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Confidence interval for an average slope coefficient

Source: R/meta_ave.R
meta.ave.slope.Rd

Computes the estimate, standard error, and confidence interval for an average slope coefficient in a simple linear regression model from two or more studies. A Satterthwaite adjustment to the degrees of freedom is used to improve the accuracy of the confidence interval for the average slope.

For more details, see Chapter 2 of Bonett (2021, Volume 5).

Usage

meta.ave.slope(alpha, n, cor, sdy, sdx, bystudy = TRUE)

Arguments

alpha

alpha level for 1-alpha confidence

n

vector of sample sizes

cor

vector of estimated correlations

sdy

vector of estimated SDs of y

sdx

vector of estimated SDs of x

bystudy

logical to also return each study estimate (TRUE) or not

Value

Returns a matrix. The first row is the average estimate across all studies. If bystudy is TRUE, there is 1 additional row for each study. The matrix has the following columns:

  • Estimate - estimated effect size

  • SE - standard error

  • LL - lower limit of the confidence interval

  • UL - upper limit of the confidence interval

  • df - degrees of freedom

References

Bonett DG (2021). Statistical Methods for Psychologists, Vol 1-5, https://dgbonett.sites.ucsc.edu/.

Examples

n <- c(45, 85, 50, 60)
cor <- c(.24, .35, .16, .20)
sdy <- c(12.2, 14.1, 11.7, 15.9)
sdx <- c(1.34, 1.87, 2.02, 2.37)
meta.ave.slope(.05, n, cor, sdy, sdx, bystudy = TRUE)
#>          Estimate        SE         LL       UL     df
#> Average 1.7731542 0.4755417  0.8335022 2.712806 149.48
#> Study 1 2.1850746 1.3084468 -0.4536599 4.823809  43.00
#> Study 2 2.6390374 0.7262491  1.1945573 4.083518  83.00
#> Study 3 0.9267327 0.8146126 -0.7111558 2.564621  48.00
#> Study 4 1.3417722 0.8456799 -0.3510401 3.034584  58.00

# Should return:
#          Estimate        SE         LL       UL     df
# Average 1.7731542 0.4755417  0.8335021 2.712806 149.48
# Study 1 2.1850746 1.3084468 -0.4536599 4.823809  43.00
# Study 2 2.6390374 0.7262491  1.1945573 4.083518  83.00
# Study 3 0.9267327 0.8146126 -0.7111558 2.564621  48.00
# Study 4 1.3417722 0.8456799 -0.3510401 3.034584  58.00