Analysis of Variance and Effect Sizes for Univariate Statistics
BIFIE.univar.test.RdComputes a Wald test which tests equality of means (univariate analysis of variance). In addition, the \(d\) and \(\eta\) effect sizes are computed.
Usage
BIFIE.univar.test(BIFIE.method, wald_test=TRUE)
# S3 method for class 'BIFIE.univar.test'
summary(object,digits=4,...)Value
A list with following entries
- stat.F
Data frame with \(F\) statistic for Wald test
- stat.eta
Data frame with \(\eta\) effect size and its inference
- stat.dstat
Data frame with Cohen's \(d\) effect size and its inference
- ...
More values
Examples
#############################################################################
# EXAMPLE 1: Imputed TIMSS dataset - One grouping variable
#############################################################################
data(data.timss1)
data(data.timssrep)
# create BIFIE.dat object
bdat <- BIFIEsurvey::BIFIE.data( data.list=data.timss1, wgt=data.timss1[[1]]$TOTWGT,
wgtrep=data.timssrep[, -1 ] )
#> +++ Generate BIFIE.data object
#> |*****|
#> |-----|
#**** Model 1: 3 variables splitted by book
res1 <- BIFIEsurvey::BIFIE.univar( bdat, vars=c("ASMMAT", "ASSSCI","scsci"),
group="books")
#> |*****|
#> |-----|
summary(res1)
#> ------------------------------------------------------------
#> BIFIEsurvey 3.8.0 ()
#>
#> Function 'BIFIE.univar'
#>
#> Call:
#> BIFIEsurvey::BIFIE.univar(BIFIEobj = bdat, vars = c("ASMMAT",
#> "ASSSCI", "scsci"), group = "books")
#>
#> Date of Analysis: 2026-01-11 08:35:30.647305
#> Time difference of 0.06618857 secs
#> Computation time: 0.06618857
#>
#> Multiply imputed dataset
#>
#> Number of persons = 4668
#> Number of imputed datasets = 5
#> Number of Jackknife zones per dataset = 75
#> Fay factor = 1
#>
#> Univariate Statistics | Means
#> var groupvar groupval Nweight Ncases M M_SE M_df M_t M_p
#> 1 ASMMAT books 1 7889.467 484.0 462.463 4.704 67.69 98.307 0
#> 2 ASMMAT books 2 20602.693 1213.2 488.408 3.455 798.28 141.366 0
#> 3 ASMMAT books 3 28233.896 1657.6 516.889 2.408 123.28 214.692 0
#> 4 ASMMAT books 4 11754.811 708.8 532.942 3.158 125.24 168.760 0
#> 5 ASMMAT books 5 9852.122 604.4 532.664 3.210 304.41 165.944 0
#> 6 ASSSCI books 1 7889.467 484.0 474.183 5.900 38.76 80.374 0
#> 7 ASSSCI books 2 20602.693 1213.2 507.314 4.099 102.59 123.778 0
#> 8 ASSSCI books 3 28233.896 1657.6 542.211 2.591 54.59 209.306 0
#> 9 ASSSCI books 4 11754.811 708.8 559.753 3.273 87.11 171.008 0
#> 10 ASSSCI books 5 9852.122 604.4 563.601 3.495 103.83 161.264 0
#> 11 scsci books 1 7889.467 484.0 2.132 0.060 Inf 35.316 0
#> 12 scsci books 2 20602.693 1213.2 1.896 0.034 Inf 56.501 0
#> 13 scsci books 3 28233.896 1657.6 1.771 0.025 Inf 71.743 0
#> 14 scsci books 4 11754.811 708.8 1.652 0.034 381.58 49.151 0
#> 15 scsci books 5 9852.122 604.4 1.654 0.038 Inf 43.270 0
#> M_fmi M_VarMI M_VarRep
#> 1 0.243 4.483 16.750
#> 2 0.071 0.704 11.092
#> 3 0.180 0.870 4.752
#> 4 0.179 1.485 8.191
#> 5 0.115 0.984 9.122
#> 6 0.321 9.318 23.625
#> 7 0.197 2.764 13.481
#> 8 0.271 1.514 4.894
#> 9 0.214 1.913 8.418
#> 10 0.196 1.998 9.817
#> 11 0.031 0.000 0.004
#> 12 0.039 0.000 0.001
#> 13 0.033 0.000 0.001
