Analysis of Experiment 2
Simon Stephan
1 Read in the data
Note: data need to be in the same folder as the analysis script. Otherwise, the path needs to be specified.
library(readr)
tdata <- read_delim("data.txt",
delim = "\t", escape_double = FALSE,
trim_ws = TRUE)## Rows: 780 Columns: 12
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: "\t"
## chr (7): subj_code, desktop_conf, attent_conf, Cond_sum, explanation, gender...
## dbl (5): condition, instr_tests, Rating_CC, Rating_SE, age
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.2 Demographics
Subject demographics:
# demographics
min(tdata$age) # minimum age ## [1] 18max(tdata$age) # maximum age## [1] 75mean(tdata$age) # mean age## [1] 37.94231sd(tdata$age) # standard deviation of age## [1] 12.73167table(tdata$gender) ##
## 1: male 2: female 3: non-binary
## 388 378 11
## 4: prefer not to say
## 33 Analyses
First prepare the data set:
- Factorize
- reshape into long format (for graphs)
- divide dv ratings by 10 to limit ratings to a range between 0 and 1 (this is how we scale the y-axis for the graphs)
3.1 Graphs
Ratings in all conditions:
## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.## Warning: `fun.y` is deprecated. Use `fun` instead.
## `fun.y` is deprecated. Use `fun` instead.
## `fun.y` is deprecated. Use `fun` instead.
Now seperately for the binary and continuous variables conditions.
Binary:
binary <- subset(tdata_long, Cond_sum == "binary-radial" | Cond_sum == "binary-channel") # subset
continuous <- subset(tdata_long, Cond_sum != "binary-radial" & Cond_sum != "binary-channel") # subset## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.## Warning: `fun.y` is deprecated. Use `fun` instead.
## `fun.y` is deprecated. Use `fun` instead.
## `fun.y` is deprecated. Use `fun` instead.
Continuous:
## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.## Warning: `fun.y` is deprecated. Use `fun` instead.
## `fun.y` is deprecated. Use `fun` instead.
## `fun.y` is deprecated. Use `fun` instead.
3.2 Appending of additional factors
The original data set as a “combined” column that codes the different factor combinations. We here append columns to the data frame that seperate the different factors:
- Transmission type: channel vs. radial
- Level of energy: unlimited vs. limited (this only exist in the continuous variables conditions)
continuous$transmission[continuous$Cond_sum == "cont.-channel-unlimited" | continuous$Cond_sum == "cont.-channel-limited"] <- "channel" ## Warning: Unknown or uninitialised column: `transmission`.continuous$transmission[continuous$Cond_sum == "cont.-radial-unlimited" | continuous$Cond_sum == "cont.-radial-limited"] <- "radial"
continuous$energy[continuous$Cond_sum == "cont.-channel-unlimited" | continuous$Cond_sum == "cont.-radial-unlimited"] <- "unlimited"## Warning: Unknown or uninitialised column: `energy`.continuous$energy[continuous$Cond_sum == "cont.-channel-limited" | continuous$Cond_sum == "cont.-radial-limited"] <- "specific"
continuous$var_type <- "continuous"type of transmission also in the case of binary variables:
binary$transmission[binary$Cond_sum == "binary-channel"] <- "channel"## Warning: Unknown or uninitialised column: `transmission`.binary$transmission[binary$Cond_sum == "binary-radial"] <- "radial"
binary$var_type <- "binary"3.3 Descriptive Stats
## : Rating_SE
## : channel
## : specific
## median mean SE.mean CI.mean.0.95 var std.dev
## 0.90000000 0.82230769 0.02104218 0.04163247 0.05756052 0.23991775
## coef.var
## 0.29176152
## ------------------------------------------------------------
## : Rating_CC
## : channel
## : specific
## median mean SE.mean CI.mean.0.95 var std.dev
## 0.30000000 0.41846154 0.02048269 0.04052549 0.05454025 0.23353854
## coef.var
## 0.55808843
## ------------------------------------------------------------
## : Rating_SE
## : radial
## : specific
## median mean SE.mean CI.mean.0.95 var std.dev
## 0.70000000 0.63846154 0.02744072 0.05429213 0.09788909 0.31287232
## coef.var
## 0.49004098
## ------------------------------------------------------------
## : Rating_CC
## : radial
## : specific
## median mean SE.mean CI.mean.0.95 var std.dev
## 0.50000000 0.47461538 0.02294146 0.04539025 0.06842039 0.26157292
## coef.var
## 0.55112609
## ------------------------------------------------------------
## : Rating_SE
## : channel
## : unlimited
## median mean SE.mean CI.mean.0.95 var std.dev
## 0.90000000 0.82230769 0.01999599 0.03956255 0.05197913 0.22798932
## coef.var
## 0.27725549
## ------------------------------------------------------------
## : Rating_CC
## : channel
## : unlimited
## median mean SE.mean CI.mean.0.95 var std.dev
## 0.60000000 0.57923077 0.02406749 0.04761812 0.07530173 0.27441161
## coef.var
## 0.47375178
## ------------------------------------------------------------
## : Rating_SE
## : radial
## : unlimited
## median mean SE.mean CI.mean.0.95 var std.dev
## 0.80000000 0.69923077 0.02438256 0.04824150 0.07728623 0.27800400
## coef.var
## 0.39758548
## ------------------------------------------------------------
## : Rating_CC
## : radial
## : unlimited
## median mean SE.mean CI.mean.0.95 var std.dev
## 0.50000000 0.59461538 0.02365806 0.04680805 0.07276148 0.26974336
## coef.var
## 0.45364342by(binary$value, list(binary$variable, binary$transmission), stat.desc , basic = FALSE)## : Rating_SE
## : channel
## median mean SE.mean CI.mean.0.95 var std.dev
## 1.00000000 0.84076923 0.02153047 0.04259857 0.06026297 0.24548517
## coef.var
## 0.29197687
## ------------------------------------------------------------
## : Rating_CC
## : channel
## median mean SE.mean CI.mean.0.95 var std.dev
## 0.95000000 0.76923077 0.02511384 0.04968835 0.08199165 0.28634184
## coef.var
## 0.37224440
## ------------------------------------------------------------
## : Rating_SE
## : radial
## median mean SE.mean CI.mean.0.95 var std.dev
## 0.80000000 0.76538462 0.02177873 0.04308975 0.06166070 0.24831573
## coef.var
## 0.32443262
## ------------------------------------------------------------
## : Rating_CC
## : radial
## median mean SE.mean CI.mean.0.95 var std.dev
## 0.80000000 0.70846154 0.02437127 0.04821916 0.07721467 0.27787528
## coef.var
## 0.392223523.4 Fitting statistical models
library(afex)## ************
## Welcome to afex. For support visit: http://afex.singmann.science/## - Functions for ANOVAs: aov_car(), aov_ez(), and aov_4()
