This paper proposes a standardized version of Swamy's test for slope homogeneity in large panels where the cross-sectional dimension (N) could be large relative to the time-series dimension (T). The test, denoted by $\hat{\Delta}$, exploits the cross-sectional dispersion of individual slopes weighted by their relative precision. In models with strictly exogenous regressors and non-normally distributed errors, the test is shown to have a standard normal distribution as $(N,T)\stackrel{j}{\rightarrow}\infty$ such that $\sqrt{N}/T^{2}\rightarrow0$. When errors are normally distributed, a mean-variance bias-adjusted version of the test is shown to be normally distributed regardless of the relative expansion rates of N and T. The test is also applied to stationary dynamic models and shown to be valid asymptotically as long as $N/T\rightarrow\kappa$, where $0\leq\kappa<\infty$. Monte Carlo experiments show that the test has the correct size and satisfactory power in panels with strictly exogenous regressors for various combinations of N and T. Similar results are obtained for dynamic panels, but only if the autoregressive coefficient is not too close to unity and $T\geq N$. The paper also considers the problem of testing homogeneity of slopes in stationary dynamic models and shows that under the null hypothesis, $\tilde{\Delta}$ tends to the standard normal distribution as long as $N/T\rightarrow\kappa$. The small sample properties of the proposed tests are investigated using Monte Carlo experiments, showing that the $\tilde{\Delta}_{adj}$ test has the correct size and good power properties. The Hausman test has the correct size but lacks power in the case of panels with exogenous regressors and randomly distributed slopes. Similar results are obtained for dynamic panels, but only if the autoregressive coefficient is not too close to unity and $T\geq N$. In cases where $N>T$ and/or the autoregressive coefficient is close to unity, a bootstrap version of the $\Delta$ test might be required. The paper proposes standardized dispersion statistics that are asymptotically normally distributed as $(N,T)\stackrel{j}{\rightarrow}\infty$ under certain conditions on the relative expansion rates of N and T. The paper also considers the application of the proposed $\bar{\Delta}$ test to stationary dynamic panel data models and shows that it is valid asymptotically under the condition $N/T\rightarrow\kappa$. The paper concludes that the proposed tests have good size and power properties and are robust to non-normal errors.This paper proposes a standardized version of Swamy's test for slope homogeneity in large panels where the cross-sectional dimension (N) could be large relative to the time-series dimension (T). The test, denoted by $\hat{\Delta}$, exploits the cross-sectional dispersion of individual slopes weighted by their relative precision. In models with strictly exogenous regressors and non-normally distributed errors, the test is shown to have a standard normal distribution as $(N,T)\stackrel{j}{\rightarrow}\infty$ such that $\sqrt{N}/T^{2}\rightarrow0$. When errors are normally distributed, a mean-variance bias-adjusted version of the test is shown to be normally distributed regardless of the relative expansion rates of N and T. The test is also applied to stationary dynamic models and shown to be valid asymptotically as long as $N/T\rightarrow\kappa$, where $0\leq\kappa<\infty$. Monte Carlo experiments show that the test has the correct size and satisfactory power in panels with strictly exogenous regressors for various combinations of N and T. Similar results are obtained for dynamic panels, but only if the autoregressive coefficient is not too close to unity and $T\geq N$. The paper also considers the problem of testing homogeneity of slopes in stationary dynamic models and shows that under the null hypothesis, $\tilde{\Delta}$ tends to the standard normal distribution as long as $N/T\rightarrow\kappa$. The small sample properties of the proposed tests are investigated using Monte Carlo experiments, showing that the $\tilde{\Delta}_{adj}$ test has the correct size and good power properties. The Hausman test has the correct size but lacks power in the case of panels with exogenous regressors and randomly distributed slopes. Similar results are obtained for dynamic panels, but only if the autoregressive coefficient is not too close to unity and $T\geq N$. In cases where $N>T$ and/or the autoregressive coefficient is close to unity, a bootstrap version of the $\Delta$ test might be required. The paper proposes standardized dispersion statistics that are asymptotically normally distributed as $(N,T)\stackrel{j}{\rightarrow}\infty$ under certain conditions on the relative expansion rates of N and T. The paper also considers the application of the proposed $\bar{\Delta}$ test to stationary dynamic panel data models and shows that it is valid asymptotically under the condition $N/T\rightarrow\kappa$. The paper concludes that the proposed tests have good size and power properties and are robust to non-normal errors.