Independent variables | |
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 or more quantitative of interval or ratio level and/or one or more categorical with independent groups, transformed into code variables | |
Dependent variable | Variable 2 | Dependent variable | |
One quantitative of interval or ratio level | One of ordinal level | One categorical with 2 independent groups | |
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. | Model chi-squared test for the complete regression model:
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n.a. | Alternative hypothesis | Alternative hypothesis | |
- | H1 two sided: $\rho_s \neq 0$ H1 right sided: $\rho_s > 0$ H1 left sided: $\rho_s < 0$ | Model chi-squared test for the complete regression model:
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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. | Model chi-squared test for the complete regression model:
The wald statistic can be defined in two ways:
Likelihood ratio chi-squared test for individual $\beta_k$:
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n.a. | Sampling distribution of $t$ if H0 were true | Sampling distribution of $X^2$ and of the Wald statistic if H0 were true | |
- | Approximately the $t$ distribution with $N - 2$ degrees of freedom | Sampling distribution of $X^2$, as computed in the model chi-squared test for the complete model:
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n.a. | Significant? | Significant? | |
- | Two sided:
| For the model chi-squared test for the complete regression model and likelihood ratio chi-squared test for individual $\beta_k$:
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n.a. | n.a. | Wald-type approximate $C\%$ confidence interval for $\beta_k$ | |
- | - | $b_k \pm z^* \times SE_{b_k}$ where the critical value $z^*$ is the value under the normal curve with the area $C / 100$ between $-z^*$ and $z^*$ (e.g. $z^*$ = 1.96 for a 95% confidence interval). | |
n.a. | n.a. | Goodness of fit measure $R^2_L$ | |
- | - | $R^2_L = \dfrac{D_{null} - D_K}{D_{null}}$ There are several other goodness of fit measures in logistic regression. In logistic regression, there is no single agreed upon measure of goodness of fit. | |
n.a. | Example context | Example context | |
- | Is there a monotonic relationship between physical health and mental health? | Can body mass index, stress level, and gender predict whether people get diagnosed with diabetes? | |
n.a. | SPSS | SPSS | |
- | Analyze > Correlate > Bivariate...
| Analyze > Regression > Binary Logistic...
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n.a. | Jamovi | Jamovi | |
- | Regression > Correlation Matrix
| Regression > 2 Outcomes - Binomial
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Practice questions | Practice questions | Practice questions | |