WebPower (version 0.5.2)

# wp.regression: Statistical Power Analysis for Linear Regression

## Description

This function is for power analysis for regression models. Regression is a statistical technique for examining the relationship between one or more independent variables (or predictors) and one dependent variable (or the outcome). Regression provides an F-statistic that can be formulated using the ratio between variation in the outcome variable that is explained by the predictors and the unexplained variation (Cohen, 1988)). The test statistc can also be experessed in terms of caomparison between Full and Reduced models (Maxwell & Delaney, 2003).

## Usage

```wp.regression(n = NULL, p1 = NULL, p2 = 0, f2 = NULL, alpha = 0.05,
power = NULL)```

## Arguments

n

Sample size.

p1

Number of predictors in the full model.

p2

Number of predictors in the reduced moedel, it is 0 by default. See the book by Maxwell and Delaney (2003) for the definition of the reduced model.

f2

Effect size. We use the statistic f2 as the measure of effect size for linear regression proposed by Cohen(1988, p.410). Cohen discussed the effect size in three different cases. The calculatation of f2 can be generalized using the idea of a full model and a reduced model by Maxwell and Delaney (2003).

alpha

significance level chosed for the test. It equals 0.05 by default.

power

Statistical power.

## Value

An object of the power analysis

## References

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd Ed). Hillsdale, NJ: Lawrence Erlbaum Associates.

Maxwell, S. E., & Delaney, H. D. (2004). Designing experiments and analyzing data: A model comparison perspective (Vol. 1). Psychology Press.

Zhang, Z., & Yuan, K.-H. (2018). Practical Statistical Power Analysis Using Webpower and R (Eds). Granger, IN: ISDSA Press.

## Examples

Run this code
```# NOT RUN {
#To calculate the statistical power given sample size and effect size:
wp.regression(n = 100, p1 = 3, f2 = 0.1, alpha = 0.05, power = NULL)
#  Power for multiple regression
#
#      n p1 p2  f2 alpha     power
#    100  3  0 0.1  0.05 0.7420463
#
#  URL: http://psychstat.org/regression

#To generate a power curve given a sequence of sample sizes:
res <- wp.regression(n = seq(50,300,50), p1 = 3, f2 = 0.1,
alpha = 0.05, power = NULL)
res
#  Power for multiple regression
#
#      n p1 p2  f2 alpha     power
#    50  3  0 0.1  0.05 0.4077879
#    100  3  0 0.1  0.05 0.7420463
#    150  3  0 0.1  0.05 0.9092082
#    200  3  0 0.1  0.05 0.9724593
#    250  3  0 0.1  0.05 0.9925216
#    300  3  0 0.1  0.05 0.9981375
#
#  URL: http://psychstat.org/regression

#To plot the power curve:
plot(res)

#To calculate the required sample size given power and effect size:
wp.regression(n = NULL, p1 = 3, f2 = 0.1, alpha = 0.05, power = 0.8)
#  Power for multiple regression
#
#           n p1 p2  f2 alpha power
#    113.0103  3  0 0.1  0.05   0.8
#
#  URL: http://psychstat.org/regression

#The statistical power given sample size and effect size when controling two predictors:
wp.regression(n = 100, p1 = 3, p2 = 2, f2 = 0.1429, alpha = 0.05, power = NULL)
#  Power for multiple regression
#
#      n p1 p2     f2 alpha     power
#    100  3  2 0.1429  0.05 0.9594695
#
#  URL: http://psychstat.org/regression

# To generate a power curve given a sequence of effect sizes:
res <- wp.regression(n = 50, p1 = 3, f2 = seq(0.05,0.5,0.05),
alpha = 0.05, power = NULL)
res
#  Power for multiple regression
#
#     n p1 p2   f2 alpha     power
#    50  3  0 0.05  0.05 0.2164842
#    50  3  0 0.10  0.05 0.4077879
#    50  3  0 0.15  0.05 0.5821296
#    50  3  0 0.20  0.05 0.7210141
#    50  3  0 0.25  0.05 0.8220164
#    50  3  0 0.30  0.05 0.8906954
#    50  3  0 0.35  0.05 0.9350154
#    50  3  0 0.40  0.05 0.9624324
#    50  3  0 0.45  0.05 0.9788077
#    50  3  0 0.50  0.05 0.9883012
#
#  URL: http://psychstat.org/regression
# }
# NOT RUN {
# }
```

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