This paper proposes a standardized version of Swamy's test for panel data models where the cross-sectional dimension ($N$) is large relative to the time series dimension ($T$). The proposed test, denoted by $\Delta$, uses the dispersion of individual slopes weighted by their relative precision. For models with strictly exogenous regressors and non-normally distributed errors, the test is shown to have a standard normal distribution as $(N, T) \xrightarrow{d} \infty$ under certain conditions. When the 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 its asymptotic validity is established under specific conditions. Monte Carlo experiments demonstrate 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 discusses the limitations of existing tests, such as the standard $F$ test and Hausman's test, and highlights the advantages of the proposed dispersion tests.This paper proposes a standardized version of Swamy's test for panel data models where the cross-sectional dimension ($N$) is large relative to the time series dimension ($T$). The proposed test, denoted by $\Delta$, uses the dispersion of individual slopes weighted by their relative precision. For models with strictly exogenous regressors and non-normally distributed errors, the test is shown to have a standard normal distribution as $(N, T) \xrightarrow{d} \infty$ under certain conditions. When the 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 its asymptotic validity is established under specific conditions. Monte Carlo experiments demonstrate 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 discusses the limitations of existing tests, such as the standard $F$ test and Hausman's test, and highlights the advantages of the proposed dispersion tests.