Problem 1:
Categorical effect of length.
Inference:
There is a significant relation between list length and spoken duration, as the P-value is less than 0.05.
In the Tukey HSD - test, the differences which are significant are:
5-3 6-3 6-4 6-5
Effect size of the model is 0.246. It means that the effect of length on time is 24.6%.
The coefficents of the model are:
(Intercept) length4 length5 length6
2.8384 0.6371 1.4755 2.5484
Code:
library(ISR3)
library(sjstats)## Warning: package 'sjstats' was built under R version 3.6.2library(lsr)
library(car)## Warning: package 'car' was built under R version 3.6.2## Loading required package: carData## Registered S3 methods overwritten by 'car':
## method from
## influence.merMod lme4
## cooks.distance.influence.merMod lme4
## dfbeta.influence.merMod lme4
## dfbetas.influence.merMod lme4data <- read.csv("spokenduration.csv")
data$length <- as.factor(rowSums(data[,2:12]))
A1<-aov(time~length,data=data)
summary(A1)## Df Sum Sq Mean Sq F value Pr(>F)
## length 3 199.7 66.56 23.17 5.06e-13 ***
## Residuals 213 611.8 2.87
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1TukeyHSD(A1)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = time ~ length, data = data)
##
## $length
## diff lwr upr p adj
## 4-3 0.6370875 -0.21173713 1.485912 0.2131346
## 5-3 1.4754972 0.63865652 2.312338 0.0000496
## 6-3 2.5483665 1.71152584 3.385207 0.0000000
## 5-4 0.8384096 -0.01041502 1.687234 0.0542585
## 6-4 1.9112790 1.06245431 2.760104 0.0000001
## 6-5 1.0728693 0.23602868 1.909710 0.0058012eta_sq(A1)etaSquared(A1)## eta.sq eta.sq.part
## length 0.24608 0.24608Lm1<-lm(time~length,data=data)
Lm1##
## Call:
## lm(formula = time ~ length, data = data)
##
## Coefficients:
## (Intercept) length4 length5 length6
## 2.8384 0.6371 1.4755 2.5484summary(A1)## Df Sum Sq Mean Sq F value Pr(>F)
## length 3 199.7 66.56 23.17 5.06e-13 ***
## Residuals 213 611.8 2.87
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova_stats(A1)Problem 2:
Subject effects
Inference:
Both variables, subject and length are significant. Length has an effect of 24.6% and subject has an effect of 47.4% on time with Eta Square, while Omega square shows a length effect of 24.2% and subject effect of 46.4%.
The individual participants, which were significantly faster are:
s02-s01 s03-s01 s04-s01 s03-s02 s07-s02 s08-s02 s04-s03 s05-s03 s06-s03 s07-s03 s08-s03 s07-s04 s08-s04 s07-s05 s08-s05 s07-s06 s08-s06
The rest are slower and non-significant.
Code:
subject<-data$subject
contrasts(subject)<-contr.sum(levels(subject))
A22<-aov(time~length+subject,data = data)
Anova(A22,type="II")anova_stats(A22)eta_sq(A22)omega_sq(A22)TukeyHSD(A22)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = time ~ length + subject, data = data)
##
## $length
## diff lwr upr p adj
## 4-3 0.6370875 0.1110684 1.163107 0.0104729
## 5-3 1.4754972 0.9569045 1.994090 0.0000000
## 6-3 2.5483665 2.0297739 3.066959 0.0000000
## 5-4 0.8384096 0.3123905 1.364429 0.0003078
## 6-4 1.9112790 1.3852598 2.437298 0.0000000
## 6-5 1.0728693 0.5542767 1.591462 0.0000013
##
## $subject
## diff lwr upr p adj
## s02-s01 -1.48151912 -2.3650003 -0.5980379 0.0000178
## s03-s01 -3.89438926 -4.7700969 -3.0186817 0.0000000
## s04-s01 -1.28487443 -2.1605820 -0.4091668 0.0003088
## s05-s01 -0.75244166 -1.6442186 0.1393353 0.1678404
## s06-s01 -0.63863715 -1.5221183 0.2448440 0.3479371
## s07-s01 0.39492774 -0.4885534 1.2784089 0.8702848
## s08-s01 0.45787089 -0.4178367 1.3335785 0.7491808
## s03-s02 -2.41287015 -3.2801283 -1.5456120 0.0000000
## s04-s02 0.19664468 -0.6706134 1.0639028 0.9970765
## s05-s02 0.72907746 -0.1544037 1.6125586 0.1900044
## s06-s02 0.84288196 -0.0322248 1.7179887 0.0682314
## s07-s02 1.87644685 1.0013401 