#install.packages("afex")
#install.packages("emmeans")
#install.packages("ggbeeswarm")
library(psych) # for the describe() command
library(ggplot2) # to visualize our results
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## Attaching package: 'ggplot2'
## The following objects are masked from 'package:psych':
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## %+%, alpha
library(expss) # for the cross_cases() command
## Loading required package: maditr
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## To select rows from data: rows(mtcars, am==0)
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## Attaching package: 'expss'
## The following object is masked from 'package:ggplot2':
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## vars
library(car) # for the leveneTest() command
## Loading required package: carData
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## Attaching package: 'car'
## The following object is masked from 'package:expss':
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## recode
## The following object is masked from 'package:psych':
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## logit
library(afex) # to run the ANOVA
## Loading required package: lme4
## Loading required package: Matrix
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## Attaching package: 'lme4'
## The following object is masked from 'package:expss':
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## dummy
## ************
## 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
## - Get and set global package options with: afex_options()
## - Set sum-to-zero contrasts globally: set_sum_contrasts()
## - For example analyses see: browseVignettes("afex")
## ************
##
## Attaching package: 'afex'
## The following object is masked from 'package:lme4':
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## lmer
library(ggbeeswarm) # to run plot results
library(emmeans) # for posthoc tests
## Welcome to emmeans.
## Caution: You lose important information if you filter this package's results.
## See '? untidy'
# For HW, import the project dataset you cleaned previously this will be the dataset you'll use throughout the rest of the semester
d <- read.csv(file="Data/projectdata.csv", header=T)
# new code! this adds a column with a number for each row. It will make it easier if we need to drop outliers later
d$row_id <- 1:nrow(d)
Note: For your HW, you will choose to run EITHER a one-way ANOVA (a single IV with at least 3 levels) OR a two-way ANOVA (two IVs, each with 2 levels). You will need to specify your hypothesis and customize your code based on the choice you make (i.e., delete code that is not relevant). We will run BOTH versions in the lab for illustrative purposes.
One-Way Hypothesis: We predict there will be a significant difference in scores for the RSE survey measuring levels of self-esteem depending on people’s response to the mhealth question asking about participant’s mental health disorders (depression, N/A aka no disorders, and bipolar).
IV = Preexisting Mental Health Disorders DV = RSE Scores
# you only need to check the variables you're using in the current analysis
# even if you checked them previously, it's always a good idea to look them over again and be sure that everything is correct
str(d)