## - Methods for calculating p-values with mixed(): 'S', 'KR', 'LRT', and 'PB'
## - 'afex_aov' and 'mixed' objects can be passed to emmeans() for follow-up tests
## - NEWS: emmeans() for ANOVA models now uses model = 'multivariate' as default.
## - Get and set global package options with: afex_options()
## - Set orthogonal sum-to-zero contrasts globally: set_sum_contrasts()
## - For example analyses see: browseVignettes("afex")
## ************##
## Attache Paket: 'afex'## Das folgende Objekt ist maskiert 'package:lme4':
##
## lmerlibrary(emmeans)
#citation("afex")For binary variables case:
a_bin <- aov_car(value ~ variable*transmission + Error(subj_code/(variable)), binary)## Converting to factor: transmission## Contrasts set to contr.sum for the following variables: transmissiona_bin## Anova Table (Type 3 tests)
##
## Response: value
## Effect df MSE F ges p.value
## 1 transmission 1, 258 0.10 5.97 * .016 .015
## 2 variable 1, 258 0.04 13.51 *** .015 <.001
## 3 transmission:variable 1, 258 0.04 0.17 <.001 .676
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1knitr::kable(nice(a_bin))| Effect | df | MSE | F | ges | p.value |
|---|---|---|---|---|---|
| transmission | 1, 258 | 0.10 | 5.97 * | .016 | .015 |
| variable | 1, 258 | 0.04 | 13.51 *** | .015 | <.001 |
| transmission:variable | 1, 258 | 0.04 | 0.17 | <.001 | .676 |
Follow-up of ANOVA for binary variables cases:
Main effect of transmission type
MainE_transmission<-emmeans(a_bin, ~transmission)
MainE_transmission## transmission emmean SE df lower.CL upper.CL
## channel 0.805 0.0197 258 0.766 0.844
## radial 0.737 0.0197 258 0.698 0.776
##
## Results are averaged over the levels of: variable
## Confidence level used: 0.95confint(pairs(MainE_transmission), level = 0.95)## contrast estimate SE df lower.CL upper.CL
## channel - radial 0.0681 0.0279 258 0.0132 0.123
##
## Results are averaged over the levels of: variable
## Confidence level used: 0.95Main effect of variable type (the type of cause)
MainE_cause<-emmeans(a_bin, ~variable)
MainE_cause## variable emmean SE df lower.CL upper.CL
## Rating_SE 0.803 0.0153 258 0.773 0.833
## Rating_CC 0.739 0.0175 258 0.704 0.773
##
## Results are averaged over the levels of: transmission
## Confidence level used: 0.95pairs(MainE_cause, level = 0.95)## contrast estimate SE df t.ratio p.value
## Rating_SE - Rating_CC 0.0642 0.0175 258 3.676 0.0003
##
## Results are averaged over the levels of: transmissionFor continuous variables case:
a_cont <- aov_car(value ~ variable*transmission*energy + Error(subj_code/(variable)), continuous)## Converting to factor: transmission, energy## Contrasts set to contr.sum for the following variables: transmission, energya_cont## Anova Table (Type 3 tests)
##
## Response: value
## Effect df MSE F ges p.value
## 1 transmission 1, 516 0.07 12.93 *** .012 <.001
## 2 energy 1, 516 0.07 27.22 *** .026 <.001
## 3 transmission:energy 1, 516 0.07 0.09 <.001 .760
## 4 variable 1, 516 0.07 196.47 *** .160 <.001
## 5 transmission:variable 1, 516 0.07 33.58 *** .031 <.001
## 6 energy:variable 1, 516 0.07 11.35 *** .011 <.001
## 7 transmission:energy:variable 1, 516 0.07 2.42 .002 .121
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1knitr::kable(nice(a_cont))| Effect | df | MSE | F | ges | p.value |
|---|---|---|---|---|---|
| transmission | 1, 516 | 0.07 | 12.93 *** | .012 | <.001 |
| energy | 1, 516 | 0.07 | 27.22 *** | .026 | <.001 |
| transmission:energy | 1, 516 | 0.07 | 0.09 | <.001 | .760 |
| variable | 1, 516 | 0.07 | 196.47 *** | .160 | <.001 |
| transmission:variable | 1, 516 | 0.07 | 33.58 *** | .031 | <.001 |
| energy:variable | 1, 516 | 0.07 | 11.35 *** | .011 | <.001 |
| transmission:energy:variable | 1, 516 | 0.07 | 2.42 | .002 | .121 |
Main effect of transmission type (radial vs. channel):
MainE_trans<-emmeans(a_cont, ~transmission)## NOTE: Results may be misleading due to involvement in interactionsMainE_trans## transmission emmean SE df lower.CL upper.CL
## channel 0.661 0.0116 516 0.638 0.683
## radial 0.602 0.0116 516 0.579 0.624
##
## Results are averaged over the levels of: energy, variable
## Confidence level used: 0.95confint(pairs(MainE_trans, level = 0.95))## contrast estimate SE df lower.CL upper.CL
## channel - radial 0.0588 0.0164 516 0.0267 0.091
##
## Results are averaged over the levels of: energy, variable
## Confidence level used: 0.95Main effect of energy level (unlimited vs. limited):
MainE_en<-emmeans(a_cont, ~energy)## NOTE: Results may be misleading due to involvement in interactionsMainE_en## energy emmean SE df lower.CL upper.CL