2.7515536 0.0000000
## s08-s02 1.93939000 1.0721319 2.8066481 0.0000000
## s04-s03 2.60951483 1.7501770 3.4688526 0.0000000
## s05-s03 3.14194760 2.2662400 4.0176552 0.0000000
## s06-s03 3.25575211 2.3884940 4.1230102 0.0000000
## s07-s03 4.28931700 3.4220589 5.1565751 0.0000000
## s08-s03 4.35226015 3.4929224 5.2115979 0.0000000
## s05-s04 0.53243277 -0.3432748 1.4081404 0.5786002
## s06-s04 0.64623728 -0.2210208 1.5134954 0.3086493
## s07-s04 1.67980217 0.8125441 2.5470603 0.0000003
## s08-s04 1.74274532 0.8834075 2.6020831 0.0000001
## s06-s05 0.11380451 -0.7696767 0.9972857 0.9999290
## s07-s05 1.14736940 0.2638882 2.0308506 0.0024160
## s08-s05 1.21031255 0.3346050 2.0860201 0.0008979
## s07-s06 1.03356489 0.1584581 1.9086717 0.0088160
## s08-s06 1.09650804 0.2292499 1.9637662 0.0035708
## s08-s07 0.06294315 -0.8043150 0.9302013 0.9999986Problem 3:
Subject x length interactions
Inferences:
The coefficients of Length are: Coefficients: (Intercept) length4 length5 length6 3.77995 0.69606 1.58464 2.29371
The dignificant length:subject values are:
length 5 - subjects 3 length 6 - subjects 3 length 6 - subjects 7 length 6 - subjects 8
Code:
LM3<-lm(time~length*subject,data=data)
summary(LM3)##
## Call:
## lm(formula = time ~ length * subject, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.9877 -0.5156 -0.0670 0.2712 7.4353
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.77995 0.39288 9.621 < 2e-16 ***
## length4 0.69606 0.53540 1.300 0.19519
## length5 1.58464 0.55561 2.852 0.00484 **
## length6 2.29371 0.53540 4.284 2.95e-05 ***
## subjects02 -1.31678 0.53540 -2.459 0.01483 *
## subjects03 -2.79334 0.53540 -5.217 4.84e-07 ***
## subjects04 -0.68955 0.53540 -1.288 0.19939
## subjects05 -0.87705 0.53540 -1.638 0.10310
## subjects06 -1.27716 0.53540 -2.385 0.01807 *
## subjects07 -0.23307 0.53540 -0.435 0.66383
## subjects08 -0.21075 0.53540 -0.394 0.69430
## length4:subjects02 -0.31613 0.75717 -0.418 0.67679
## length5:subjects02 -0.42280 0.75717 -0.558 0.57725
## length6:subjects02 0.04725 0.74247 0.064 0.94933
## length4:subjects03 -0.73289 0.74247 -0.987 0.32488
## length5:subjects03 -1.92839 0.75717 -2.547 0.01168 *
## length6:subjects03 -1.76637 0.74247 -2.379 0.01837 *
## length4:subjects04 -0.27865 0.74247 -0.375 0.70787
## length5:subjects04 -0.68173 0.75717 -0.900 0.36909
## length6:subjects04 -1.44438 0.74247 -1.945 0.05324 .
## length4:subjects05 -0.13802 0.75717 -0.182 0.85556
## length5:subjects05 0.38635 0.75717 0.510 0.61048
## length6:subjects05 0.17643 0.75717 0.233 0.81601
## length4:subjects06 0.39881 0.75717 0.527 0.59902
## length5:subjects06 0.68824 0.75717 0.909 0.36455
## length6:subjects06 1.42169 0.74247 1.915 0.05706 .
## length4:subjects07 0.22712 0.75717 0.300 0.76454
## length5:subjects07 0.54483 0.75717 0.720 0.47270
## length6:subjects07 1.67169 0.74247 2.252 0.02553 *
## length4:subjects08 0.30060 0.74247 0.405 0.68605
## length5:subjects08 0.55599 0.75717 0.734 0.46370
## length6:subjects08 1.79446 0.74247 2.417 0.01662 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9623 on 185 degrees of freedom
## Multiple R-squared: 0.7889, Adjusted R-squared: 0.7535
## F-statistic: 22.3 on 31 and 185 DF, p-value: < 2.2e-16A3<-aov(time~length*subject,data=data)
A3## Call:
## aov(formula = time ~ length * subject, data = data)
##
## Terms:
## length subject length:subject Residuals
## Sum of Squares 199.6831 384.6762 55.7669 171.3300
## Deg. of Freedom 3 7 21 185
##
## Residual standard error: 0.9623452
## Estimated effects may be unbalancedsummary(A3)## Df Sum Sq Mean Sq F value Pr(>F)
## length 3 199.7 66.56 71.872 < 2e-16 ***
## subject 7 384.7 54.95 59.338 < 2e-16 ***
## length:subject 21 55.8 2.66 2.867 7.77e-05 ***
## Residuals 185 171.3 0.93
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1TukeyHSD(A3)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = time ~ length * subject, data = data)
