PS296 Chapter Notes - Chapter 9: Explained Variation, Church Attendance, Confidence Interval
Testing the Significance of a Correlation Coefficient
-correlation coefficients suffer from sampling error and deviate from true correlations in the
population by some amount
-small deviations from the true value of zero are to be expected, large deviations are not
-population correlation coefficient rho is the correlation coefficient in the population
(denoted ρ, ex H0: p = 0)
Student's t (equation for statistical significance / confidence interval)
-degrees of freedom = N – 2 where N = the number of pairs, which will be 2 times N
-confidence interval of 0.042 – 0.619 (rounded to 3 decimals) = 95% confidence
-if you compute 1000 95% confidence intervals on some statistic, 950 of those will include
the true population correlation and 50 of them will not
-we don't say that a confidence level is 95% but rather that there is a probabiliy of .95 of
including p
Intercorrelation Matrixes:
-intercorrelation matrix is a matrix table showing the pairwise correlations between all
variables
-scatterplot matrix is a table in whose cells are the scatterplots of the row and column
Document Summary
Correlation coefficients suffer from sampling error and deviate from true correlations in the population by some amount. Small deviations from the true value of zero are to be expected, large deviations are not. Population correlation coefficient rho is the correlation coefficient in the population (denoted , ex h0: p = 0) Student"s t (equation for statistical significance / confidence interval) Degrees of freedom = n 2 where n = the number of pairs, which will be 2 times n. Confidence interval of 0. 042 0. 619 (rounded to 3 decimals) = 95% confidence. If you compute 1000 95% confidence intervals on some statistic, 950 of those will include the true population correlation and 50 of them will not. We don"t say that a confidence level is 95% but rather that there is a probabiliy of . 95 of including p. Intercorrelation matrix is a matrix table showing the pairwise correlations between all variables.