## 'data.frame': 1258 obs. of 8 variables:
## $ X : int 1 321 401 469 520 1390 1422 1849 2183 2247 ...
## $ gender : chr "female" "male" "female" "female" ...
## $ mhealth: chr "none or NA" "none or NA" "obsessive compulsive disorder" "depression" ...
## $ rse : num 2.3 3.8 3.1 3 2.6 3 1.3 2.1 3 3.2 ...
## $ pss : num 3.25 2.25 2.25 2.25 2.75 2.75 4.75 3.25 3.5 2.25 ...
## $ phq : num 1.33 1.89 2.44 1.22 1.56 ...
## $ gad : num 1.86 1 2.14 1.71 1.14 ...
## $ row_id : int 1 2 3 4 5 6 7 8 9 10 ...
# make our categorical variables of interest factors
# because we'll use our newly created row ID variable for this analysis, so make sure it's coded as a factor, too.
d$mhealth <- as.factor(d$mhealth)
d$row_id <- as.factor(d$row_id)
# We're going to recode our race variable into two groups for the Two-Way ANOVA: poc and white
# in doing so, we are creating a new variable "poc" that has 2 levels
d <- subset(d, mhealth != "anxiety disorder") # use subset() to remove all participants from the additional level
table(d$mhealth, useNA = "always") # verify that now there are ZERO participants in the additional level
##
## anxiety disorder bipolar
## 0 6
## depression eating disorders
## 32 30
## none or NA obsessive compulsive disorder
## 970 26
## other ptsd
## 37 27
## <NA>
## 0
d$mhealth <- droplevels(d$mhealth) # use droplevels() to drop the empty factor
table(d$mhealth, useNA = "always") # verify that now the entire factor level is removed
##
## bipolar depression
## 6 32
## eating disorders none or NA
## 30 970
## obsessive compulsive disorder other
## 26 37
## ptsd <NA>
## 27 0
d <- subset(d, mhealth != "eating disorders") # use subset() to remove all participants from the additional level
table(d$mhealth, useNA = "always") # verify that now there are ZERO participants in the additional level
##
## bipolar depression
## 6 32
## eating disorders none or NA
## 0 970
## obsessive compulsive disorder other
## 26 37
## ptsd <NA>
## 27 0
d$mhealth <- droplevels(d$mhealth) # use droplevels() to drop the empty factor
table(d$mhealth, useNA = "always") # verify that now the entire factor level is removed
##
## bipolar depression
## 6 32
## none or NA obsessive compulsive disorder
## 970 26
## other ptsd
## 37 27
## <NA>
## 0
d <- subset(d, mhealth != "other") # use subset() to remove all participants from the additional level
table(d$mhealth, useNA = "always") # verify that now there are ZERO participants in the additional level
##
## bipolar depression
## 6 32
## none or NA obsessive compulsive disorder
## 970 26
## other ptsd
## 0 27
## <NA>
## 0
d$mhealth <- droplevels(d$mhealth) # use droplevels() to drop the empty factor
table(d$mhealth, useNA = "always") # verify that now the entire factor level is removed
##
## bipolar depression
## 6 32
## none or NA obsessive compulsive disorder
## 970 26
## ptsd <NA>
## 27 0
d <- subset(d, mhealth != "obsessive compulsive disorder") # use subset() to remove all participants from the additional level
table(d$mhealth, useNA = "always") # verify that now there are ZERO participants in the additional level
##
## bipolar depression
## 6 32
## none or NA obsessive compulsive disorder
## 970 0
## ptsd <NA>
## 27 0
d$mhealth <- droplevels(d$mhealth) # use droplevels() to drop the empty factor
table(d$mhealth, useNA = "always") # verify that now the entire factor level is removed
##
## bipolar depression none or NA ptsd <NA>
## 6 32 970 27 0
d <- subset(d, mhealth != "ptsd") # use subset() to remove all participants from the additional level
table(d$mhealth, useNA = "always") # verify that now there are ZERO participants in the additional level
##
## bipolar depression none or NA ptsd <NA>
## 6 32 970 0 0
d$mhealth <- droplevels(d$mhealth) # use droplevels() to drop the empty factor
table(d$mhealth, useNA = "always") # verify that now the entire factor level is removed
##
## bipolar depression none or NA <NA>
## 6 32 970 0
# For your HW, you can choose to combine levels like we did here, OR you can simply choose which existing levels you want to compare/test -- to do this option, you'll need to copy/paste the "drop levels" code from the t-test lab/HW and delete the recoding code line above.
# check that all our categorical variables of interest are now factors
str(d)
