Test of a monotonic trend in medians for an ordered between-subjects factor

Computes simultaneous confidence intervals for all adjacent pairwise comparisons of population medians using sample group medians and standard errors as input. If one or more lower limits are greater than 0 and no upper limit is less than 0, then conclude that the population medians are monotonic decreasing. If one or more upper limits are less than 0 and no lower limits are greater than 0, then conclude that the population medians are monotonic increasing. Reject the hypothesis of a monotonic trend if any lower limit is greater than 0 and any upper limit is less than 0. The sample median and standard error for each group can be computed using the ci.median function.

For more details, see Section 1.21 of Bonett (2021, Volume 2)

Usage

test.mono.median.bs(alpha, m, se)

Arguments

alpha: alpha level for simultaneous 1-alpha confidence
m: vector of estimated group medians
se: vector of estimated group standard errors

Value

Returns a matrix with the number of rows equal to the number of adjacent pairwise comparisons. The columns are:

Estimate - estimated median difference
SE - standard error
LL - one-sided lower limit of the confidence interval
UL - one-sided upper limit of the confidence interval

References

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

m <- c(12.86, 24.57, 36.29, 53.21)
se <- c(2.85, 2.99, 3.73, 3.88)
test.mono.median.bs(.05, m, se)
#>      Estimate       SE        LL         UL
#>  1 2   -11.71 4.130690 -21.59879 -1.8212115
#>  2 3   -11.72 4.780481 -23.16438 -0.2756247
#>  3 4   -16.92 5.382128 -29.80471 -4.0352947

# Should return:
#      Estimate       SE        LL         UL
#  1 2   -11.71 4.130690 -21.59879 -1.8212115
#  2 3   -11.72 4.780481 -23.16438 -0.2756247
#  3 4   -16.92 5.382128 -29.80471 -4.0352947