## specific 0.588 0.0116 516 0.566 0.611
## unlimited 0.674 0.0116 516 0.651 0.697
##
## Results are averaged over the levels of: transmission, variable
## Confidence level used: 0.95confint(pairs(MainE_en, level = 0.95))## contrast estimate SE df lower.CL upper.CL
## specific - unlimited -0.0854 0.0164 516 -0.118 -0.0532
##
## Results are averaged over the levels of: transmission, variable
## Confidence level used: 0.95Get means in the different conditions:
a1 <- a_cont
ls1 <- lsmeans(a1, c("variable","transmission","energy"))
ls1## variable transmission energy lsmean SE df lower.CL upper.CL
## Rating_SE channel specific 0.822 0.0234 516 0.776 0.868
## Rating_CC channel specific 0.418 0.0228 516 0.374 0.463
## Rating_SE radial specific 0.638 0.0234 516 0.592 0.684
## Rating_CC radial specific 0.475 0.0228 516 0.430 0.519
## Rating_SE channel unlimited 0.822 0.0234 516 0.776 0.868
## Rating_CC channel unlimited 0.579 0.0228 516 0.534 0.624
## Rating_SE radial unlimited 0.699 0.0234 516 0.653 0.745
## Rating_CC radial unlimited 0.595 0.0228 516 0.550 0.639
##
## Confidence level used: 0.95ls2 <- lsmeans(a1, c("variable","transmission")) # joint evaluation (basically gives the same table)
ls2## variable transmission lsmean SE df lower.CL upper.CL
## Rating_SE channel 0.822 0.0165 516 0.790 0.855
## Rating_CC channel 0.499 0.0161 516 0.467 0.531
## Rating_SE radial 0.669 0.0165 516 0.636 0.701
## Rating_CC radial 0.535 0.0161 516 0.503 0.566
##
## Results are averaged over the levels of: energy
## Confidence level used: 0.95ls3 <- lsmeans(a1, c("variable","energy")) # joint evaluation (basically gives the same table)
ls3## variable energy lsmean SE df lower.CL upper.CL
## Rating_SE specific 0.730 0.0165 516 0.698 0.763
## Rating_CC specific 0.447 0.0161 516 0.415 0.478
## Rating_SE unlimited 0.761 0.0165 516 0.728 0.793
## Rating_CC unlimited 0.587 0.0161 516 0.555 0.619
##
## Results are averaged over the levels of: transmission
## Confidence level used: 0.95Again for all 12 means that we obtained:
# same ANOVA as before
lmeModel <- lmer(value ~ variable*Cond_sum + (1|subj_code), data=tdata_long)
lmeModel <- aov_car(value ~ variable*Cond_sum + Error(subj_code/(variable)), tdata_long)## Contrasts set to contr.sum for the following variables: Cond_sum# follow-up analysis
ls1 <- lsmeans(lmeModel, c("Cond_sum","variable")) # joint evaluation (basically gives the same table)
ls1## Cond_sum variable lsmean SE df lower.CL upper.CL
## binary-radial Rating_SE 0.765 0.0228 774 0.721 0.810
## binary-channel Rating_SE 0.841 0.0228 774 0.796 0.886
## cont.-radial-unlimited Rating_SE 0.699 0.0228 774 0.654 0.744
## cont.-radial-limited Rating_SE 0.638 0.0228 774 0.594 0.683
## cont.-channel-unlimited Rating_SE 0.822 0.0228 774 0.777 0.867
## cont.-channel-limited Rating_SE 0.822 0.0228 774 0.777 0.867
## binary-radial Rating_CC 0.708 0.0235 774 0.662 0.755
## binary-channel Rating_CC 0.769 0.0235 774 0.723 0.815
## cont.-radial-unlimited Rating_CC 0.595 0.0235 774 0.549 0.641
## cont.-radial-limited Rating_CC 0.475 0.0235 774 0.429 0.521
## cont.-channel-unlimited Rating_CC 0.579 0.0235 774 0.533 0.625
## cont.-channel-limited Rating_CC 0.418 0.0235 774 0.372 0.465
##
## Confidence level used: 0.95Get all differences (later the relevant subset will be extracted):
t <- pairs(ls1) # compares rating differences
t <- confint(t, level = 0.95) # get the CIs of the differences
t## contrast
## (binary-radial Rating_SE) - (binary-channel Rating_SE)
## (binary-radial Rating_SE) - (cont.-radial-unlimited Rating_SE)
## (binary-radial Rating_SE) - (cont.-radial-limited Rating_SE)
## (binary-radial Rating_SE) - (cont.-channel-unlimited Rating_SE)
## (binary-radial Rating_SE) - (cont.-channel-limited Rating_SE)
## (binary-radial Rating_SE) - (binary-radial Rating_CC)
## (binary-radial Rating_SE) - (binary-channel Rating_CC)
## (binary-radial Rating_SE) - (cont.-radial-unlimited Rating_CC)
## (binary-radial Rating_SE) - (cont.-radial-limited Rating_CC)
## (binary-radial Rating_SE) - (cont.-channel-unlimited Rating_CC)
## (binary-radial Rating_SE) - (cont.-channel-limited Rating_CC)
## (binary-channel Rating_SE) - (cont.