##
## $length
## diff lwr upr p adj
## 4-3 0.6370875 0.1545130 1.119662 0.0042165
## 5-3 1.4754972 0.9997358 1.951258 0.0000000
## 6-3 2.5483665 2.0726052 3.024128 0.0000000
## 5-4 0.8384096 0.3558352 1.320984 0.0000692
## 6-4 1.9112790 1.4287045 2.393853 0.0000000
## 6-5 1.0728693 0.5971080 1.548631 0.0000001
##
## $subject
## diff lwr upr p adj
## s02-s01 -1.48151912 -2.29222902 -0.67080921 0.0000021
## s03-s01 -3.89438926 -4.69796588 -3.09081264 0.0000000
## s04-s01 -1.28487443 -2.08845105 -0.48129782 0.0000558
## s05-s01 -0.75244166 -1.57076403 0.06588071 0.0965523
## s06-s01 -0.63863715 -1.44934706 0.17207275 0.2402505
## s07-s01 0.39492774 -0.41578217 1.20563764 0.8100917
## s08-s01 0.45787089 -0.34570573 1.26144751 0.6564680
## s03-s02 -2.41287015 -3.20869326 -1.61704703 0.0000000
## s04-s02 0.19664468 -0.59917843 0.99246780 0.9949493
## s05-s02 0.72907746 -0.08163245 1.53978736 0.1125582
## s06-s02 0.84288196 0.03985668 1.64590724 0.0321722
## s07-s02 1.87644685 1.07342157 2.67947213 0.0000000
## s08-s02 1.93939000 1.14356689 2.73521312 0.0000000
## s04-s03 2.60951483 1.82095966 3.39807000 0.0000000
## s05-s03 3.14194760 2.33837098 3.94552422 0.0000000
## s06-s03 3.25575211 2.45992900 4.05157522 0.0000000
## s07-s03 4.28931700 3.49349388 5.08514011 0.0000000
## s08-s03 4.35226015 3.56370498 5.14081532 0.0000000
## s05-s04 0.53243277 -0.27114384 1.33600939 0.4636940
## s06-s04 0.64623728 -0.14958583 1.44206039 0.2064235
## s07-s04 1.67980217 0.88397906 2.47562528 0.0000000
## s08-s04 1.74274532 0.95419015 2.53130049 0.0000000
## s06-s05 0.11380451 -0.69690540 0.92451441 0.9998716
## s07-s05 1.14736940 0.33665949 1.95807930 0.0006112
## s08-s05 1.21031255 0.40673593 2.01388917 0.0001926
## s07-s06 1.03356489 0.23053961 1.83659017 0.0027980
## s08-s06 1.09650804 0.30068493 1.89233115 0.0009660
## s08-s07 0.06294315 -0.73287996 0.85876627 0.9999975
##
## $`length:subject`
## diff lwr upr p adj
## 4:s01-3:s01 0.696056095 -1.361061956 2.753174147 0.9999917
## 5:s01-3:s01 1.584635000 -0.550137290 3.719407290 0.5382671
## 6:s01-3:s01 2.293712667 0.236594615 4.350830718 0.0107875
## 3:s02-3:s01 -1.316778762 -3.373896813 0.740339290 0.8264416
## 4:s02-3:s01 -0.936849333 -3.071621623 1.197922957 0.9986411
## 5:s02-3:s01 -0.154948048 -2.212066099 1.902170004 1.0000000
## 6:s02-3:s01 1.024181381 -1.032936671 3.081299432 0.9900570
## 3:s03-3:s01 -2.793341090 -4.850459142 -0.736223039 0.0002180
## 4:s03-3:s01 -2.830171533 -4.887289585 -0.773053482 0.0001588
## 5:s03-3:s01 -3.137091219 -5.194209271 -1.079973168 0.0000099
## 6:s03-3:s01 -2.265997376 -4.323115428 -0.208879325 0.0130658
## 3:s04-3:s01 -0.689546048 -2.746664099 1.367572004 0.9999932
## 4:s04-3:s01 -0.272135476 -2.329253528 1.784982575 1.0000000
## 5:s04-3:s01 0.213355524 -1.843762528 2.270473575 1.0000000
## 6:s04-3:s01 0.159784095 -1.897333956 2.216902147 1.0000000
## 3:s05-3:s01 -0.877046762 -2.934164813 1.180071290 0.9991790
## 4:s05-3:s01 -0.319010667 -2.453782957 1.815761623 1.0000000
## 5:s05-3:s01 1.093935810 -0.963182242 3.151053861 0.9756354
## 6:s05-3:s01 1.593098667 -0.541673623 3.727870957 0.5260856
## 3:s06-3:s01 -1.277158048 -3.334276099 0.779960004 0.8669852
## 4:s06-3:s01 -0.182291833 -2.317064123 1.952480457 1.0000000
## 5:s06-3:s01 0.995721381 -1.061396671 3.052839432 0.9934274
## 6:s06-3:s01 2.438243810 0.381125758 4.495361861 0.0037925
## 3:s07-3:s01 -0.233073190 -2.290191242 1.824044861 1.0000000
## 4:s07-3:s01 0.690104000 -1.444668290 2.824876290 0.9999970
## 5:s07-3:s01 1.896391238 -0.160726813 3.953509290 