data_scalescomputed$condition12 <- as.factor(data_scalescomputed$condition12)
data_scalescomputed %>%
ggplot(aes(x = condition12, y = scale1_index, fill = condition12)) +
geom_boxplot(alpha = .5) +
geom_jitter(alpha = .5, width = 0.2)7 Infer
8 Moving into analyses
thoughts from Jenny : I wonder whether it would be useful to structure this in terms of lets combine skills from previous chapters to..
- ask a question,
- get plots/descriptives
- then answer it with inferentials?
- And repeat that process for t-test, linear regression and anova?
8.1 Plots and descriptives
Now, let’s test whether this scale varies by condition (condition 1 vs. condition 2 in condition12).
Before jumping into t-tests, let’s first visualise the data (scale1_index) to get a sense of what it looks like.
The first command here tells R to treat condition12 as a categorical variable that groups the data (technically, a factor). This is helpful for plotting. The code uses the dataframe$variablename structure to do a command on just one variable.
The second command pipes the data into a command to create a boxplot (geom_boxplot) with the datapoints plotted as well (geom_jitter).The width command makes the plotting of the dots a bit narrower to help with interpretation.
Based on the boxplot, we’d expect a t-test to be nonsignificant - the wide boxes of the plots for each condition overlap, even though the mean of condition 2 is slightly higher than condition 1 (the horizontal line through the box).
8.2 t-test
The first line of code uses the base R command to run a t-test. It tells R to do the test on the data_scalescomputed data frame, asking whether scale1_index varies by (~) condition. var. sets the assumption of variance and conf.level sets the desired alpha of the test. That command is wrapped in the handy t_apa function, which makes the output much easier to read (and pull directly into a write-up!), and also allows us to get a confidence interval on the effect size (es_ci).
For reporting, you’d probably also want to know the means and standard deviations by condition. The next bit of code asks R to do this, using the summarise function, separately for each condition. Reminder to use na.rm here to account for any missing values.
The gt() command shows the requested dataframe in a nice formatting.
t_apa(t.test(data = data_scalescomputed, scale1_index ~ condition12, var. = TRUE, conf.level = .95), es_ci = TRUE)
scale1_by_condition12 <- data_scalescomputed %>%
group_by(condition12) %>%
summarise(mean_scale1 = mean(scale1_index, na.rm = TRUE),
sd_scale1 = sd(scale1_index, na.rm = TRUE))
gt(scale1_by_condition12)9 Linear regression
lw_addnarrativehere
- outcome: variable_6
- step 1: demographics_categ
- step 2: variable_4
- step 3: scale1_index
this asks the lm package to use predictor to predict outcome
lm(outcome ~ predictor )
regression1 <- lm(data = data_scalescomputed, variable6 ~ demographicscateg + variable4 + scale1_index)
summary(regression1)lw_addnarrativehere simulates hierarchical stepwise regression?
regressionlm1 <- lm(data = data_scalescomputed, variable6 ~ demographicscateg)
regressionlm2 <- lm(data = data_scalescomputed, variable6 ~ demographicscateg + variable4)
regressionlm3 <- lm(data = data_scalescomputed, variable6 ~ demographicscateg + variable4 + scale1_index)
summary(regressionlm1)
summary(regressionlm2)
summary(regressionlm3)
apa.reg.table(regressionlm1, regressionlm2, regressionlm3, filename = here("output_files","RegressionTable3_APA.doc"), table.number = 3)
report(regressionlm3)10 Analysis of Variance (ANOVA)
lw add narrative
4 (between participants - condition1234) x2 (between participants - individual difference categorical variable - demographicscateg) design
outcome: scale1_index
## first tell R that condition and demographicscateg are categorical (factors)
data_scalescomputed$condition1234 <- as.factor(data_scalescomputed$condition1234)
data_scalescomputed$demographicscateg <- as.factor(data_scalescomputed$demographicscateg)
## this creates a dataframe that contains the summary statistics (means, standard deviations, etc.)
scale1_stats <- ezStats(data = data_scalescomputed,
dv = scale1_index,
wid = participantid,
between = c("condition1234","demographicscateg"))
print(scale1_stats)
## this carries out an anova with condition1234 and demographicscateg as between-participants factors
## the output includes statistical tests of the main effect of condition1234, the main effect of demographicscateg, and the interaction between the two
scale1_anova <- ezANOVA(data = data_scalescomputed,
dv = scale1_index,
wid = participantid,
between = c("condition1234","demographicscateg"),
return_aov = TRUE)
print(scale1_anova)
## NOTE THAT THE FOLLOWING WOULD BE DONE TO FURTHER INVESTIGATE AN INTERACTION OR A DIFFERENCE IN A MULTI-CATEGORICAL VARIABLE.
## to build the contrasts we want to do (e.g., baseline vs. midpoint for PhD), we need to ask emmeans to create output to see what the rows represent.
scale1_emm <- emmeans(scale1_anova$aov, ~ condition1234 * demographicscateg)
scale1_emm
## now we can create a set of named vectors that represent each of the 8 means, based on the position in the 8-item list from emmeans.
cond1categ1 = c(1,0,0,0,0,0,0,0)
cond2categ1 = c(0,1,0,0,0,0,0,0)
cond3categ1 = c(0,0,1,0,0,0,0,0)
cond4categ1 = c(0,0,0,1,0,0,0,0)
cond1categ2 = c(0,0,0,0,1,0,0,0)
cond2categ2 = c(0,0,0,0,0,1,0,0)
cond3categ2 = c(0,0,0,0,0,0,1,0)
cond4categ2 = c(0,0,0,0,0,0,0,1)
cond1 = c(1,0,0,0,1,0,0,0)
cond2 = c(0,1,0,0,0,1,0,0)
cond3 = c(0,0,1,0,0,0,1,0)
cond4 = c(0,0,0,1,0,0,0,1)
## now we can ask for contrasts based on these vectors; we will explore the main effect of condition1234 by comparing each of the conditions to one another
scale1_contrasts <- contrast(scale1_emm, method = list("cond1 - cond2" = cond1 - cond2,
"cond1 - cond3" = cond1 - cond3,
"cond1 - cond4" = cond1 - cond4,
"cond2 - cond3" = cond2 - cond3,
"cond2 - cond4" = cond2 - cond4,
"cond3 - cond4" = cond3 - cond4))
scale1_contrasts
## here's a version with confidence intervals instead of t and p values
scale1_contrastsCI <- scale1_contrasts %>%
confint()
scale1_contrastsCI
#you may have a specific planned contrast to run. Here let's imagine you want to compare condition 2 to all of the other 3 conditions in one comparison.
scale1_plannedcontraststats <- ezStats(data = data_scalescomputed,
dv = scale1_index,
wid = participantid,
between = c("condition1234"))
scale1_plannedcontraststats
cond2v134 = c(0,1,0,0,0,1,0,0)
cond134v2 = c(1,0,1,1,1,0,1,1)
scale1_plannedcontrasts <- contrast(scale1_emm, method = list("condition 1 vs all the rest" = cond2v134 - cond134v2))
scale1_plannedcontrastsLet’s make a figure!
data_scalescomputed %>%
ggplot(aes(x = condition1234, y = scale1_index, fill = demographicscateg)) +
geom_boxplot() +
theme_light()
data_scalescomputed %>%
ggplot(aes(x = condition1234, y = scale1_index)) +
geom_boxplot() +
theme_light()