-radial-unlimited Rating_SE)
## (binary-channel Rating_SE) - (cont.-radial-limited Rating_SE)
## (binary-channel Rating_SE) - (cont.-channel-unlimited Rating_SE)
## (binary-channel Rating_SE) - (cont.-channel-limited Rating_SE)
## (binary-channel Rating_SE) - (binary-radial Rating_CC)
## (binary-channel Rating_SE) - (binary-channel Rating_CC)
## (binary-channel Rating_SE) - (cont.-radial-unlimited Rating_CC)
## (binary-channel Rating_SE) - (cont.-radial-limited Rating_CC)
## (binary-channel Rating_SE) - (cont.-channel-unlimited Rating_CC)
## (binary-channel Rating_SE) - (cont.-channel-limited Rating_CC)
## (cont.-radial-unlimited Rating_SE) - (cont.-radial-limited Rating_SE)
## (cont.-radial-unlimited Rating_SE) - (cont.-channel-unlimited Rating_SE)
## (cont.-radial-unlimited Rating_SE) - (cont.-channel-limited Rating_SE)
## (cont.-radial-unlimited Rating_SE) - (binary-radial Rating_CC)
## (cont.-radial-unlimited Rating_SE) - (binary-channel Rating_CC)
## (cont.-radial-unlimited Rating_SE) - (cont.-radial-unlimited Rating_CC)
## (cont.-radial-unlimited Rating_SE) - (cont.-radial-limited Rating_CC)
## (cont.-radial-unlimited Rating_SE) - (cont.-channel-unlimited Rating_CC)
## (cont.-radial-unlimited Rating_SE) - (cont.-channel-limited Rating_CC)
## (cont.-radial-limited Rating_SE) - (cont.-channel-unlimited Rating_SE)
## (cont.-radial-limited Rating_SE) - (cont.-channel-limited Rating_SE)
## (cont.-radial-limited Rating_SE) - (binary-radial Rating_CC)
## (cont.-radial-limited Rating_SE) - (binary-channel Rating_CC)
## (cont.-radial-limited Rating_SE) - (cont.-radial-unlimited Rating_CC)
## (cont.-radial-limited Rating_SE) - (cont.-radial-limited Rating_CC)
## (cont.-radial-limited Rating_SE) - (cont.-channel-unlimited Rating_CC)
## (cont.-radial-limited Rating_SE) - (cont.-channel-limited Rating_CC)
## (cont.-channel-unlimited Rating_SE) - (cont.-channel-limited Rating_SE)
## (cont.-channel-unlimited Rating_SE) - (binary-radial Rating_CC)
## (cont.-channel-unlimited Rating_SE) - (binary-channel Rating_CC)
## (cont.-channel-unlimited Rating_SE) - (cont.-radial-unlimited Rating_CC)
## (cont.-channel-unlimited Rating_SE) - (cont.-radial-limited Rating_CC)
## (cont.-channel-unlimited Rating_SE) - (cont.-channel-unlimited Rating_CC)
## (cont.-channel-unlimited Rating_SE) - (cont.-channel-limited Rating_CC)
## (cont.-channel-limited Rating_SE) - (binary-radial Rating_CC)
## (cont.-channel-limited Rating_SE) - (binary-channel Rating_CC)
## (cont.-channel-limited Rating_SE) - (cont.-radial-unlimited Rating_CC)
## (cont.-channel-limited Rating_SE) - (cont.-radial-limited Rating_CC)
## (cont.-channel-limited Rating_SE) - (cont.-channel-unlimited Rating_CC)
## (cont.-channel-limited Rating_SE) - (cont.-channel-limited Rating_CC)
## (binary-radial Rating_CC) - (binary-channel Rating_CC)
## (binary-radial Rating_CC) - (cont.-radial-unlimited Rating_CC)
## (binary-radial Rating_CC) - (cont.-radial-limited Rating_CC)
## (binary-radial Rating_CC) - (cont.-channel-unlimited Rating_CC)
## (binary-radial Rating_CC) - (cont.-channel-limited Rating_CC)
## (binary-channel Rating_CC) - (cont.-radial-unlimited Rating_CC)
## (binary-channel Rating_CC) - (cont.-radial-limited Rating_CC)
## (binary-channel Rating_CC) - (cont.-channel-unlimited Rating_CC)
## (binary-channel Rating_CC) - (cont.-channel-limited Rating_CC)
## (cont.-radial-unlimited Rating_CC) - (cont.-radial-limited Rating_CC)
## (cont.-radial-unlimited Rating_CC) - (cont.-channel-unlimited Rating_CC)
## (cont.-radial-unlimited Rating_CC) - (cont.-channel-limited Rating_CC)
## (cont.-radial-limited Rating_CC) - (cont.-channel-unlimited Rating_CC)
## (cont.-radial-limited Rating_CC) - (cont.-channel-limited Rating_CC)
## (cont.-channel-unlimited Rating_CC) - (cont.