A function to calculate a confidence interval for the population regression coefficient of interest using the standard approach and the noncentral approach when the regression coefficients are standardized.
1 2 3 4 
b.k 
value of the regression coefficient for the kth predictor variable 
SE.b.k 
standard error for the kth predictor variable 
s.Y 
standard deviation of Y, the dependent variable 
s.X 
standard deviation of X, the predictor variable of interest 
N 
sample size 
K 
the number of predictors 
R2.Y_X 
the squared multiple correlation coefficient predicting Y from the k predictor variables 
R2.k_X.without.k 
the squared multiple correlation coefficient predicting the kth predictor variable (i.e., the predictor of interest) from the remaining K1 predictor variables 
conf.level 
desired level of confidence for the computed interval (i.e., 1  the Type I error rate) 
R2.Y_X.without.k 
the squared multiple correlation coefficient predicting Y from the K1 predictor variable with the kth predictor of interest excluded 
t.value 
the tvalue evaluating the null hypothesis that the population regression coefficient for the kth predictor equals zero 
alpha.lower 
the Type I error rate for the lower confidence interval limit 
alpha.upper 
the Type I error rate for the upper confidence interval limit 
Noncentral 

Suppress.Statement 

... 
optional additional specifications for nested functions 
This function calls upon ci.reg.coef
in MBESS, but has a different naming system. See ci.reg.coef
for more details.
For standardized variables, do not specify the standard deviation of the variables and input the
standardized regression coefficient for b.k
.
Returns the confidence limits for the standardized regression coefficients of interest from the standard approach to confidence interval formation or from the noncentral approach to confidence interval formation using the noncentral tdistribution.
Not all of the values need to be specified, only those that contain all of the necessary information in order to compute the confidence interval (options are thus given for the values that need to be specified).
Ken Kelley (University of Notre Dame; KKelley@ND.Edu)
Kelley, K. (2007). Confidence intervals for standardized effect sizes: Theory, application, and implementation. Journal of Statistical Software, 20(8), 1–24.
Kelley, K. & Maxwell, S. E. (2003). Sample size for Multiple Regression: Obtaining regression coefficients that are accurate, not simply significant. Psychological Methods, 8, 305–321.
Kelley, K. & Maxwell, S. E. (2008). Power and accuracy for omnibus and targeted effects: Issues of sample size planning with applications to Multiple Regression. Handbook of Social Research Methods, J. Brannon, P. Alasuutari, and L. Bickman (Eds.). New York, NY: Sage Publications.
Smithson, M. (2003). Confidence intervals. New York, NY: Sage Publications.
Steiger, J. H. (2004). Beyond the F Test: Effect size confidence intervals and tests of close fit in the Analysis of Variance and Contrast Analysis. Psychological Methods, 9, 164–182.
ss.aipe.reg.coef
, conf.limits.nct
, ci.reg.coef
, ci.src
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