0.1222565
## 6:s07-3:s01 3.732328667 1.675210615 5.789446718 0.0000000
## 3:s08-3:s01 -0.210751619 -2.267869671 1.846366432 1.0000000
## 4:s08-3:s01 0.785900095 -1.271217956 2.843018147 0.9998956
## 5:s08-3:s01 1.929873238 -0.127244813 3.986991290 0.1026039
## 6:s08-3:s01 3.877417667 1.820299615 5.934535718 0.0000000
## 5:s01-4:s01 0.888578905 -1.168539147 2.945696956 0.9989669
## 6:s01-4:s01 1.597656571 -0.378758523 3.574071666 0.3459300
## 3:s02-4:s01 -2.012834857 -3.989249952 -0.036419763 0.0397525
## 4:s02-4:s01 -1.632905429 -3.690023480 0.424212623 0.3855771
## 5:s02-4:s01 -0.851004143 -2.827419237 1.125410952 0.9990229
## 6:s02-4:s01 0.328125286 -1.648289809 2.304540380 1.0000000
## 3:s03-4:s01 -3.489397186 -5.465812280 -1.512982091 0.0000001
## 4:s03-4:s01 -3.526227629 -5.502642723 -1.549812534 0.0000001
## 5:s03-4:s01 -3.833147314 -5.809562409 -1.856732220 0.0000000
## 6:s03-4:s01 -2.962053471 -4.938468566 -0.985638377 0.0000165
## 3:s04-4:s01 -1.385602143 -3.362017237 0.590812952 0.6640584
## 4:s04-4:s01 -0.968191571 -2.944606666 1.008223523 0.9921451
## 5:s04-4:s01 -0.482700571 -2.459115666 1.493714523 1.0000000
## 6:s04-4:s01 -0.536272000 -2.512687095 1.440143095 1.0000000
## 3:s05-4:s01 -1.573102857 -3.549517952 0.403312237 0.3795887
## 4:s05-4:s01 -1.015066762 -3.072184813 1.042051290 0.9912635
## 5:s05-4:s01 0.397879714 -1.578535380 2.374294809 1.0000000
## 6:s05-4:s01 0.897042571 -1.160075480 2.954160623 0.9987820
## 3:s06-4:s01 -1.973214143 -3.949629237 0.003200952 0.0510018
## 4:s06-4:s01 -0.878347929 -2.935465980 1.178770123 0.9991571
## 5:s06-4:s01 0.299665286 -1.676749809 2.276080380 1.0000000
## 6:s06-4:s01 1.742187714 -0.234227380 3.718602809 0.1838071
## 3:s07-4:s01 -0.929129286 -2.905544380 1.047285809 0.9957997
## 4:s07-4:s01 -0.005952095 -2.063070147 2.051165956 1.0000000
## 5:s07-4:s01 1.200335143 -0.776079952 3.176750237 0.8917223
## 6:s07-4:s01 3.036272571 1.059857477 5.012687666 0.0000080
## 3:s08-4:s01 -0.906807714 -2.883222809 1.069607380 0.9971483
## 4:s08-4:s01 0.089844000 -1.886571095 2.066259095 1.0000000
## 5:s08-4:s01 1.233817143 -0.742597952 3.210232237 0.8602302
## 6:s08-4:s01 3.181361571 1.204946477 5.157776666 0.0000019
## 6:s01-5:s01 0.709077667 -1.348040385 2.766195718 0.9999876
## 3:s02-5:s01 -2.901413762 -4.958531813 -0.844295710 0.0000852
## 4:s02-5:s01 -2.521484333 -4.656256623 -0.386712043 0.0040407
## 5:s02-5:s01 -1.739583048 -3.796701099 0.317535004 0.2551176
## 6:s02-5:s01 -0.560453619 -2.617571671 1.496664432 0.9999999
## 3:s03-5:s01 -4.377976090 -6.435094142 -2.320858039 0.0000000
## 4:s03-5:s01 -4.414806533 -6.471924585 -2.357688482 0.0000000
## 5:s03-5:s01 -4.721726219 -6.778844271 -2.664608168 0.0000000
## 6:s03-5:s01 -3.850632376 -5.907750428 -1.793514325 0.0000000
## 3:s04-5:s01 -2.274181048 -4.331299099 -0.217062996 0.0123509
## 4:s04-5:s01 -1.856770476 -3.913888528 0.200347575 0.1492360
## 5:s04-5:s01 -1.371279476 -3.428397528 0.685838575 0.7613437
## 6:s04-5:s01 -1.424850905 -3.481968956 0.632267147 0.6888414
## 3:s05-5:s01 -2.461681762 -4.518799813 -0.404563710 0.0031790
## 4:s05-5:s01 -1.903645667 -4.038417957 0.231126623 0.1663665
## 5:s05-5:s01 -0.490699190 -2.547817242 1.566418861 1.0000000
## 6:s05-5:s01 0.008463667 -2.126308623 2.143235957 1.0000000
## 3:s06-5:s01 -2.861793048 -4.918911099 -0.804674996 0.0001206
## 4:s06-5:s01 -1.766926833 -3.901699123 0.367845457 0.2968224
## 5:s06-5:s01 -0.588913619 -2.646031671 1.468204432 0.9999998
## 6:s06-5:s01 0.853608810 -1.203509242 2.910726861 0.9994957
## 3:s07-5:s01 -1.817708190 -3.874826242 0.239409861 0.1800747
## 4:s07-5:s01 -0.894531000 -3.029303290 1.240241290 0.9993978
## 5:s07-5:s01 0.311756238 -1.745361813 2.368874290 1.0000000
## 6:s07-5:s01 