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Examples
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If we adjust the standard errors for heteroskedasticity the t-statistic falls to -1.87 but the inference remains the same.
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While this says that right to work states have about 1% point less unemployment on average, the t-statistic testing the null hypothesis that the coefficient on the right to work state variable is actually zero is computed to be - 1.935.
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Osborn and Briffa did not even do a simple t-test although this is available merely by obtaining the correlation as the regression coefficient between two scaled series, yielding the t-statistic in the process.
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Perhaps one could introduce Jones and Mann to the t-statistic, recently introduced around 1920 to test significance allowing for the number of measurements.
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The adjusted r-squared was -0.002; the t-statistic was only 0.85 and the DW an unbelievable 0.06.
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Phillips showed that the t-statistic does not settle down as N increases, but diverges.
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Unless otherwise indicated all variance and correlation coefficients are valid at the 95% level using the t-statistic with correction for serial correlation Davis 1976.
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As I understand what he said there, when he regressed the foxtail series on the relevant grid cell temperature he found the “r2 is 0.002; the adjusted r2 is -0.006; the t-statistic for proxy on temperature is an insignificant 0.52 without even worrying about autocorrelation and the DW is 0.986.”
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With small samples lt 20 use the t-statistic, not the z-score.
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Phillips showed that the t-statistic does not settle down as N increases, but diverges.
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