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 get total summary skip 'by' argument: take_all(mtcars, mean)

## 
## Use 'expss_output_viewer()' to display tables in the RStudio Viewer.
##  To return to the console output, use 'expss_output_default()'.

## 
## Attaching package: 'expss'

## The following object is masked from 'package:ggplot2':
## 
##     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':
## 
##     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: There will be a significant difference in perceived loneliness by people’s type of mental health disorder, between anxiety, depression, and bipolar

IV = Mental health disorder DV = Perceived loneliness

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':    668 obs. of  8 variables:
##  $ X          : int  321 520 1422 1849 2247 2526 2609 2814 3053 3108 ...
##  $ age        : chr  "1 under 18" "1 under 18" "1 under 18" "1 under 18" ...
##  $ mhealth    : chr  "none or NA" "none or NA" "none or NA" "anxiety disorder" ...
##  $ big5_neu   : num  3.67 5.33 3.67 6 3.33 ...
##  $ pas_covid  : num  2.33 3 2.67 2.56 3 ...
##  $ isolation_c: num  1.25 1 3.5 3.5 2 2.5 1.75 1 2 1.25 ...
##  $ mfq_26     : num  4.3 2.7 2.95 2.4 4.7 4.35 4.25 4.55 4.95 4.95 ...
##  $ 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

f_filtered <- d[d$mhealth %in% c("anxiety disorder", "depression", "bipolar"), ]


# 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':    668 obs. of  8 variables:
##  $ X          : int  321 520 1422 1849 2247 2526 2609 2814 3053 3108 ...
##  $ age        : chr  "1 under 18" "1 under 18" "1 under 18" "1 under 18" ...
##  $ mhealth    : Factor w/ 8 levels "anxiety disorder",..: 5 5 5 1 5 5 5 5 5 5 ...
##  $ big5_neu   : num  3.67 5.33 3.67 6 3.33 ...
##  $ pas_covid  : num  2.33 3 2.67 2.56 3 ...
##  $ isolation_c: num  1.25 1 3.5 3.5 2 2.5 1.75 1 2 1.25 ...
##  $ mfq_26     : num  4.3 2.7 2.95 2.4 4.7 4.35 4.25 4.55 4.95 4.95 ...
##  $ row_id     : Factor w/ 668 levels "1","2","3","4",..: 1 2 3 4 5 6 7 8 9 10 ...

# check our DV skew and kurtosis
describe(d$isolation_c)

##    vars   n mean   sd median trimmed  mad min max range  skew kurtosis   se
## X1    1 668 2.29 0.81   2.25     2.3 1.11   1 3.5   2.5 -0.02    -1.24 0.03

# we'll use the describeBy() command to view our DV's skew and kurtosis across our IVs' levels
describeBy(d$isolation_c, group = d$mhealth )

## 
##  Descriptive statistics by group 
## group: anxiety disorder
##    vars  n mean   sd median trimmed  mad min max range  skew kurtosis   se
## X1    1 76 2.67 0.77   2.88    2.74 0.93   1 3.5   2.5 -0.59    -0.92 0.09
## ------------------------------------------------------------ 
## group: bipolar
##    vars n mean   sd median trimmed  mad  min  max range  skew kurtosis  se
## X1    1 3 2.83 0.52      3    2.83 0.37 2.25 3.25     1 -0.29    -2.33 0.3
## ------------------------------------------------------------ 
## group: depression
##    vars  n mean   sd median trimmed  mad  min max range  skew kurtosis   se
## X1    1 10 2.78 0.78   2.88    2.88 0.93 1.25 3.5  2.25 -0.56    -1.09 0.25
## ------------------------------------------------------------ 
## group: eating disorders
##    vars  n mean   sd median trimmed  mad  min max range  skew kurtosis   se
## X1    1 17 2.59 0.73   2.75    2.62 0.74 1.25 3.5  2.25 -0.34    -1.35 0.18
## ------------------------------------------------------------ 
## group: none or NA
##    vars   n mean  sd median trimmed  mad min max range skew kurtosis   se
## X1    1 517 2.17 0.8      2    2.15 1.11   1 3.5   2.5 0.16    -1.18 0.04
## ------------------------------------------------------------ 
## group: obsessive compulsive disorder
##    vars  n mean  sd median trimmed  mad min max range skew kurtosis   se
## X1    1 15 2.62 0.6    2.5    2.63 0.74 1.5 3.5     2    0    -1.26 0.16
## ------------------------------------------------------------ 
## group: other
##    vars  n mean   sd median trimmed  mad  min max range  skew kurtosis   se
## X1    1 18 2.94 0.59   3.25    2.98 0.37 1.75 3.5  1.75 -0.61    -1.19 0.14
## ------------------------------------------------------------ 
## group: ptsd
##    vars  n mean   sd median trimmed  mad min max range  skew kurtosis   se
## X1    1 12 2.77 0.74   2.88    2.88 0.93   1 3.5   2.5 -0.93     0.03 0.21