2.147693667 0.090575615 4.204811718 0.0285937
## 3:s08-5:s01 -1.795386619 -3.852504671 0.261731432 0.1996744
## 4:s08-5:s01 -0.798734905 -2.855852956 1.258383147 0.9998564
## 5:s08-5:s01 0.345238238 -1.711879813 2.402356290 1.0000000
## 6:s08-5:s01 2.292782667 0.235664615 4.349900718 0.0108576
## 3:s02-6:s01 -3.610491429 -5.586906523 -1.634076334 0.0000000
## 4:s02-6:s01 -3.230562000 -5.287680052 -1.173443948 0.0000041
## 5:s02-6:s01 -2.448660714 -4.425075809 -0.472245620 0.0016259
## 6:s02-6:s01 -1.269531286 -3.245946380 0.706883809 0.8213560
## 3:s03-6:s01 -5.087053757 -7.063468852 -3.110638663 0.0000000
## 4:s03-6:s01 -5.123884200 -7.100299295 -3.147469105 0.0000000
## 5:s03-6:s01 -5.430803886 -7.407218980 -3.454388791 0.0000000
## 6:s03-6:s01 -4.559710043 -6.536125137 -2.583294948 0.0000000
## 3:s04-6:s01 -2.983258714 -4.959673809 -1.006843620 0.0000134
## 4:s04-6:s01 -2.565848143 -4.542263237 -0.589433048 0.0006102
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## 6:s06-4:s04 2.710379286 0.733964191 4.686794380 0.0001718
## 3:s07-4:s04 0.039062286 -1.937352809 2.015477380 1.0000000
## 4:s07-4:s04 0.962239476 -1.094878575 3.019357528 0.9961174
## 5:s07-4:s04 2.168526714 0.192111620 4.144941809 0.0138884
## 6:s07-4:s04 4.004464143 2.028049048 5.980879237 0.0000000
## 3:s08-4:s04 0.061383857 -1.915031237 2.037798952 1.0000000
## 4:s08-4:s04 1.058035571 -0.918379523 3.034450666 0.9734785
## 5:s08-4:s04 2.202008714 0.225593620 4.178423809 0.0109228
## 6:s08-4:s04 4.149553143 2.173138048 6.125968237 0.0000000
## 6:s04-5:s04 -0.053571429 -2.029986523 1.922843666 1.0000000
## 3:s05-5:s04 -1.090402286 -3.066817380 0.886012809 0.9615681
## 4:s05-5:s04 -0.532366190 -2.589484242 1.524751861 1.0000000
## 5:s05-5:s04 0.880580286 -1.095834809 2.856995380 0.9982431
## 6:s05-5:s04 1.379743143 -0.677374909 3.436861194 0.7503818
## 3:s06-5:s04 -1.490513571 -3.466928666 0.485901523 0.5019583
## 4:s06-5:s04 -0.395647357 -2.452765409 1.661470694 1.0000000
## 5:s06-5:s04 0.782365857 -1.194049237 2.758780952 0.9997913
## 6:s06-5:s04 2.224888286 0.248473191 4.201303380 0.0092444
## 3:s07-5:s04 -0.446428714 -2.422843809 1.529986380 1.0000000
## 4:s07-5:s04 0.476748476 -1.580369575 2.533866528 1.0000000
## 5:s07-5:s04 1.683035714 -0.293379380 3.659450809 0.2422340
## 6:s07-5:s04 3.518973143 1.542558048 5.495388237 0.0000001
## 3:s08-5:s04 -0.424107143 -2.400522237 1.552307952 1.0000000
## 4:s08-5:s04 0.572544571 -1.403870523 2.548959666 0.9999998
## 5:s08-5:s04 1.716517714 -0.259897380 3.692932809 0.2077842
## 6:s08-5:s04 3.664062143 1.687647048 5.640477237 0.0000000
## 3:s05-6:s04 -1.036830857 -3.013245952 0.939584237 0.9795787
## 4:s05-6:s04 -0.478794762 -2.535912813 1.578323290 1.0000000
## 5:s05-6:s04 0.934151714 -1.042263380 2.910566809 0.9954312
## 6:s05-6:s04 1.433314571 -0.623803480 3.490432623 0.6768025
## 3:s06-6:s04 -1.436942143 -3.413357237 0.539472952 0.5852329
## 4:s06-6:s04 -0.342075929 -2.399193980 1.715042123 1.0000000
## 5:s06-6:s04 0.835937286 -1.140477809 2.812352380 0.9992878
## 6:s06-6:s04 2.278459714 0.302044620 4.254874809 0.0062037
## 3:s07-6:s04 -0.392857286 -2.369272380 1.583557809 1.0000000
## 4:s07-6:s04 0.530319905 -1.526798147 2.587437956 1.0000000
## 5:s07-6:s04 1.736607143 -0.239807952 3.713022237 0.1888411
## 6:s07-6:s04 3.572544571 1.596129477 5.548959666 0.0000000
## 3:s08-6:s04 -0.370535714 -2.346950809 1.605879380 1.0000000
## 4:s08-6:s04 0.626116000 -1.350299095 2.602531095 0.9999981
## 5:s08-6:s04 1.770089143 -0.206325952 3.746504237 0.1601034
## 6:s08-6:s04 3.717633571 1.741218477 5.694048666 0.0000000
## 4:s05-3:s05 0.558036095 -1.499081956 2.615154147 1.0000000
## 5:s05-3:s05 1.970982571 -0.005432523 3.947397666 0.0517104
## 6:s05-3:s05 