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Computes tests and confidence intervals of effects in a 2x2 mixed design for means

Source: R/statpsych1.R
ci.2x2.mean.mixed.Rd

Computes confidence intervals and tests for the AB interaction effect, main effect of A, main effect of B, simple main effects of A, and simple main effects of B in a 2x2 mixed factorial design with a quantitative response variable where Factor A is a within-subjects factor and Factor B is a between-subjects factor. A Satterthwaite adjustment to the degrees of freedom is used and equality of population variances is not assumed.

For more details, see Section 4.16 of Bonett (2021, Volume 1)

Usage

ci.2x2.mean.mixed(alpha, y11, y12, y21, y22)

Arguments

alpha

alpha level for 1-alpha confidence

y11

vector of scores at level 1 of A and level 1 of B (group 1)

y12

vector of scores at level 1 of A and level 2 of B (group 2)

y21

vector of scores at level 2 of A and level 1 of B (group 1)

y22

vector of scores at level 2 of A and level 2 of B (group 2)

Value

Returns a 7-row matrix (one row per effect). The columns are:

  • Estimate - estimate of effect

  • SE - standard error

  • t - t test statistic

  • df - degrees of freedom

  • p - two-sided p-value

  • LL - lower limit of the confidence interval

  • UL - upper limit of the confidence interval

References

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

Examples

y11 <- c(18, 19, 20, 17, 20, 16)
y12 <- c(19, 16, 16, 14, 16, 18)
y21 <- c(19, 18, 19, 20, 17, 16)
y22 <- c(16, 10, 12,  9, 13, 15)
ci.2x2.mean.mixed(.05, y11, y12, y21, y22)
#>            Estimate        SE       t   df       p         LL        UL
#> AB:      -3.8333333 0.9803627 -3.9101 8.35 0.00412 -6.0776652 -1.589001
#> A:        2.0833333 0.4901814  4.2501 8.35 0.00254  0.9611674  3.205499
#> B:        3.7500000 1.0226599  3.6669 7.60 0.00693  1.3699617  6.130038
#> A at b1:  0.1666667 0.8333333  0.2000 5.00 0.84936 -1.9754849  2.308818
#> A at b2:  4.0000000 0.5163978  7.7460 5.00 0.00057  2.6725572  5.327443
#> B at a1:  1.8333333 0.9803627  1.8701 9.94 0.09117 -0.3528396  4.019506
#> B at a2:  5.6666667 1.2692955  4.4644 7.67 0.00233  2.7176000  8.615733

# Should return:
#            Estimate        SE       t   df       p         LL        UL
# AB:      -3.8333333 0.9803627 -3.9101 8.35 0.00412 -6.0778198 -1.588847
# A:        2.0833333 0.4901814  4.2501 8.35 0.00254  0.9610901  3.205577
# B:        3.7500000 1.0226599  3.6669 7.60 0.00693  1.3700362  6.129964
# A at b1:  0.1666667 0.8333333  0.2000 5.00 0.84936 -1.9754849  2.308818
# A at b2:  4.0000000 0.5163978  7.7460 5.00 0.00057  2.6725572  5.327443
# B at a1:  1.8333333 0.9803627  1.8701 9.94 0.09117 -0.3527241  4.019391
# B at a2:  5.6666667 1.2692955  4.4644 7.67 0.00233  2.7173445  8.615989