# also use histograms to examine your continuous variable
hist(d$isolation_c)

# and cross_cases() to examine your categorical variables' cell count
cross_cases(d, mhealth)

	#Total
mhealth
anxiety disorder	76
bipolar	3
depression	10
eating disorders	17
none or NA	517
obsessive compulsive disorder	15
other	18
ptsd	12
#Total cases	668

# 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)

## 
##              anxiety disorder                       bipolar 
##                            76                             3 
##                    depression              eating disorders 
##                            10                            17 
##                    none or NA obsessive compulsive disorder 
##                           517                            15 
##                         other                          ptsd 
##                            18                            12

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(isolation_c~mhealth, data = d)

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value Pr(>F)
## group   7   1.471 0.1745
##       660

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

# 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(isolation_c~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 mental health group levels. A small sample size for one of the levels (bipolar) of our variable limits our power and increases our Type II error rate.

Levene’s test was not significant for our three-level mental health variable with the One-Way ANOVA. We are ignoring this and continuing with the analysis anyway for class purposes.

6 Run an ANOVA

# One-Way
aov_model_filtered <- aov_ez(data = f_filtered ,
                    id = "X",
                    between = c("mhealth"),
                    dv = "isolation_c",
                    anova_table = list(es = "pes"))

## Contrasts set to contr.sum for the following variables: mhealth

7 View Output

nice(aov_model_filtered)

## Anova Table (Type 3 tests)
## 
## Response: isolation_c
##    Effect    df  MSE    F  pes p.value
## 1 mhealth 2, 86 0.59 0.14 .003    .872
## ---
## 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_filtered, x = "mhealth")

# NOTE: for the Two-Way, we will decide which plot version makes the MOST SENSE based on the data / rationale when we make the nice Figure 2 at the end

9 Run Posthoc Tests (One-Way)

ONLY run posthoc IF the ANOVA test is SIGNIFICANT! E.g., only run the posthoc tests on pet type if there is a main effect for pet type

emmeans(aov_model_filtered, specs="mhealth", adjust="sidak")

##  mhealth          emmean     SE df lower.CL upper.CL
##  anxiety disorder   2.67 0.0879 86     2.46     2.89
##  bipolar            2.83 0.4420 86     1.76     3.91
##  depression         2.77 0.2420 86     2.18     3.37
## 
## Confidence level used: 0.95 
## Conf-level adjustment: sidak method for 3 estimates

pairs(emmeans(aov_model_filtered, specs="mhealth", adjust="sidak"))

##  contrast                      estimate    SE df t.ratio p.value
##  anxiety disorder - bipolar     -0.1623 0.451 86  -0.360  0.9312
##  anxiety disorder - depression  -0.1039 0.258 86  -0.403  0.9144
##  bipolar - depression            0.0583 0.504 86   0.116  0.9927
## 
## P value adjustment: tukey method for comparing a family of 3 estimates

10 Run Posthoc Tests (Two-Way)

ONLY run posthoc IF the ANOVA test is SIGNIFICANT! E.g., only run the posthoc tests on pet type if there is a main effect for pet type.

```

11 Write Up Results

11.1 One-Way ANOVA

To test our hypothesis that there will be a significant difference in people’s level of perceived loneliness based on the mental health disorder (anxiety, depression, bipolar), we used a one-way ANOVA. Our data was unbalanced, with many more people who are diagnosed with anxiety disorder (n = 76) than who have depression disorder (10) or bipolar disorder (n = 3). This significantly reduces the power of our test and increases the chances of a Type II error. We did not identify or remove a single outlier following visual analysis of Cook’s Distance and Residuals VS Leverage plots. A non-significant Levene’s test (p = 0.17) also indicates that our data violates the assumption of homogeneity of variance. This suggests that there is an increased chance of Type I error. We continued with our analysis for the purpose of this class.

We found a significant effect of mental health disorder, F(7,660) = 8.22, p < 0.001, η_p² = .080 (medium effect size; Cohen, 1988). Posthoc tests using Sidak’s adjustment revealed that participants who have anxiety disorder (M* = 2.67, SE = 0.09) reported less loneliness than those who have depression (M = 2.77, SE = 0.25) and less loneliness than those who have bipolar disorder (M = 2.83, SE = 0.45); participants who have bipolar disorder reported the highest amount of loneliness overall (see Figure 1 for a comparison).

References

Cohen J. (1988). Statistical Power Analysis for the Behavioral Sciences. New York, NY: Routledge Academic.

Running a One-Way ANOVA

Eli Davis

2025-06-20