"%||%"<-function(a, b) {if (!is.null(a)) a else b}geom_half_violin <-function(mapping =NULL, data =NULL, stat ="ydensity",position ="dodge", trim =TRUE, scale ="area",show.legend =NA, inherit.aes =TRUE, ...) {layer(data = data,mapping = mapping,stat = stat,geom = GeomHalfViolin,position = position,show.legend = show.legend,inherit.aes = inherit.aes,params =list(trim = trim,scale = scale, ... ) )}GeomHalfViolin <-ggproto("Violinist", Geom,setup_data =function(data, params) { data$width <- data$width %||% params$width %||% (resolution(data$x, FALSE) *0.9)# ymin, ymax, xmin, and xmax define the bounding rectangle for each group data %>%group_by(group) %>%mutate(ymin =min(y),ymax =max(y),xmin = x,xmax = x + width /2) },draw_group =function(data, panel_scales, coord) {# Find the points for the line to go all the way around data <-transform(data, xminv = x,xmaxv = x + violinwidth * (xmax - x))# Make sure it's sorted properly to draw the outline newdata <-rbind(plyr::arrange(transform(data, x = xminv), y), plyr::arrange(transform(data, x = xmaxv), -y))# Close the polygon: set first and last point the same# Needed for coord_polar and such newdata <-rbind(newdata, newdata[1,]) ggplot2:::ggname("geom_flat_violin", GeomPolygon$draw_panel(newdata, panel_scales, coord)) },draw_key = draw_key_polygon,default_aes =aes(weight =1, colour ="grey20", fill ="white", size =0.5,alpha =NA, linetype ="solid"),required_aes =c("x", "y") )
# use ggplotify::as.grob to convert plots into grobs firstiplot_arm <-as.grob(iplot_arm)iplot_humanoid <-as.grob(iplot_humanoid)iplot_human <-as.grob(iplot_human)
Code
draw_label_theme <-function(label, theme =NULL, element ="text", ...) {if (is.null(theme)) { theme <- ggplot2::theme_get() }if (!element %in%names(theme)) {stop("Element must be a valid ggplot theme element name") } elements <- ggplot2::calc_element(element, theme) cowplot::draw_label(label, fontfamily = elements$family,fontface = elements$face,colour = elements$color,size = elements$size, ... )}# set titlesiplot_agent_title <-ggdraw() +draw_label_theme("Interaction Plots by Agent", element ="plot.title",x =0.05, hjust =0, vjust =1)
Code
# arrange 3 interaction plots horizontally using cowplot::plot_grid# remember to provide list() not vector plot_grid(plotlist =list(iplot_arm, iplot_humanoid, iplot_human), align ="h", nrow =1, rel_widths =c(2.2, 2, 2.1))
3x2x2 ANOVA
Code
mod_322 <-aov_car(formula = mean_of_3_rounds~ motion_type * outcome_type * agent +Error(participant/(motion_type * outcome_type * agent)),dv ="mean_of_3_rounds", es ="pes", type =3, include_aov =TRUE, data = reactionTime)nice(mod_322)
Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
Sum Sq num Df Error SS den Df F value Pr(>F)
(Intercept) 2448931 1 371279 6 39.5756 0.0007513 ***
outcome_type 150870 1 22748 6 39.7935 0.0007404 ***
agent 50584 2 74526 12 4.0725 0.0446777 *
outcome_type:agent 52289 2 226034 12 1.3880 0.2869107
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Mauchly Tests for Sphericity
Test statistic p-value
agent 0.29488 0.047218
outcome_type:agent 0.46774 0.149628
Greenhouse-Geisser and Huynh-Feldt Corrections
for Departure from Sphericity
GG eps Pr(>F[GG])
agent 0.58647 0.07977 .