-channel-limited Rating_CC)
## estimate SE df lower.CL upper.CL
## -0.07538 0.0323 774 -0.18124 0.03047
## 0.06615 0.0323 774 -0.03970 0.17200
## 0.12692 0.0323 774 0.02107 0.23277
## -0.05692 0.0323 774 -0.16277 0.04893
## -0.05692 0.0323 774 -0.16277 0.04893
## 0.05692 0.0302 774 -0.04220 0.15605
## -0.00385 0.0328 774 -0.11122 0.10353
## 0.17077 0.0328 774 0.06339 0.27814
## 0.29077 0.0328 774 0.18339 0.39814
## 0.18615 0.0328 774 0.07878 0.29353
## 0.34692 0.0328 774 0.23955 0.45430
## 0.14154 0.0323 774 0.03569 0.24739
## 0.20231 0.0323 774 0.09646 0.30816
## 0.01846 0.0323 774 -0.08739 0.12431
## 0.01846 0.0323 774 -0.08739 0.12431
## 0.13231 0.0328 774 0.02493 0.23968
## 0.07154 0.0302 774 -0.02759 0.17067
## 0.24615 0.0328 774 0.13878 0.35353
## 0.36615 0.0328 774 0.25878 0.47353
## 0.26154 0.0328 774 0.15416 0.36891
## 0.42231 0.0328 774 0.31493 0.52968
## 0.06077 0.0323 774 -0.04508 0.16662
## -0.12308 0.0323 774 -0.22893 -0.01723
## -0.12308 0.0323 774 -0.22893 -0.01723
## -0.00923 0.0328 774 -0.11661 0.09814
## -0.07000 0.0328 774 -0.17738 0.03738
## 0.10462 0.0302 774 0.00549 0.20374
## 0.22462 0.0328 774 0.11724 0.33199
## 0.12000 0.0328 774 0.01262 0.22738
## 0.28077 0.0328 774 0.17339 0.38814
## -0.18385 0.0323 774 -0.28970 -0.07799
## -0.18385 0.0323 774 -0.28970 -0.07799
## -0.07000 0.0328 774 -0.17738 0.03738
## -0.13077 0.0328 774 -0.23814 -0.02339
## 0.04385 0.0328 774 -0.06353 0.15122
## 0.16385 0.0302 774 0.06472 0.26297
## 0.05923 0.0328 774 -0.04814 0.16661
## 0.22000 0.0328 774 0.11262 0.32738
## 0.00000 0.0323 774 -0.10585 0.10585
## 0.11385 0.0328 774 0.00647 0.22122
## 0.05308 0.0328 774 -0.05430 0.16045
## 0.22769 0.0328 774 0.12032 0.33507
## 0.34769 0.0328 774 0.24032 0.45507
## 0.24308 0.0302 774 0.14395 0.34220
## 0.40385 0.0328 774 0.29647 0.51122
## 0.11385 0.0328 774 0.00647 0.22122
## 0.05308 0.0328 774 -0.05430 0.16045
## 0.22769 0.0328 774 0.12032 0.33507
## 0.34769 0.0328 774 0.24032 0.45507
## 0.24308 0.0328 774 0.13570 0.35045
## 0.40385 0.0302 774 0.30472 0.50297
## -0.06077 0.0332 774 -0.16965 0.04811
## 0.11385 0.0332 774 0.00497 0.22272
## 0.23385 0.0332 774 0.12497 0.34272
## 0.12923 0.0332 774 0.02035 0.23811
## 0.29000 0.0332 774 0.18112 0.39888
## 0.17462 0.0332 774 0.06574 0.28349
## 0.29462 0.0332 774 0.18574 0.40349
## 0.19000 0.0332 774 0.08112 0.29888
## 0.35077 0.0332 774 0.24189 0.45965
## 0.12000 0.0332 774 0.01112 0.22888
## 0.01538 0.0332 774 -0.09349 0.12426
## 0.17615 0.0332 774 0.06728 0.28503
## -0.10462 0.0332 774 -0.21349 0.00426
## 0.05615 0.0332 774 -0.05272 0.16503
## 0.16077 0.0332 774 0.05189 0.26965
##
## Confidence level used: 0.95
## Conf-level adjustment: tukey method for comparing a family of 12 estimatesTake the relevant subset of differences:
t <- subset(t, contrast == "(binary-channel Rating_SE) - (binary-channel Rating_CC)" |
contrast == "(binary-radial Rating_SE) - (binary-radial Rating_CC)" |
contrast == "(cont.-channel-limited Rating_SE) - (cont.-channel-limited Rating_CC)" |
contrast == "(cont.-radial-limited Rating_SE) - (cont.-radial-limited Rating_CC)" |
contrast == "(cont.-channel-unlimited Rating_SE) - (cont.-channel-unlimited Rating_CC)" |
contrast == "(cont.-radial-unlimited Rating_SE) - (cont.-radial-unlimited Rating_CC)")
# binary channel
lo <- t[1,5]
hi <- t[1,6]
(bin_channel_width <- hi - lo) # get the CI widths## [1] 0.1982546(bin_channel_width_moe <- (hi - lo)/2) # and half widths## [1] 0.09912729# binary radial
lo <- t[2,5]
hi <- t[2,6]
(bin_radial_width <- hi - lo)## [1] 0.1982546(bin_radial_width_moe <- (hi - lo)/2)## [1] 0.09912729# cont channel limited
lo <- t[3,5]
hi <- t[3,6]
(cont_channel_limited_width <- hi - lo)## [1] 0.1982546(cont_channel_limited_width_moe <- (hi - lo)/2)## [1] 0.09912729# cont radial limited
lo <- t[4,5]
hi <- t[4,6]
(cont_radial_limited_width <- hi - lo)## [1] 0.1982546(cont_radial_limited_width_moe <- (hi - lo)/2)## [1] 0.09912729# cont channel unlimited
lo <- t[5,5]
hi <- t[5,6]
(cont_channel_unlimited_width <- hi - lo)## [1] 0.1982546(cont_channel_unlimited_width_moe <- (hi - lo)/2)## [1] 0.09912729# cont radial unlimited
lo <- t[6,5]
hi <- t[6,6]
(cont_radial_unlimited_width <- hi - lo)## [1] 0.1982546(cont_radial_unlimited_width_moe <- (hi - lo)/2)## [1] 0.09912729cond <- c("bin_channel_width", "bin_radial_width", "cont_channel_limited_width", "cont_radial_limited_width",
"cont_channel_unlimited_width", "cont_radial_unlimited_width")
ci_width <- c(bin_channel_width, bin_radial_width, cont_channel_limited_width, cont_radial_limited_width,
cont_channel_unlimited_width, cont_radial_unlimited_width)
CI_widths <- data.frame(cond, ci_width) # CI width < 0.20 was used as the stopping rule for data collection# factor the different differences (needed for a plot later)
t$contrast <- factor(t$contrast, levels = c("(binary-radial Rating_SE) - (binary-radial Rating_CC)",
"(binary-channel Rating_SE) - (binary-channel Rating_CC)",
"(cont.-radial-unlimited Rating_SE) - (cont.-radial-unlimited Rating_CC)",
