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I have a problem with the interpretation of a test result in which the p-value is 8.6e-28. How should it be interpreted? What is the e for?

Specifically, I used White's Test for the homoscedasticity assumption of a linear regression:

White's general test statistic :  150.0535  Chi-sq( 9)  P-value =  8.6e-28
whuber
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Ljudmila Ivanova
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  • Heteroscedasticity in the residuals can be a symptom of the residuals having a deterministic structure (Pulses/Level Shifts/Seasonal Pulses/Local Time Trends OR auto-correlative structure OR the variance of the residuals changing at fixed points in time OR the variance of the residuals being proportionate to the level of the observed Y OR the variance of the residuals having an ARIMA process. – IrishStat Feb 23 '15 at 15:27

2 Answers2

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The e is standard scientific notation for powers of $10$: 8.6e-28 means $8.6 \cdot 10^{-28}$.

The White test tests for heteroscedasticity of a variable's distribution, most commonly in the residuals of your regression. A significant result indicates that your data are significantly heteroscedastic, and thus the assumption of homoscedasticity in the regression residuals is violated. In your case the data violate the assumption of homoscedasticity, as your $p$ value is $8.6 \cdot 10^{-28}$. The e is standard scientific notation for powers of $10$.

Nick Cox
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Chris Novak
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$8.6\mathrm{e}{-28} = 8.6 \times 10^{-28}$

This means a highly statistically significant result. If alpha (0.05) is greater than the p-value, then we can reject the null hypothesis. Hence we can say that homoscedasticity cannot be assumed.

Silverfish
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user43247
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