outcome_type:agent 0.65263 0.28723
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
HF eps Pr(>F[HF])
agent 0.6433063 0.0736056
outcome_type:agent 0.7600888 0.2880767
Code
# gave up on converting the Mauchly w to chi-squared, cant report a statistic I dont understandk =6#repeated measuresn =30W =0.865# De Mauchly's Wd <-1-((2*((k -1)^2)+(k-1)+2)/(6*(k-1)*(n-1)))Chikwadraat <--1*(n-1)*d*log(W)df <- (k*(k-1)/2)-1pchisq(Chikwadraat, df, lower.tail=FALSE)
subset_robots_TOST <- subset_bio_error |>filter(agent !="Human")# mean and SD of subset_robotsmean_and_SD_robots <- subset_robots_TOST |>group_by(agent) |>summarise(mean =mean(mean_of_3_rounds, na.rm=T), sd =sd(mean_of_3_rounds, na.rm=T))# actual effect size = Cohen's d = (433.7096 - 438.7734) ⁄ 177.337259 = 0.028555. res1a =t_TOST(x =subset(subset_robots_TOST, agent=="Robotic Arm")$mean_of_3_rounds,y =subset(subset_robots_TOST, agent=="Humanoid")$mean_of_3_rounds, paired =TRUE,eqb =62, rm_correction =TRUE)print(res1a)
Paired t-test
The equivalence test was significant, t(51) = 2.1, p = 0.02
The null hypothesis test was non-significant, t(51) = -0.187p = 0.85
NHST: don't reject null significance hypothesis that the effect is equal to zero
TOST: reject null equivalence hypothesis
TOST Results
t df p.value
t-test -0.1866 51 0.853
TOST Lower 2.0984 51 0.020
TOST Upper -2.4717 51 0.008
Effect Sizes
Estimate SE C.I. Conf. Level
Raw -5.06386 27.1328 [-50.519, 40.3913] 0.9
Hedges's g(rm) -0.02803 0.1556 [-0.2527, 0.1969] 0.9
Note: SMD confidence intervals are an approximation. See vignette("SMD_calcs").
Code
describe(res1a)
[1] "Using the Paired t-test, a null hypothesis significance test (NHST), and a equivalence test, via two one-sided tests (TOST), were performed with an alpha-level of 0.05. These tested the null hypotheses that true mean difference is equal to 0 (NHST), and true mean difference is more extreme than -62 and 62 (TOST). The equivalence test was significant, t(51) = 2.098, p = 0.02 (mean difference = -5.06 90% C.I.[-50.5, 40.391]; Hedges's g(rm) = -0.028 90% C.I.[-0.253, 0.197]). At the desired error rate, it can be stated that the true mean difference is between -62 and 62."
Paired t-test
data: mean_of_3_rounds by agent
t = 0.18663, df = 51, p-value = 0.4263
alternative hypothesis: true mean difference is greater than 0
90 percent confidence interval:
-30.16459 Inf
sample estimates:
mean difference
5.063856
Code
# Paired t-test# data: mean_of_3_rounds by agent# t = 0.18663, df = 51, p-value = 0.4263# alternative hypothesis: true mean difference is greater than 0# 95 percent confidence interval:# -40.39126 Inf# 90 percent confidence interval:# -30.16459 Inf# sample estimates:# mean difference # 5.063856 t.test(mean_of_3_rounds ~ agent, paired =TRUE, alternative ="less",data = subset_robots_TOST, conf.level =0.90)
Paired t-test
data: mean_of_3_rounds by agent
t = 0.18663, df = 51, p-value = 0.5737
alternative hypothesis: true mean difference is less than 0
90 percent confidence interval:
-Inf 40.2923
sample estimates:
mean difference
5.063856
Code
# Paired t-test# data: mean_of_3_rounds by agent# t = 0.18663, df = 51, p-value = 0.5737# alternative hypothesis: true mean difference is less than 0# 95 percent confidence interval:# -Inf 50.51898# 90 percent confidence interval:# -Inf 40.2923# sample estimates:# mean difference # 5.063856 # Paired t-test# # The equivalence test was significant, t(51) = 2.1, p = 0.02# The null hypothesis test was non-significant, t(51) = -0.187p = 0.85# NHST: don't reject null significance hypothesis that the effect is equal to zero # TOST: reject null equivalence hypothesis## t df p.value# t-test -0.1866325 51 0.853 # TOST Lower 2.0984274 51 0.020 # TOST Upper -2.4716923 51 0.008# # Estimate SE C.I.# Raw -5.06385601 27.1327687 [-50.519, 40.3913] 90% confint# Hedges's g(z) -0.02549847 0.1386976 [-0.2501, 0.1994] 90% confintsubset_robots_TOST$mean_of_3_rounds <-as.numeric(subset_robots_TOST$mean_of_3_rounds)leveneTest(mean_of_3_rounds ~ agent, data = subset_robots_TOST)
Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 1 0.3205 0.5725