#> 14 0.102 0.000 0.001
#> 15 0.061 0.000 0.001
#>
#> Univariate Statistics | Standard Deviations
#> var groupvar groupval Nweight Ncases SD SD_SE SD_df SD_t SD_p
#> 1 ASMMAT books 1 7889.467 484.0 59.667 3.350 60.78 138.043 0
#> 2 ASMMAT books 2 20602.693 1213.2 59.146 1.774 163.20 275.269 0
#> 3 ASMMAT books 3 28233.896 1657.6 57.654 1.335 95.77 387.101 0
#> 4 ASMMAT books 4 11754.811 708.8 57.709 1.863 640.19 286.114 0
#> 5 ASMMAT books 5 9852.122 604.4 59.502 2.537 37.73 209.995 0
#> 6 ASSSCI books 1 7889.467 484.0 71.334 3.286 642.31 144.321 0
#> 7 ASSSCI books 2 20602.693 1213.2 66.532 1.806 91.17 280.916 0
#> 8 ASSSCI books 3 28233.896 1657.6 62.825 1.643 22.53 329.936 0
#> 9 ASSSCI books 4 11754.811 708.8 62.818 2.075 110.46 269.812 0
#> 10 ASSSCI books 5 9852.122 604.4 62.951 2.759 64.39 204.256 0
#> 11 scsci books 1 7889.467 484.0 1.049 0.027 Inf 77.933 0
#> 12 scsci books 2 20602.693 1213.2 0.924 0.020 Inf 96.421 0
#> 13 scsci books 3 28233.896 1657.6 0.815 0.020 Inf 86.572 0
#> 14 scsci books 4 11754.811 708.8 0.786 0.032 972.60 51.580 0
#> 15 scsci books 5 9852.122 604.4 0.851 0.031 Inf 53.503 0
#> SD_fmi SD_VarMI SD_VarRep
#> 1 0.257 2.399 8.344
#> 2 0.157 0.411 2.655
#> 3 0.204 0.304 1.419
#> 4 0.079 0.229 3.195
#> 5 0.326 1.746 4.339
#> 6 0.079 0.710 9.943
#> 7 0.209 0.569 2.578
#> 8 0.421 0.948 1.563
#> 9 0.190 0.683 3.485
#> 10 0.249 1.581 5.716
#> 11 0.014 0.000 0.001
#> 12 0.035 0.000 0.000
#> 13 0.044 0.000 0.000
#> 14 0.064 0.000 0.001
#> 15 0.026 0.000 0.001
# analysis of variance
tres1 <- BIFIEsurvey::BIFIE.univar.test(res1)
#> |-----|
summary(tres1)
#> ------------------------------------------------------------
#> BIFIEsurvey 3.8.0 ()
#>
#> Function 'BIFIE.univar.test'
#>
#> Call:
#> BIFIEsurvey::BIFIE.univar.test(BIFIE.method = res1)
#>
#> Date of Analysis: 2026-01-11 08:35:30.72077
#> Time difference of 0.005226851 secs
#> Computation time: 0.005226851
#>
#> Multiply imputed dataset
#>
#> Number of persons = 4668
#> Number of imputed datasets = 5
#> Number of Jackknife zones per dataset = 75
#> Fay factor = 1
#>
#> F Test (ANOVA)
#> variable group D1 D2 df1 D1_df2 D2_df2 D1_p D2_p
#> 1 ASMMAT books 63.9526 29.3047 4 35.0 4.1 0.0000 0.0029
#> 2 ASSSCI books 59.3973 20.1403 4 40.7 2.9 0.0000 0.0181
#> 3 scsci books 17.1813 17.2584 4 6.4 350.9 0.0015 0.0000
#>
#> Eta Squared
#> var group eta2 eta eta_SE fmi df VarMI VarRep
#> 1 ASMMAT books 0.1294 0.3597 0.0211 0.1954 104.79 0.0001 0.0004
#> 2 ASSSCI books 0.1564 0.3954 0.0206 0.0549 Inf 0.0000 0.0004
#> 3 scsci books 0.0254 0.1593 0.0194 0.0716 780.12 0.0000 0.0003
#>
#> Cohen's d Statistic
#> var group groupval1 groupval2 M1 M2 SD d d_SE
#> 1 ASMMAT books 1 2 462.4629 488.4080 59.4069 -0.4373 0.0855
#> 2 ASMMAT books 1 3 462.4629 516.8889 58.6692 -0.9283 0.1007
#> 3 ASMMAT books 1 4 462.4629 532.9423 58.6959 -1.2013 0.1026
#> 4 ASMMAT books 1 5 462.4629 532.6644 59.5847 -1.1788 0.1153
#> 5 ASMMAT books 2 3 488.4080 516.8889 58.4049 -0.4876 0.0547
#> 6 ASMMAT books 2 4 488.4080 532.9423 58.4317 -0.7620 0.0655
#> 7 ASMMAT books 2 5 488.4080 532.6644 59.3245 -0.7459 0.0773
#> 8 ASMMAT books 3 4 516.8889 532.9423 57.6815 -0.2782 0.0578