"(cont.-radial-limited Rating_SE) - (cont.-radial-limited Rating_CC)",
"(cont.-channel-unlimited Rating_SE) - (cont.-channel-unlimited Rating_CC)",
"(cont.-channel-limited Rating_SE) - (cont.-channel-limited Rating_CC)"),
labels = c("binary-radial",
"binary-channel",
"cont.-radial-unlimited",
"cont.-radial-limited",
"cont.-channel-unlimited",
"cont.-channel-limited"
)
)3.5 Graphs
3.5.1 Overall
## Warning: Ignoring unknown aesthetics: y
3.5.2 Subplots
Continuous vs. Binary:
cont2 <- subset(continuous, select = c(1:4,7))
bin2 <- subset(binary, select = c(1:4,6))
cont_vs_binary <- rbind(cont2, bin2)library(afex)
library(emmeans)
a1 <- aov_car(value ~ variable*var_type + Error(subj_code/(variable)), cont_vs_binary)## Converting to factor: var_type## Contrasts set to contr.sum for the following variables: var_type#a1ls1 <- lsmeans(a1, c("variable","var_type"))
ls1## variable var_type lsmean SE df lower.CL upper.CL
## Rating_SE binary 0.803 0.0167 778 0.770 0.836
## Rating_CC binary 0.739 0.0170 778 0.705 0.772
## Rating_SE continuous 0.746 0.0118 778 0.722 0.769
## Rating_CC continuous 0.517 0.0120 778 0.493 0.540
##
## Confidence level used: 0.95t <- confint(pairs(ls1), level = 0.95)
t## contrast estimate SE df lower.CL
## Rating_SE binary - Rating_CC binary 0.06423 0.0221 778 0.00739
## Rating_SE binary - Rating_SE continuous 0.05750 0.0204 778 0.00498
## Rating_SE binary - Rating_CC continuous 0.28635 0.0205 778 0.23345
## Rating_CC binary - Rating_SE continuous -0.00673 0.0207 778 -0.06000
## Rating_CC binary - Rating_CC continuous 0.22212 0.0208 778 0.16848
## Rating_SE continuous - Rating_CC continuous 0.22885 0.0156 778 0.18866
## upper.CL
## 0.1211
## 0.1100
## 0.3392
## 0.0465
## 0.2757
## 0.2690
##
## Confidence level used: 0.95
## Conf-level adjustment: tukey method for comparing a family of 4 estimatest <- subset(t, contrast == "Rating_SE binary - Rating_CC binary" |
contrast == "Rating_SE continuous - Rating_CC continuous")## Warning: Ignoring unknown aesthetics: y
Unlimited vs. Limited Energy:
library(afex)
library(emmeans)
a1 <- aov_car(value ~ variable*energy + Error(subj_code/(variable)), continuous)## Converting to factor: energy## Contrasts set to contr.sum for the following variables: energya1## Anova Table (Type 3 tests)
##
## Response: value
## Effect df MSE F ges p.value
## 1 energy 1, 518 0.07 26.66 *** .025 <.001
## 2 variable 1, 518 0.07 184.36 *** .153 <.001
## 3 energy:variable 1, 518 0.07 10.65 ** .010 .001
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1ls1 <- lsmeans(a1, c("variable","energy"))
ls1## variable energy lsmean SE df lower.CL upper.CL
## Rating_SE specific 0.730 0.0172 518 0.697 0.764
## Rating_CC specific 0.447 0.0162 518 0.415 0.478
## Rating_SE unlimited 0.761 0.0172 518 0.727 0.795
## Rating_CC unlimited 0.587 0.0162 518 0.555 0.619
##
## Confidence level used: 0.95t <- confint(pairs(ls1), level = 0.95)
t## contrast estimate SE df lower.CL
## Rating_SE specific - Rating_CC specific 0.2838 0.0238 518 0.2224
## Rating_SE specific - Rating_SE unlimited -0.0304 0.0243 518 -0.0931
## Rating_SE specific - Rating_CC unlimited 0.1435 0.0236 518 0.0826
## Rating_CC specific - Rating_SE unlimited -0.3142 0.0236 518 -0.3751
## Rating_CC specific - Rating_CC unlimited -0.1404 0.0229 518 -0.1993
## Rating_SE unlimited - Rating_CC unlimited 0.1738 0.0238 518 0.1124
## upper.CL
## 0.3453
## 0.0324
## 0.2043
## -0.2534
## -0.0815
## 0.2353
##
## Confidence level used: 0.95
## Conf-level adjustment: tukey method for comparing a family of 4 estimatest <- subset(t, contrast == "Rating_SE specific - Rating_CC specific" |
contrast == "Rating_SE unlimited - Rating_CC unlimited")## Warning: Ignoring unknown aesthetics: y
Radial vs. Channel Transmission:
library(afex)
library(emmeans)
a1 <- aov_car(value ~ variable*transmission + Error(subj_code/(variable)), continuous)## Converting to factor: transmission## Contrasts set to contr.sum for the following variables: transmissiona1## Anova Table (Type 3 tests)
##
## Response: value
## Effect df MSE F ges p.value
## 1 transmission 1, 518 0.07 12.33 *** .012 <.001
## 2 variable 1, 518 0.07 192.10 *** .154 <.001
## 3 transmission:variable 1, 518 0.07 32.84 *** .030 <.001
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1ls1 <- lsmeans(a1, c("variable","transmission"))
ls1## variable transmission lsmean SE df lower.CL upper.CL