102
Code
# Levene's Test for Homogeneity of Variance (center = median)# Df F value Pr(>F)# group 1 0.2562 0.6138# 102 subset_humanlike_TOST <- subset_bio_error |>filter(agent !="Robotic Arm")leveneTest(mean_of_3_rounds ~ agent, data = subset_humanlike_TOST)
Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 1 0.9894 0.3222
102
Code
# Df F value Pr(>F)# group 1 0.9894 0.3222# 102 # mean, sd humanlike mean_and_SD_humans <- subset_humanlike_TOST |>group_by(agent) |>summarise(mean =mean(mean_of_3_rounds, na.rm=T), sd =sd(mean_of_3_rounds, na.rm=T))res1b =t_TOST(x =subset(subset_humanlike_TOST, agent=="Humanoid")$mean_of_3_rounds,y =subset(subset_humanlike_TOST, agent=="Human")$mean_of_3_rounds, paired =TRUE,eqb =68)# current effect size 0.742795print(res1b)
Paired t-test
The equivalence test was non-significant, t(51) = 2.67, p = 0.99
The null hypothesis test was significant, t(51) = 5.06p < 0.01
NHST: reject null significance hypothesis that the effect is equal to zero
TOST: don't reject null equivalence hypothesis
TOST Results
t df p.value
t-test 5.060 51 < 0.001
TOST Lower 7.454 51 < 0.001
TOST Upper 2.666 51 0.995
Effect Sizes
Estimate SE C.I. Conf. Level
Raw 143.7374 28.4064 [96.1486, 191.3262] 0.9
Hedges's g(z) 0.6913 0.1544 [0.4371, 0.9396] 0.9
Note: SMD confidence intervals are an approximation. See vignette("SMD_calcs").
Code
describe(res1b)
[1] "Using the Paired t-test, a null hypothesis significance test (NHST), and a equivalence test, via two one-sided tests (TOST), were performed with an alpha-level of 0.05. These tested the null hypotheses that true mean difference is equal to 0 (NHST), and true mean difference is more extreme than -68 and 68 (TOST). The equivalence test was not significant (p = 0.995). The NHST was significant, t(51) = 5.06, p < 0.001 (mean difference = 143.737 90% C.I.[96.149, 191.326]; Hedges's g(z) = 0.691 90% C.I.[0.437, 0.94]). At the desired error rate, it can be stated that the true mean difference is not equal to 0 (i.e., no equivalence)."
mod_nonbio <-aov_ez(id ="participant", dv ="mean_of_3_rounds", within ="agent", es ="pes", type =3, include_aov =TRUE,data = subset_nonbio_error)anova(mod_nonbio)
#between robotssubset_robots_nonbio <- subset_nonbio_error |>filter(agent !="Human")# mean and SD of subset_robotsmean_and_SD_robots_nonbio <- subset_robots_nonbio |>group_by(agent) |>summarise(mean =mean(mean_of_3_rounds, na.rm=T), sd =sd(mean_of_3_rounds, na.rm=T))# actual effect size d= 0.748104res2a =t_TOST(x =subset(subset_robots_nonbio, agent=="Robotic Arm")$mean_of_3_rounds,y =subset(subset_robots_nonbio, agent=="Humanoid")$mean_of_3_rounds, paired =TRUE,eqb =51.7)print(res2a)
Paired t-test
The equivalence test was non-significant, t(51) = 2.05, p = 0.98
The null hypothesis test was significant, t(51) = 3.857p < 0.01
NHST: reject null significance hypothesis that the effect is equal to zero
TOST: don't reject null equivalence hypothesis
TOST Results
t df p.value
t-test 3.857 51 < 0.001
TOST Lower 5.669 51 < 0.001
TOST Upper 2.046 51 0.977
Effect Sizes
Estimate SE C.I. Conf. Level
Raw 110.115 28.546 [62.2923, 157.9378] 0.9
Hedges's g(z) 0.527 0.148 [0.2841, 0.7651] 0.9
Note: SMD confidence intervals are an approximation. See vignette("SMD_calcs").