2.470145429 0.413027377 4.527263480 0.0029815
## 3:s06-3:s05 -0.400111286 -2.376526380 1.576303809 1.0000000
## 4:s06-3:s05 0.694754929 -1.362363123 2.751872980 0.9999920
## 5:s06-3:s05 1.872768143 -0.103646952 3.849183237 0.0924605
## 6:s06-3:s05 3.315290571 1.338875477 5.291705666 0.0000005
## 3:s07-3:s05 0.643973571 -1.332441523 2.620388666 0.9999964
## 4:s07-3:s05 1.567150762 -0.489967290 3.624268813 0.4787109
## 5:s07-3:s05 2.773438000 0.797022905 4.749853095 0.0000970
## 6:s07-3:s05 4.609375429 2.632960334 6.585790523 0.0000000
## 3:s08-3:s05 0.666295143 -1.310119952 2.642710237 0.9999923
## 4:s08-3:s05 1.662946857 -0.313468237 3.639361952 0.2646256
## 5:s08-3:s05 2.806920000 0.830504905 4.783335095 0.0000713
## 6:s08-3:s05 4.754464429 2.778049334 6.730879523 0.0000000
## 5:s05-4:s05 1.412946476 -0.644171575 3.470064528 0.7055391
## 6:s05-4:s05 1.912109333 -0.222662957 4.046881623 0.1599582
## 3:s06-4:s05 -0.958147381 -3.015265432 1.098970671 0.9963705
## 4:s06-4:s05 0.136718833 -1.998053457 2.271491123 1.0000000
## 5:s06-4:s05 1.314732048 -0.742386004 3.371850099 0.8286835
## 6:s06-4:s05 2.757254476 0.700136425 4.814372528 0.0002963
## 3:s07-4:s05 0.085937476 -1.971180575 2.143055528 1.0000000
## 4:s07-4:s05 1.009114667 -1.125657623 3.143886957 0.9954231
## 5:s07-4:s05 2.215401905 0.158283853 4.272519956 0.0183934
## 6:s07-4:s05 4.051339333 1.994221282 6.108457385 0.0000000
## 3:s08-4:s05 0.108259048 -1.948859004 2.165377099 1.0000000
## 4:s08-4:s05 1.104910762 -0.952207290 3.162028813 0.9723395
## 5:s08-4:s05 2.248883905 0.191765853 4.306001956 0.0146849
## 6:s08-4:s05 4.196428333 2.139310282 6.253546385 0.0000000
## 6:s05-5:s05 0.499162857 -1.557955194 2.556280909 1.0000000
## 3:s06-5:s05 -2.371093857 -4.347508952 -0.394678763 0.0030324
## 4:s06-5:s05 -1.276227643 -3.333345694 0.780890409 0.8678632
## 5:s06-5:s05 -0.098214429 -2.074629523 1.878200666 1.0000000
## 6:s06-5:s05 1.344308000 -0.632107095 3.320723095 0.7244360
## 3:s07-5:s05 -1.327009000 -3.303424095 0.649406095 0.7484811
## 4:s07-5:s05 -0.403831810 -2.460949861 1.653286242 1.0000000
## 5:s07-5:s05 0.802455429 -1.173959666 2.778870523 0.9996628
## 6:s07-5:s05 2.638392857 0.661977763 4.614807952 0.0003255
## 3:s08-5:s05 -1.304687429 -3.281102523 0.671727666 0.7781591
## 4:s08-5:s05 -0.308035714 -2.284450809 1.668379380 1.0000000
## 5:s08-5:s05 0.835937429 -1.140477666 2.812352523 0.9992878
## 6:s08-5:s05 2.783481857 0.807066763 4.759896952 0.0000884
## 3:s06-6:s05 -2.870256714 -4.927374766 -0.813138663 0.0001120
## 4:s06-6:s05 -1.775390500 -3.910162790 0.359381790 0.2872777
## 5:s06-6:s05 -0.597377286 -2.654495337 1.459740766 0.9999998
## 6:s06-6:s05 0.845145143 -1.211972909 2.902263194 0.9995801
## 3:s07-6:s05 -1.826171857 -3.883289909 0.230946194 0.1730231
## 4:s07-6:s05 -0.902994667 -3.037766957 1.231777623 0.9992867
## 5:s07-6:s05 0.303292571 -1.753825480 2.360410623 1.0000000
## 6:s07-6:s05 2.139230000 0.082111948 4.196348052 0.0301734
## 3:s08-6:s05 -1.803850286 -3.860968337 0.253267766 0.1920707
## 4:s08-6:s05 -0.807198571 -2.864316623 1.249919480 0.9998238
## 5:s08-6:s05 0.336774571 -1.720343480 2.393892623 1.0000000
## 6:s08-6:s05 2.284319000 0.227200948 4.341437052 0.0115152
## 4:s06-3:s06 1.094866214 -0.962251837 3.151984266 0.9753685
## 5:s06-3:s06 2.272879429 0.296464334 4.249294523 0.0064703
## 6:s06-3:s06 3.715401857 1.738986763 5.691816952 0.0000000
## 3:s07-3:s06 1.044084857 -0.932330237 3.020499952 0.9776307
## 4:s07-3:s06 1.967262048 -0.089856004 4.024380099 0.0837756
## 5:s07-3:s06 3.173549286 1.197134191 5.149964380 0.0000020
## 6:s07-3:s06 5.009486714 3.033071620 6.985901809 0.0000000
## 3:s08-3:s06 1.066406429 -0.910008666 3.042821523 0.9707153
## 4:s08-3:s06 2.063058143 