## Rating_SE channel 0.822 0.0166 518 0.790 0.855
## Rating_CC channel 0.499 0.0167 518 0.466 0.532
## Rating_SE radial 0.669 0.0166 518 0.636 0.701
## Rating_CC radial 0.535 0.0167 518 0.502 0.567
##
## Confidence level used: 0.95t <- confint(pairs(ls1), level = 0.95)
t## contrast estimate SE df lower.CL upper.CL
## Rating_SE channel - Rating_CC channel 0.3235 0.0234 518 0.2633 0.3836
## Rating_SE channel - Rating_SE radial 0.1535 0.0234 518 0.0931 0.2139
## Rating_SE channel - Rating_CC radial 0.2877 0.0235 518 0.2271 0.3483
## Rating_CC channel - Rating_SE radial -0.1700 0.0235 518 -0.2306 -0.1094
## Rating_CC channel - Rating_CC radial -0.0358 0.0236 518 -0.0967 0.0251
## Rating_SE radial - Rating_CC radial 0.1342 0.0234 518 0.0740 0.1944
##
## Confidence level used: 0.95
## Conf-level adjustment: tukey method for comparing a family of 4 estimatest <- subset(t, contrast == "Rating_SE channel - Rating_CC channel" |
contrast == "Rating_SE radial - Rating_CC radial")## Warning: Ignoring unknown aesthetics: y
Cohen’s ds:
dat <- subset(tdata, Cond_sum == "cont_channel_limited")
# since we have a repeated-meausres design, we now need the correlations of the ratings
library(dplyr) # for pipe operator
dat -> t
r <- cor(t$Rating_CC, t$Rating_SE)
r## [1] -0.3961798# now compute ES and SE and CI of it
# using the esc package because it gives SE of the ES directly
library(esc)
# get means and sds
m1 <- dat %>%
summarize(Mean1 = mean(Rating_SE))
sd1 <- dat %>%
summarize(SD1 = sd(Rating_SE))
m2 <- dat %>%
summarize(Mean2 = mean(Rating_CC))
sd2 <- dat %>%
summarize(SD2 = sd(Rating_CC))
d <- esc_mean_sd(
grp1m = m1[,1], grp1sd = sd1[,1], grp1n = length(dat$subj_code),
grp2m = m2[,1], grp2sd = sd2[,1], grp2n = length(dat$subj_code),
r = r,
es.type = "d"
)
d##
## Effect Size Calculation for Meta Analysis
##
## Conversion: mean and sd (within-subject) to effect size d
## Effect Size: 1.0209
## Standard Error: 0.1319
## Variance: 0.0174
## Lower CI: 0.7624
## Upper CI: 1.2793
## Weight: 57.5085d$ci.lo## Mean1
## 1 0.7624d$ci.hi## Mean1
## 1 1.279307d_ci <- (d$ci.lo - d$ci.hi)
d_ci## Mean1
## 1 -0.5169066d_ch_limit <- d$es
d_ch_limit_lo <- d$ci.lo
d_ch_limit_hi <- d$ci.hidat <- subset(tdata, Cond_sum == "cont_channel_unlimited")
# since we have a repeated-meausres design, we now need the correlations of the ratings
library(dplyr) # for pipe operator
dat -> t
r <- cor(t$Rating_CC, t$Rating_SE)
r## [1] -0.1201605# now compute ES and SE and CI of it
# using the esc package because it gives SE of the ES directly
library(esc)
# get means and sds
m1 <- dat %>%
summarize(Mean1 = mean(Rating_SE))
sd1 <- dat %>%
summarize(SD1 = sd(Rating_SE))
m2 <- dat %>%
summarize(Mean2 = mean(Rating_CC))
sd2 <- dat %>%
summarize(SD2 = sd(Rating_CC))
d <- esc_mean_sd(
grp1m = m1[,1], grp1sd = sd1[,1], grp1n = length(dat$subj_code),
grp2m = m2[,1], grp2sd = sd2[,1], grp2n = length(dat$subj_code),
r = r,
es.type = "d"
)
d##
## Effect Size Calculation for Meta Analysis
##
## Conversion: mean and sd (within-subject) to effect size d
## Effect Size: 0.6443
## Standard Error: 0.1272
## Variance: 0.0162
## Lower CI: 0.3950
## Upper CI: 0.8937
## Weight: 61.7931d$ci.lo## Mean1
## 1 0.3950105d$ci.hi## Mean1
## 1 0.8936746d_ci <- (d$ci.lo - d$ci.hi)
d_ci## Mean1
## 1 -0.498664d_ch_unlimit <- d$es
d_ch_unlimit_lo <- d$ci.lo
d_ch_unlimit_hi <- d$ci.hidat <- subset(tdata, Cond_sum == "cont_radial_limited")
# since we have a repeated-meausres design, we now need the correlations of the ratings
library(dplyr) # for pipe operator
dat -> t
r <- cor(t$Rating_CC, t$Rating_SE)
r## [1] 0.07832772# now compute ES and SE and CI of it
# using the esc package because it gives SE of the ES directly
library(esc)
# get means and sds
m1 <- dat %>%
summarize(Mean1 = mean(Rating_SE))
sd1 <- dat %>%
summarize(SD1 = sd(Rating_SE))
m2 <- dat %>%
summarize(Mean2 = mean(Rating_CC))
sd2 <- dat %>%
summarize(SD2 = sd(Rating_CC))
d <- esc_mean_sd(
grp1m = m1[,1], grp1sd = sd1[,1], grp1n = length(dat$subj_code),
grp2m = m2[,1], grp2sd = sd2[,1], grp2n = length(dat$subj_code),
r = r,
es.type = "d"
)
d##
## Effect Size Calculation for Meta Analysis
##
## Conversion: mean and sd (within-subject) to effect size d
## Effect Size: 0.4182
## Standard Error: 0.1254
## Variance: 0.0157
## Lower CI: 0.1725
## Upper CI: 0.6640
## Weight: 63.6093d$ci.lo## Mean1
## 1 0.1724664d$ci.hi## Mean1
## 1 0.6639598d_ci <- (d$ci.lo - d$ci.hi)
d_ci## Mean1