Code
describe(res2a)
[1] "Using the Paired t-test, a null hypothesis significance test (NHST), and a equivalence test, via two one-sided tests (TOST), were performed with an alpha-level of 0.05. These tested the null hypotheses that true mean difference is equal to 0 (NHST), and true mean difference is more extreme than -51.7 and 51.7 (TOST). The equivalence test was not significant (p = 0.977). The NHST was significant, t(51) = 3.857, p < 0.001 (mean difference = 110.115 90% C.I.[62.292, 157.938]; Hedges's g(z) = 0.527 90% C.I.[0.284, 0.765]). At the desired error rate, it can be stated that the true mean difference is not equal to 0 (i.e., no equivalence)."
Paired t-test
data: mean_of_3_rounds by agent
t = 10.554, df = 51, p-value = 1.989e-14
alternative hypothesis: true mean difference is not equal to 0
90 percent confidence interval:
222.9332 307.0648
sample estimates:
mean difference
264.999
Code
robots_d <- effectsize::cohens_d(mean_of_3_rounds ~ agent, paired =TRUE, data = subset_robots_nonbio)# data: mean_of_3_rounds by agent# t = -3.8575, df = 51, p-value = 0.000323# alternative hypothesis: true mean difference is not equal to 0# 90 percent confidence interval:# -157.93782 -62.29229# sample estimates:# mean difference # -110.1151 # data: mean_of_3_rounds by agent# t = 10.554, df = 51, p-value = 1.989e-14# alternative hypothesis: true mean difference is not equal to 0# 90 percent confidence interval:# 222.9332 307.0648# sample estimates:# mean difference # 264.999 subset_robots_nonbio$mean_of_3_rounds <-as.numeric(subset_robots_nonbio$mean_of_3_rounds)leveneTest(mean_of_3_rounds ~ agent, data = subset_robots_nonbio)
Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 1 9.3556 0.00284 **
102
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Code
# Levene's Test for Homogeneity of Variance (center = median)# Df F value Pr(>F) # group 1 9.3556 0.00284 **# 102 power_t_TOST(n =52,delta =5.06,eqb =62,alpha = .05,type ="paired")
Paired TOST power calculation
power = 1
beta = 0
alpha = 0.05
n = 52
delta = 5.06
sd = 1
bounds = -62, 62
NOTE: n is number of *pairs*
Paired t-test
The equivalence test was non-significant, t(51) = -8.6, p = 1
The null hypothesis test was significant, t(51) = -10.6p < 0.01
NHST: reject null significance hypothesis that the effect is equal to zero
TOST: don't reject null equivalence hypothesis
TOST Results
t df p.value
t-test -10.554 51 < 0.001
TOST Lower -8.562 51 1
TOST Upper -12.545 51 < 0.001
Effect Sizes
Estimate SE C.I. Conf. Level
Raw -264.999 25.110 [-307.0648, -222.9332] 0.9
Hedges's g(z) -1.442 0.198 [-1.7616, -1.1123] 0.9
Note: SMD confidence intervals are an approximation. See vignette("SMD_calcs").
Code
# Welch Two Sample t-test# # The equivalence test was non-significant, t(89.5) = -7.7, p = 1# The null hypothesis test was significant, t(89.5) = -9.53p < 0.01# NHST: reject null significance hypothesis that the effect is equal to zero # TOST: don't reject null equivalence hypothesisleveneTest(mean_of_3_rounds ~ agent, data = subset_humanlike_nonbio)
Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 1 9.4417 0.00272 **
102
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Code
# Df F value Pr(>F) # group 1 9.4417 0.00272 **# 102 humanoid_resid <- subset_humanlike_nonbio |>filter(agent =="Humanoid") |>mutate(resid = mean_of_3_rounds -mean(mean_of_3_rounds))#qqPlot(humanoid_resid$resid)