0.086643048 4.039473237 0.0286657
## 5:s08-3:s06 3.207031286 1.230616191 5.183446380 0.0000014
## 6:s08-3:s06 5.154575714 3.178160620 7.130990809 0.0000000
## 5:s06-4:s06 1.178013214 -0.879104837 3.235131266 0.9410126
## 6:s06-4:s06 2.620535643 0.563417591 4.677653694 0.0009175
## 3:s07-4:s06 -0.050781357 -2.107899409 2.006336694 1.0000000
## 4:s07-4:s06 0.872395833 -1.262376457 3.007168123 0.9996194
## 5:s07-4:s06 2.078683071 0.021565020 4.135801123 0.0439197
## 6:s07-4:s06 3.914620500 1.857502448 5.971738552 0.0000000
## 3:s08-4:s06 -0.028459786 -2.085577837 2.028658266 1.0000000
## 4:s08-4:s06 0.968191929 -1.088926123 3.025309980 0.9957227
## 5:s08-4:s06 2.112165071 0.055047020 4.169283123 0.0357591
## 6:s08-4:s06 4.059709500 2.002591448 6.116827552 0.0000000
## 6:s06-5:s06 1.442522429 -0.533892666 3.418937523 0.5765444
## 3:s07-5:s06 -1.228794571 -3.205209666 0.747620523 0.8652654
## 4:s07-5:s06 -0.305617381 -2.362735432 1.751500671 1.0000000
## 5:s07-5:s06 0.900669857 -1.075745237 2.877084952 0.9974465
## 6:s07-5:s06 2.736607286 0.760192191 4.713022380 0.0001356
## 3:s08-5:s06 -1.206473000 -3.182888095 0.769942095 0.8863164
## 4:s08-5:s06 -0.209821286 -2.186236380 1.766593809 1.0000000
## 5:s08-5:s06 0.934151857 -1.042263237 2.910566952 0.9954312
## 6:s08-5:s06 2.881696286 0.905281191 4.858111380 0.0000354
## 3:s07-6:s06 -2.671317000 -4.647732095 -0.694901905 0.0002435
## 4:s07-6:s06 -1.748139810 -3.805257861 0.308978242 0.2460180
## 5:s07-6:s06 -0.541852571 -2.518267666 1.434562523 0.9999999
## 6:s07-6:s06 1.294084857 -0.682330237 3.270499952 0.7916674
## 3:s08-6:s06 -2.648995429 -4.625410523 -0.672580334 0.0002965
## 4:s08-6:s06 -1.652343714 -3.628758809 0.324071380 0.2769574
## 5:s08-6:s06 -0.508370571 -2.484785666 1.468044523 1.0000000
## 6:s08-6:s06 1.439173857 -0.537241237 3.415588952 0.5817593
## 4:s07-3:s07 0.923177190 -1.133940861 2.980295242 0.9980175
## 5:s07-3:s07 2.129464429 0.153049334 4.105879523 0.0182695
## 6:s07-3:s07 3.965401857 1.988986763 5.941816952 0.0000000
## 3:s08-3:s07 0.022321571 -1.954093523 1.998736666 1.0000000
## 4:s08-3:s07 1.018973286 -0.957441809 2.995388380 0.9838073
## 5:s08-3:s07 2.162946429 0.186531334 4.139361523 0.0144490
## 6:s08-3:s07 4.110490857 2.134075763 6.086905952 0.0000000
## 5:s07-4:s07 1.206287238 -0.850830813 3.263405290 0.9238669
## 6:s07-4:s07 3.042224667 0.985106615 5.099342718 0.0000240
## 3:s08-4:s07 -0.900855619 -2.957973671 1.156262432 0.9986897
## 4:s08-4:s07 0.095796095 -1.961321956 2.152914147 1.0000000
## 5:s08-4:s07 1.239769238 -0.817348813 3.296887290 0.8995182
## 6:s08-4:s07 3.187313667 1.130195615 5.244431718 0.0000062
## 6:s07-5:s07 1.835937429 -0.140477666 3.812352523 0.1133981
## 3:s08-5:s07 -2.107142857 -4.083557952 -0.130727763 0.0213039
## 4:s08-5:s07 -1.110491143 -3.086906237 0.865923952 0.9523924
## 5:s08-5:s07 0.033482000 -1.942933095 2.009897095 1.0000000
## 6:s08-5:s07 1.981026429 0.004611334 3.957441523 0.0485869
## 3:s08-6:s07 -3.943080286 -5.919495380 -1.966665191 0.0000000
## 4:s08-6:s07 -2.946428571 -4.922843666 -0.970013477 0.0000191
## 5:s08-6:s07 -1.802455429 -3.778870523 0.173959666 0.1355809
## 6:s08-6:s07 0.145089000 -1.831326095 2.121504095 1.0000000
## 4:s08-3:s08 0.996651714 -0.979763380 2.973066809 0.9880763
## 5:s08-3:s08 2.140624857 0.164209763 4.117039952 0.0169044
## 6:s08-3:s08 4.088169286 2.111754191 6.064584380 0.0000000
## 5:s08-4:s08 1.143973143 -0.832441952 3.120388237 0.9337044
## 6:s08-4:s08 3.091517571 1.115102477 5.067932666 0.0000046
## 6:s08-5:s08 1.947544429 -0.028870666 3.923959523 0.0596818Problem 4:
ANCOVA
Inference:
In the linear model, only Length and Subject 6 are significant. In the length:subjects, Length - subject 3,4,7 and 8 are significant.
