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Published byMarina Prudden Modified over 3 years ago

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Tests of Significance for Regression & Correlation b* will equal the population parameter of the slope rather thanbecause beta has another meaning with respect to regression coefficients. b is normally distributed about b* with a standard error of To test the null hypothesis that b* = 0, then When there is a single predictor variable, then testing b is the same as testing r not equal to zero. Distributed as N-2 df. Again, distributed with N-2 df

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The difference between two independent slopes (like a t-test for two means) If the null hypothesis is true (b1* = b2*), then the sampling distribution of b1-b2 is normal with a mean of 0 and a standard error of… Thus, And is distributed with N1 + N2 –4 df Because we know… Therefore….

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Transformed…. Thus… (is we assume homogeneity of error variance then we can pool the two estimates.) This can be substituted for the individual error variances in the above formula. Distributed with N1+N2 –4 df

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The difference between independent correlations Whenis not equal to zero, the sampling distribution of r is NOT normal and its becomes more skewed more approaches 1.0 and the random error is not easily estimated. The same is the case for Fisher’s solution is that we transform r into r’ Then r’ is approximately normally distributed and the standard error is… Sometimes called the z transformation. As a z score, the critical value is 1.96

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Test for difference between two related correlation coefficients Note that to apply this test the correlation is required. Distributed with N-3 df. Because the two correlations are not independent, we must take this into account (remember the issue with ANOVA). In this case, specially, we must incorporate a term that reflects the degree to which the two test themselves are related.

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