## 1 -0.4914934d_rad_limit <- d$es
d_rad_limit_lo <- d$ci.lo
d_rad_limit_hi <- d$ci.hidat <- subset(tdata, Cond_sum == "cont_radial_unlimited")
# since we have a repeated-meausres design, we now need the correlations of the ratings
library(dplyr) # for pipe operator
dat -> t
r <- cor(t$Rating_CC, t$Rating_SE)
r## [1] 0.3193679# now compute ES and SE and CI of it
# using the esc package because it gives SE of the ES directly
library(esc)
# get means and sds
m1 <- dat %>%
summarize(Mean1 = mean(Rating_SE))
sd1 <- dat %>%
summarize(SD1 = sd(Rating_SE))
m2 <- dat %>%
summarize(Mean2 = mean(Rating_CC))
sd2 <- dat %>%
summarize(SD2 = sd(Rating_CC))
d <- esc_mean_sd(
grp1m = m1[,1], grp1sd = sd1[,1], grp1n = length(dat$subj_code),
grp2m = m2[,1], grp2sd = sd2[,1], grp2n = length(dat$subj_code),
r = r,
es.type = "d"
)
d##
## Effect Size Calculation for Meta Analysis
##
## Conversion: mean and sd (within-subject) to effect size d
## Effect Size: 0.3273
## Standard Error: 0.1249
## Variance: 0.0156
## Lower CI: 0.0826
## Upper CI: 0.5721
## Weight: 64.1410d$ci.lo## Mean1
## 1 0.08259827d$ci.hi## Mean1
## 1 0.5720505d_ci <- (d$ci.lo - d$ci.hi)
d_ci## Mean1
## 1 -0.4894522d_rad_unlimit <- d$es
d_rad_unlimit_lo <- d$ci.lo
d_rad_unlimit_hi <- d$ci.hidat <- subset(tdata, Cond_sum == "binary_radial")
# since we have a repeated-meausres design, we now need the correlations of the ratings
library(dplyr) # for pipe operator
dat -> t
r <- cor(t$Rating_CC, t$Rating_SE)
r## [1] 0.4559072# now compute ES and SE and CI of it
# using the esc package because it gives SE of the ES directly
library(esc)
# get means and sds
m1 <- dat %>%
summarize(Mean1 = mean(Rating_SE))
sd1 <- dat %>%
summarize(SD1 = sd(Rating_SE))
m2 <- dat %>%
summarize(Mean2 = mean(Rating_CC))
sd2 <- dat %>%
summarize(SD2 = sd(Rating_CC))
d <- esc_mean_sd(
grp1m = m1[,1], grp1sd = sd1[,1], grp1n = length(dat$subj_code),
grp2m = m2[,1], grp2sd = sd2[,1], grp2n = length(dat$subj_code),
r = r,
es.type = "d"
)
d##
## Effect Size Calculation for Meta Analysis
##
## Conversion: mean and sd (within-subject) to effect size d
## Effect Size: 0.2065
## Standard Error: 0.1244
## Variance: 0.0155
## Lower CI: -0.0372
## Upper CI: 0.4503
## Weight: 64.6552d$ci.lo## Mean1
## 1 -0.03721408d$ci.hi## Mean1
## 1 0.4502877d_ci <- (d$ci.lo - d$ci.hi)
d_ci## Mean1
## 1 -0.4875018d_bin_rad <- d$es
d_bin_rad_lo <- d$ci.lo
d_bin_rad_hi <- d$ci.hidat <- subset(tdata, Cond_sum == "binary_channel")
# since we have a repeated-meausres design, we now need the correlations of the ratings
library(dplyr) # for pipe operator
dat -> t
r <- cor(t$Rating_CC, t$Rating_SE)
r## [1] 0.4227151# now compute ES and SE and CI of it
# using the esc package because it gives SE of the ES directly
library(esc)
# get means and sds
m1 <- dat %>%
summarize(Mean1 = mean(Rating_SE))
sd1 <- dat %>%
summarize(SD1 = sd(Rating_SE))
m2 <- dat %>%
summarize(Mean2 = mean(Rating_CC))
sd2 <- dat %>%
summarize(SD2 = sd(Rating_CC))
d <- esc_mean_sd(
grp1m = m1[,1], grp1sd = sd1[,1], grp1n = length(dat$subj_code),
grp2m = m2[,1], grp2sd = sd2[,1], grp2n = length(dat$subj_code),
r = r,
es.type = "d"
)
d##
## Effect Size Calculation for Meta Analysis
##
## Conversion: mean and sd (within-subject) to effect size d
## Effect Size: 0.2486
## Standard Error: 0.1245
## Variance: 0.0155
## Lower CI: 0.0045
## Upper CI: 0.4926
## Weight: 64.5018d$ci.lo## Mean1
## 1 0.004532089d$ci.hi## Mean1
## 1 0.4926133d_ci <- (d$ci.lo - d$ci.hi)
d_ci## Mean1
## 1 -0.4880812d_bin_ch <- d$es
d_bin_ch_lo <- d$ci.lo
d_bin_ch_hi <- d$ci.hicontrast <- c("binary-radial", "binary-channel", "cont.-radial-unlimited", "cont.-radial-limited", "cont.-channel-unlimited", "cont.-channel-limited")
estimate <- c(d_bin_rad[,1], d_bin_ch[,1], d_rad_unlimit[,1], d_rad_limit[,1], d_ch_unlimit[,1], d_ch_limit[,1])
ci_lo <- c(d_bin_rad_lo[,1], d_bin_ch_lo[,1], d_rad_unlimit_lo[,1], d_rad_limit_lo[,1], d_ch_unlimit_lo[,1], d_ch_limit_lo[,1])
ci_hi <- c(d_bin_rad_hi[,1], d_bin_ch_hi[,1], d_rad_unlimit_hi[,1], d_rad_limit_hi[,1], d_ch_unlimit_hi[,1], d_ch_limit_hi[,1])
ds <- data.frame(contrast, estimate, ci_lo, ci_hi)
ds$contrast <- factor(ds$contrast, levels = c("binary-radial", "binary-channel",
"cont.-radial-unlimited", "cont.-radial-limited", "cont.-channel-unlimited", "cont.-channel-limited"))## Warning: Ignoring unknown aesthetics: y