The effect size of length from eta square - 0.243, which means that the length effect is 24.3% on time. The effect size of subject from eta square - 0.474, which means that the subject effect is 47.4% on time.
The effect size of length from omega square - 0.242, which means that the length effect is 24.2% on time. The effect size of subject from omega square - 0.466, which means that the subject effect is 46.6% on time.
Code:
data1 <- read.csv("spokenduration.csv")
data1$length1 <- rowSums(data[,2:12])
LM4<-lm(time~length1*subject,data = data1)
A4<-aov(time~length1*subject,data=data1)
summary(LM4)##
## Call:
## lm(formula = time ~ length1 * subject, data = data1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.8926 -0.5372 -0.0917 0.2532 7.7347
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.423005 0.775431 1.835 0.06797 .
## length1 0.777260 0.165903 4.685 5.15e-06 ***
## subjects02 -1.480358 1.076788 -1.375 0.17073
## subjects03 -0.973507 1.072445 -0.908 0.36510
## subjects04 0.844742 1.072445 0.788 0.43181
## subjects05 -1.233145 1.087902 -1.134 0.25835
## subjects06 -2.689087 1.076788 -2.497 0.01332 *
## subjects07 -1.999330 1.076788 -1.857 0.06481 .
## subjects08 -2.081263 1.072445 -1.941 0.05370 .
## length1:subjects02 0.000225 0.230743 0.001 0.99922
## length1:subjects03 -0.649749 0.230329 -2.821 0.00527 **
## length1:subjects04 -0.473912 0.230329 -2.058 0.04093 *
## length1:subjects05 0.106404 0.234623 0.454 0.65067
## length1:subjects06 0.454270 0.230743 1.969 0.05036 .
## length1:subjects07 0.530359 0.230743 2.298 0.02256 *
## length1:subjects08 0.563588 0.230329 2.447 0.01527 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9452 on 201 degrees of freedom
## Multiple R-squared: 0.7787, Adjusted R-squared: 0.7622
## F-statistic: 47.15 on 15 and 201 DF, p-value: < 2.2e-16summary(A4)## Df Sum Sq Mean Sq F value Pr(>F)
## length1 1 197.1 197.10 220.603 < 2e-16 ***
## subject 7 384.9 54.98 61.541 < 2e-16 ***
## length1:subject 7 49.9 7.12 7.974 1.54e-08 ***
## Residuals 201 179.6 0.89
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Anova(A4,type="II")Anova(LM4,type="II")eta_sq(A4)omega_sq(A4)TukeyHSD(A4,which='subject')## Warning in replications(paste("~", xx), data = mf): non-factors ignored: length1## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## length1, subject## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = time ~ length1 * subject, data = data1)
##
## $subject
## diff lwr upr p adj
## s02-s01 -1.47793460 -2.27350166 -0.68236754 0.0000012
## s03-s01 -3.89466634 -4.68323336 -3.10609933 0.0000000
## s04-s01 -1.28515151 -2.07371853 -0.49658450 0.0000351
## s05-s01 -0.75299582 -1.55603316 0.05004152 0.0838362
## s06-s01 -0.63505264 -1.43061970 0.16051443 0.2257274
## s07-s01 0.39851225 -0.39705481 1.19407931 0.7879385
## s08-s01 0.45759381 -0.33097321 1.24616082 0.6360178
## s03-s02 -2.41673174 -3.19769008 -1.63577341 0.0000000
## s04-s02 0.19278309 -0.58817525 0.97374142 0.9950208
## s05-s02 0.72493878 -0.07062828 1.52050584 0.1030212
## s06-s02 0.84288196 0.05485599 1.63090794 0.0267010
## s07-s02 1.87644685 1.08842088 2.66447282 0.0000000
## s08-s02 1.93552841 1.15457007 2.71648674 0.0000000
## s04-s03 2.60951483 1.83568869 3.38334097 0.0000000
## s05-s03 3.14167052 2.35310351 3.93023754 0.0000000
## s06-s03 3.25961371 2.47865537 4.04057204 0.0000000
## s07-s03 4.29317859 3.51222026 5.07413693 0.0000000
## s08-s03 4.35226015 3.57843401 5.12608629 0.0000000
## s05-s04 0.53215569 -0.25641132 1.32072271 0.4398585
## s06-s04 0.65009888 -0.13085946 1.43105721 0.1810415
## s07-s04 1.68366377 0.90270543 2.46462210 0.0000000
## s08-s04 1.74274532 0.96891918 2.51657146 0.0000000
## s06-s05 0.11794318 -0.67762388 0.91351025 0.9998166
## s07-s05 1.15150807 0.35594101 1.94707513 0.0004004
## s08-s05 1.21058963 0.42202261 1.99915664 0.0001277
## s07-s06 1.03356489 0.24553892 1.82159086 0.0020881
## s08-s06 1.09264644 0.31168811 1.87360478 0.0007324
## s08-s07 0.05908156 -0.72187678 0.84003989 0.9999981