## 'data.frame': 1008 obs. of 8 variables:
## $ X : int 1 321 469 520 1390 1422 2183 2247 2482 2526 ...
## $ gender : chr "female" "male" "female" "female" ...
## $ mhealth: Factor w/ 3 levels "bipolar","depression",..: 3 3 2 3 3 3 3 3 3 3 ...
## $ rse : num 2.3 3.8 3 2.6 3 1.3 3 3.2 1.8 2.1 ...
## $ pss : num 3.25 2.25 2.25 2.75 2.75 4.75 3.5 2.25 4.25 3.5 ...
## $ phq : num 1.33 1.89 1.22 1.56 1.22 ...
## $ gad : num 1.86 1 1.71 1.14 1 ...
## $ row_id : Factor w/ 1258 levels "1","2","3","4",..: 1 2 4 5 6 7 9 10 11 12 ...
# check our DV skew and kurtosis
describe(d$rse)
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1008 2.74 0.69 2.8 2.77 0.74 1 4 3 -0.37 -0.48 0.02
# we'll use the describeBy() command to view our DV's skew and kurtosis across our IVs' levels
describeBy(d$rse, group = d$mhealth)
##
## Descriptive statistics by group
## group: bipolar
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 6 1.78 0.52 1.65 1.78 0.52 1.1 2.5 1.4 0.18 -1.75 0.21
## ------------------------------------------------------------
## group: depression
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 32 2.54 0.6 2.6 2.58 0.59 1.1 3.5 2.4 -0.57 -0.22 0.11
## ------------------------------------------------------------
## group: none or NA
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 970 2.75 0.69 2.8 2.78 0.74 1 4 3 -0.38 -0.48 0.02
# also use histograms to examine your continuous variable
hist(d$rse)
# and cross_cases() to examine your categorical variables' cell count
cross_cases(d, mhealth)
#Total | |
---|---|
mhealth | |
bipolar | 6 |
depression | 32 |
none or NA | 970 |
#Total cases | 1008 |
# REMEMBER your test's level of POWER is determined by your SMALLEST subsample
# One-Way
table(d$mhealth)
##
## bipolar depression none or NA
## 6 32 970
# use the leveneTest() command from the car package to test homogeneity of variance
# uses the 'formula' setup: formula is y~x1*x2, where y is our DV and x1 is our first IV and x2 is our second IV
# One-Way
leveneTest(rse~mhealth, data = d)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 2 1.267 0.2821
## 1005
# use this commented out section below ONLY IF if you need to remove outliers
# to drop a single outlier, use this code:
d <- subset(d, row_id!=c(1108))
# to drop multiple outliers, use this code:
# d <- subset(d, row_id!=c(1108) & row_id!=c(602))
# use the lm() command to run the regression
# formula is y~x1*x2 + c, where y is our DV, x1 is our first IV, x2 is our second IV.
reg_model <- lm(rse~mhealth, data = d) #for One-Way
# Cook's distance
plot(reg_model, 4)
# Residuals VS Leverage
plot(reg_model, 5)
Our cell sizes are very unbalanced between the mhealth group levels as bipolar and depression have much smaller sizes than None/NA. A small sample size for one of the levels of our variable limits our power and increases our Type II error rate.
Levene’s test was not significant for our three-level mhealth variable with the One-Way ANOVA.
# One-Way
aov_model <- aov_ez(data = d,
id = "X",
between = c("mhealth"),
dv = "rse",
anova_table = list(es = "pes"))
## Contrasts set to contr.sum for the following variables: mhealth
nice(aov_model)
## Anova Table (Type 3 tests)
##
## Response: rse
## Effect df MSE F pes p.value
## 1 mhealth 2, 1004 0.47 7.37 *** .014 <.001
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
ANOVA Effect Size [partial eta-squared] cutoffs from Cohen (1988): * η^2 < 0.01 indicates a trivial effect * η^2 >= 0.01 indicates a small effect * η^2 >= 0.06 indicates a medium effect * η^2 >= 0.14 indicates a large effect
# One-Way
afex_plot(aov_model, x = "mhealth")
emmeans(aov_model, specs="mhealth", adjust="sidak")
## mhealth emmean SE df lower.CL upper.CL
## bipolar 1.78 0.279 1004 1.12 2.45
## depression 2.54 0.121 1004 2.25 2.83
## none or NA 2.75 0.022 1004 2.70 2.81
##
## Confidence level used: 0.95
## Conf-level adjustment: sidak method for 3 estimates
pairs(emmeans(aov_model, specs="mhealth", adjust="sidak"))
## contrast estimate SE df t.ratio p.value
## bipolar - depression -0.76 0.304 1004 -2.498 0.0338
## bipolar - none or NA -0.97 0.280 1004 -3.462 0.0016
## depression - none or NA -0.21 0.123 1004 -1.706 0.2035
##
## P value adjustment: tukey method for comparing a family of 3 estimates
To test our hypothesis that there will be a significant difference in people’s rse scores measuring self-esteem based on the mhealth type signifying different mental disorders (depression, bipolar, none or NA), we used a one-way ANOVA. Our data was unbalanced, with many more people who do not have a mental health participating in our survey (n = 956) than who experience depression (n = 32) or bipolar disorder (n = 6). This significantly reduces the power of our test and increases the chances of a Type II error. However, we did NOT have a significant Levene’s test (p = .331), which indicates that our data is in compliance with the assumption of homogeneity of variance. We continued with our analysis for the purpose of this class.
We found a significant effect of pet type, F(2, 991) = 7.57, p < .001, ηp2 = .015 (small effect size; Cohen, 1988). Posthoc tests using Sidak’s adjustment revealed that participants who experience depression (M = 2.54, SE = 0.12) reported higher RSE scores measuring Self-Esteem than those who own experience bipolar disorder (M = 1.78, SE = 0.28) but lower RSE scores than those who do not have any mental health disorders or issues (M = 2.76, SE = 0.02); participants who do not have a mental health disorder reported the highest RSE scores overall (see Figure 1 for a comparison).
References
Cohen J. (1988). Statistical Power Analysis for the Behavioral Sciences. New York, NY: Routledge Academic.