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Confidence interval for an average mean ratio from 2-group studies

Source: R/meta_ave.R
meta.ave.meanratio2.Rd

Computes the estimate, standard error, and confidence interval for a geometric average mean ratio from two or more 2-group studies. A Satterthwaite adjustment to the degrees of freedom is used to improve the accuracy of the confidence intervals. Equality of variances within or across studies is not assumed.

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

Usage

meta.ave.meanratio2(alpha, m1, m2, sd1, sd2, n1, n2, bystudy = TRUE)

Arguments

alpha

alpha level for 1-alpha confidence

m1

vector of estimated means for group 1

m2

vector of estimated means for group 2

sd1

vector of estimated SDs for group 1

sd2

vector of estimated SDs for group 2

n1

vector of group 1 sample sizes

n2

vector of group 2 sample sizes

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

  • exp(Estimate) - exponentiated estimate

  • exp(LL) - lower limit of the exponentiated confidence interval

  • exp(UL) - upper limit of the exponentiated confidence interval

  • df - degrees of freedom

References

Bonett DG, Price RM (2020). “Confidence intervals for ratios of means and medians.” Journal of Educational and Behavioral Statistics, 45(6), 750–770. ISSN 1076-9986, doi:10.3102/1076998620934125 .

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

Examples

m1 <- c(7.4, 6.9)
m2 <- c(6.3, 5.7)
sd1 <- c(1.7, 1.5)
sd2 <- c(2.3, 2.0)
n1 <- c(40, 20)
n2 <- c(40, 20)
meta.ave.meanratio2(.05, m1, m2, sd1, sd2, n1, n2, bystudy = TRUE)
#>          Estimate         SE          LL        UL exp(Estimate)  exp(LL)
#> Average 0.1759928 0.05738065 0.061437026 0.2905486      1.192429 1.063364
#> Study 1 0.1609304 0.06820167 0.024749712 0.2971110      1.174603 1.025059
#> Study 2 0.1910552 0.09229675 0.002986265 0.3791242      1.210526 1.002991
#>          exp(UL)       df
#> Average 1.337161 66.26000
#> Study 1 1.345965 65.69929
#> Study 2 1.461004 31.71341

# Should return:
#          Estimate         SE          LL        UL  exp(Estimate)
# Average 0.1759928 0.05738065 0.061437186 0.2905484       1.192429
# Study 1 0.1609304 0.06820167 0.024749712 0.2971110       1.174603
# Study 2 0.1910552 0.09229675 0.002986265 0.3791242       1.210526
#          exp(LL)  exp(UL)    df
# Average 1.063364 1.337161 66.27
# Study 1 1.025059 1.345965 65.70
# Study 2 1.002991 1.461004 31.71