1 Loading Libraries

#install.packages("afex")
#install.packages("emmeans")
#install.packages("ggbeeswarm")

library(psych) # for the describe() command
library(ggplot2) # to visualize our results
## 
## Attaching package: 'ggplot2'
## The following objects are masked from 'package:psych':
## 
##     %+%, alpha
library(expss) # for the cross_cases() command
## Loading required package: maditr
## 
## To select rows from data: rows(mtcars, am==0)
## 
## 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
## 
## 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
## 
## 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':
## 
##     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'

2 Importing Data

# 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)

3 State Your Hypothesis

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

4 Check Your Variables

# 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

5 Check Your Assumptions

5.1 ANOVA Assumptions

  • DV should be normally distributed across levels of the IV (we checked previously using “describeBy” function)
  • All levels of the IVs should have an equal number of cases and there should be no empty cells. Cells with low numbers decreases the power of the test (which increases chance of Type II error)
  • Homogeneity of variance should be assured (using Levene’s Test)
  • Outliers should be identified and removed – we will actually remove them this time!
  • If you have confirmed everything above, the sampling distribution should be normal.

5.1.1 Check levels of IVs

# One-Way
table(d$mhealth)
## 
##    bipolar depression none or NA 
##          6         32        970

5.1.2 Check homogeneity of variance

# 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

5.1.3 Check for outliers using Cook’s distance and Residuals VS Leverage plot

5.1.3.1 Run a Regression to get these outlier plots

# 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

5.1.3.2 Check for outliers (One-Way)

# Cook's distance
plot(reg_model, 4)

# Residuals VS Leverage
plot(reg_model, 5)

5.2 Issues with My Data

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.

6 Run an 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

7 View Output

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

8 Visualize Results

# One-Way
afex_plot(aov_model, x = "mhealth")

9 Run Posthoc Tests (One-Way)

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

10 Write Up Results

10.1 One-Way ANOVA

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.