#> 9 ASMMAT books 3 5 516.8889 532.6644 58.5857 -0.2692 0.0592
#> 10 ASMMAT books 4 5 532.9423 532.6644 58.6124 0.0046 0.0665
#> 11 ASSSCI books 1 2 474.1829 507.3136 68.9746 -0.4801 0.0935
#> 12 ASSSCI books 1 3 474.1829 542.2113 67.2139 -1.0119 0.0870
#> 13 ASSSCI books 1 4 474.1829 559.7534 67.2106 -1.2729 0.1097
#> 14 ASSSCI books 1 5 474.1829 563.6009 67.2732 -1.3290 0.1122
#> 15 ASSSCI books 2 3 507.3136 542.2113 64.7048 -0.5395 0.0583
#> 16 ASSSCI books 2 4 507.3136 559.7534 64.7014 -0.8104 0.0656
#> 17 ASSSCI books 2 5 507.3136 563.6009 64.7664 -0.8693 0.0913
#> 18 ASSSCI books 3 4 542.2113 559.7534 62.8211 -0.2790 0.0591
#> 19 ASSSCI books 3 5 542.2113 563.6009 62.8880 -0.3402 0.0680
#> 20 ASSSCI books 4 5 559.7534 563.6009 62.8845 -0.0614 0.0761
#> 21 scsci books 1 2 2.1318 1.8956 0.9881 0.2390 0.0626
#> 22 scsci books 1 3 2.1318 1.7712 0.9393 0.3839 0.0635
#> 23 scsci books 1 4 2.1318 1.6515 0.9267 0.5183 0.0781
#> 24 scsci books 1 5 2.1318 1.6542 0.9549 0.5001 0.0675
#> 25 scsci books 2 3 1.8956 1.7712 0.8710 0.1428 0.0468
#> 26 scsci books 2 4 1.8956 1.6515 0.8575 0.2847 0.0551
#> 27 scsci books 2 5 1.8956 1.6542 0.8879 0.2719 0.0587
#> 28 scsci books 3 4 1.7712 1.6515 0.8007 0.1496 0.0517
#> 29 scsci books 3 5 1.7712 1.6542 0.8331 0.1405 0.0563
#> 30 scsci books 4 5 1.6515 1.6542 0.8189 -0.0033 0.0620
#> d_t d_df d_p d_fmi d_VarMI d_VarRep
#> 1 -5.1124 24.48 0.0000 0.4043 0.0025 0.0044
#> 2 -9.2220 22.31 0.0000 0.4235 0.0036 0.0058
#> 3 -11.7108 53.95 0.0000 0.2723 0.0024 0.0077
#> 4 -10.2246 55.71 0.0000 0.2680 0.0030 0.0097
#> 5 -8.9169 424.49 0.0000 0.0971 0.0002 0.0027
#> 6 -11.6320 168.14 0.0000 0.1542 0.0006 0.0036
#> 7 -9.6437 634.38 0.0000 0.0794 0.0004 0.0055
#> 8 -4.8112 141.20 0.0000 0.1683 0.0005 0.0028
#> 9 -4.5455 Inf 0.0000 0.0461 0.0001 0.0033
#> 10 0.0694 Inf 0.9447 0.0363 0.0001 0.0043
#> 11 -5.1361 22.78 0.0000 0.4190 0.0031 0.0051
#> 12 -11.6292 110.22 0.0000 0.1905 0.0012 0.0061
#> 13 -11.5999 49.89 0.0000 0.2832 0.0028 0.0086
#> 14 -11.8402 303.11 0.0000 0.1149 0.0012 0.0112
#> 15 -9.2531 90.19 0.0000 0.2106 0.0006 0.0027
#> 16 -12.3568 Inf 0.0000 0.0458 0.0002 0.0041
#> 17 -9.5183 49.51 0.0000 0.2842 0.0020 0.0060
#> 18 -4.7233 50.06 0.0000 0.2827 0.0008 0.0025
#> 19 -5.0018 61.59 0.0000 0.2548 0.0010 0.0034
#> 20 -0.8066 28.12 0.4267 0.3771 0.0018 0.0036
#> 21 3.8163 Inf 0.0001 0.0134 0.0000 0.0039
#> 22 6.0471 Inf 0.0000 0.0486 0.0002 0.0038
#> 23 6.6358 758.33 0.0000 0.0726 0.0004 0.0057
#> 24 7.4094 962.53 0.0000 0.0645 0.0002 0.0043
#> 25 3.0497 Inf 0.0023 0.0483 0.0001 0.0021
#> 26 5.1677 907.26 0.0000 0.0664 0.0002 0.0028
#> 27 4.6313 666.69 0.0000 0.0775 0.0002 0.0032
#> 28 2.8922 351.10 0.0041 0.1067 0.0002 0.0024
#> 29 2.4963 Inf 0.0126 0.0199 0.0001 0.0031
#> 30 -0.0537 220.77 0.9572 0.1346 0.0004 0.0033
#**** Model 2: One variable splitted by gender
res2 <- BIFIEsurvey::BIFIE.univar( bdat, vars=c("ASMMAT"), group="female" )
#> |*****|
#> |-----|
summary(res2)
#> ------------------------------------------------------------
#> BIFIEsurvey 3.8.0 ()
#>
#> Function 'BIFIE.univar'
#>
#> Call:
#> BIFIEsurvey::BIFIE.univar(BIFIEobj = bdat, vars = c("ASMMAT"),
#> group = "female")
#>
#> Date of Analysis: 2026-01-11 08:35:30.734813
#> Time difference of 0.02295876 secs
#> Computation time: 0.02295876
#>
#> Multiply imputed dataset
#>
#> Number of persons = 4668
#> Number of imputed datasets = 5
#> Number of Jackknife zones per dataset = 75
#> Fay factor = 1
#>
#> Univariate Statistics | Means
#> var groupvar groupval Nweight Ncases M M_SE M_df M_t M_p
#> 1 ASMMAT female 0 40129.77 2388.6 512.851 3.256 Inf 157.526 0
#> 2 ASMMAT female 1 38203.22 2279.4 503.542 2.605 454.07 193.306 0
#> M_fmi M_VarMI M_VarRep
#> 1 0.028 0.247 10.303
#> 2 0.094 0.531 6.149
#>
#> Univariate Statistics | Standard Deviations
#> var groupvar groupval Nweight Ncases SD SD_SE SD_df SD_t SD_p
#> 1 ASMMAT female 0 40129.77 2388.6 63.484 1.379 78.52 372.009 0
#> 2 ASMMAT female 1 38203.22 2279.4 61.496 1.325 102.78 380.057 0
#> SD_fmi SD_VarMI SD_VarRep
#> 1 0.226 0.357 1.472
#> 2 0.197 0.289 1.409
# analysis of variance
tres2 <- BIFIEsurvey::BIFIE.univar.test(res2)
#> |-----|
summary(tres2)
#> ------------------------------------------------------------
#> BIFIEsurvey 3.8.0 ()
#>
#> Function 'BIFIE.univar.test'
#>
#> Call:
#> BIFIEsurvey::BIFIE.univar.test(BIFIE.method = res2)
#>
#> Date of Analysis: 2026-01-11 08:35:30.763999
#> Time difference of 0.001686335 secs
#> Computation time: 0.001686335
#>
#> Multiply imputed dataset
#>
#> Number of persons = 4668
#> Number of imputed datasets = 5
#> Number of Jackknife zones per dataset = 75
#> Fay factor = 1
#>
#> F Test (ANOVA)
#> variable group D1 D2 df1 D1_df2 D2_df2 D1_p D2_p
#> 1 ASMMAT female 12.048 11.37 1 4 105.3 0.0256 0.001
#>
#> Eta Squared
#> var group eta2 eta eta_SE fmi df VarMI VarRep
#> 1 ASMMAT female 0.0055 0.0742 0.0207 0.0628 Inf 0 0.0004
#>
#> Cohen's d Statistic
#> var group groupval1 groupval2 M1 M2 SD d d_SE
#> 1 ASMMAT female 0 1 512.8511 503.5417 62.4978 0.1489 0.0417
#> d_t d_df d_p d_fmi d_VarMI d_VarRep
#> 1 3.5694 Inf 0.0004 0.063 0.0001 0.0016
if (FALSE) { # \dontrun{
#**** Model 3: Univariate statistic: math
res3 <- BIFIEsurvey::BIFIE.univar( bdat, vars=c("ASMMAT") )
summary(res3)
tres3 <- BIFIEsurvey::BIFIE.univar.test(res3)
#############################################################################
# EXAMPLE 2: Imputed TIMSS dataset - Two grouping variables
#############################################################################
data(data.timss1)
data(data.timssrep)
# create BIFIE.dat object
bdat <- BIFIEsurvey::BIFIE.data( data.list=data.timss1, wgt=data.timss1[[1]]$TOTWGT,
wgtrep=data.timssrep[, -1 ] )
#**** Model 1: 3 variables splitted by book and female
res1 <- BIFIEsurvey::BIFIE.univar(bdat, vars=c("ASMMAT", "ASSSCI","scsci"),
group=c("books","female"))
summary(res1)
# analysis of variance
tres1 <- BIFIEsurvey::BIFIE.univar.test(res1)
summary(tres1)
# extract data frame with Cohens d statistic
dstat <- tres1$stat.dstat
# extract d values for gender comparisons with same value of books
# -> 'books' refers to the first variable
ind <- which(
unlist( lapply( strsplit( dstat$groupval1, "#"), FUN=function(vv){vv[1]}) )==
unlist( lapply( strsplit( dstat$groupval2, "#"), FUN=function(vv){vv[1]}) )
)
dstat[ ind, ]
} # }