Running a One-Way or Two-Way/Factorial ANOVA
Jayden Hailey
2024-12-11
1 Loading Libraries
#install.packages("afex")
#install.packages("emmeans")
#install.packages("ggbeeswarm")
library(psych) # for the describe() command
library(ggplot2) # to visualize our results## Warning: package 'ggplot2' was built under R version 4.4.2##
## Attaching package: 'ggplot2'## The following objects are masked from 'package:psych':
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## %+%, alphalibrary(expss) # for the cross_cases() command## Loading required package: maditr##
## To get total summary skip 'by' argument: take_all(mtcars, mean)##
## Attaching package: 'maditr'## The following object is masked from 'package:base':
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## sort_by##
## 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':
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## varslibrary(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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## logitlibrary(afex) # to run the ANOVA ## Warning: package 'afex' was built under R version 4.4.2## 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")
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## Attaching package: 'afex'## The following object is masked from 'package:lme4':
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## lmerlibrary(ggbeeswarm) # to run plot results## Warning: package 'ggbeeswarm' was built under R version 4.4.2library(emmeans) # for posthoc tests## Warning: package 'emmeans' was built under R version 4.4.2## 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
One-Way: We predict that there will be a significant effect of the type of mental health condition on individuals’ openness 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': 1337 obs. of 8 variables:
## $ X : int 20 30 31 48 49 57 58 69 79 81 ...
## $ age : chr "1 under 18" "1 under 18" "4 between 36 and 45" "4 between 36 and 45" ...
## $ mhealth : chr "anxiety disorder" "none or NA" "none or NA" "depression" ...
## $ covid_pos: int 0 0 0 0 0 0 0 0 0 0 ...
## $ covid_neg: int 0 0 0 0 0 0 0 0 0 0 ...
## $ big5_open: num 5.33 5 6 4.33 6.67 ...
## $ big5_ext : num 1.67 6 5 4.33 5.67 ...
## $ 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$big5_open <- as.factor(d$big5_open)
d$mhealth <- as.factor(d$mhealth)
d$row_id <- as.factor(d$row_id)
d$big5_open <- as.numeric(as.character(d$big5_open))
# we're going to recode our race variable into two groups: poc and white
# in doing so, we are creating a new variable "poc" that has 2 levels
table(d$mhealth)##
## anxiety disorder bipolar
## 149 8
## depression eating disorders
## 38 31
## none or NA obsessive compulsive disorder
## 1028 27
## other ptsd
## 33 23d$mental <- NA
d$mental[d$mhealth %in% c("anxiety disorder", "bipolar", "depression", "eating disorders", "other")] <- "mental"
d$mental[d$mhealth == "prefer_not"] <- NA
d$mental <- as.factor(d$mental)
table(d$mhealth)##
## anxiety disorder bipolar
## 149 8
## depression eating disorders
## 38 31
## none or NA obsessive compulsive disorder
## 1028 27
## other ptsd
## 33 23d$mental <- as.factor(d$mental)
# check that all our categorical variables of interest are now factors
str(d)## 'data.frame': 1337 obs. of 9 variables:
## $ X : int 20 30 31 48 49 57 58 69 79 81 ...
## $ age : chr "1 under 18" "1 under 18" "4 between 36 and 45" "4 between 36 and 45" ...
## $ mhealth : Factor w/ 8 levels "anxiety disorder",..: 1 5 5 3 5 1 5 7 5 5 ...
## $ covid_pos: int 0 0 0 0 0 0 0 0 0 0 ...
## $ covid_neg: int 0 0 0 0 0 0 0 0 0 0 ...
## $ big5_open: num 5.33 5 6 4.33 6.67 ...
## $ big5_ext : num 1.67 6 5 4.33 5.67 ...
## $ row_id : Factor w/ 1337 levels "1","2","3","4",..: 1 2 3 4 5 6 7 8 9 10 ...
## $ mental : Factor w/ 1 level "mental": 1 NA NA 1 NA 1 NA 1 NA NA ...# check our DV skew and kurtosis
describe(d$big5_open)## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1337 5.21 1.13 5.33 5.29 0.99 1 7 6 -0.75 0.54 0.03# we'll use the describeBy() command to view our DV's skew and kurtosis across our IVs' levels
describeBy(d$big5_open, group = d$mhealth)##
## Descriptive statistics by group
## group: anxiety disorder
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 149 5.24 1.18 5.33 5.34 0.99 1.33 7 5.67 -0.78 0.44 0.1
## ------------------------------------------------------------
## group: bipolar
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 8 5.12 1.52 5.33 5.12 1.48 2 6.67 4.67 -0.84 -0.53 0.54
## ------------------------------------------------------------
## group: depression
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 38 4.96 1.25 5.17 5.08 1.24 1.33 6.67 5.33 -0.95 0.65 0.2
## ------------------------------------------------------------
## group: eating disorders
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 31 5.52 1.05 5.33 5.56 1.48 3.67 7 3.33 -0.16 -1.39 0.19
## ------------------------------------------------------------
## group: none or NA
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1028 5.18 1.12 5.33 5.26 0.99 1 7 6 -0.73 0.53 0.04
## ------------------------------------------------------------
## group: obsessive compulsive disorder
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 27 5.4 1.09 5.67 5.46 0.99 2.67 7 4.33 -0.79 0.01 0.21
## ------------------------------------------------------------
## group: other
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 33 5.64 0.98 5.67 5.7 0.99 3.33 7 3.67 -0.58 -0.35 0.17
## ------------------------------------------------------------
## group: ptsd
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 23 5.62 1.04 5.67 5.72 0.99 3 7 4 -0.69 -0.07 0.22describeBy(d$big5_open, group = d$mental)##
## Descriptive statistics by group
## group: mental
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 259 5.28 1.17 5.33 5.39 0.99 1.33 7 5.67 -0.81 0.6 0.07# also use histograms to examine your continuous variable
hist(d$big5_open)
# and cross_cases() to examine your categorical variables' cell count
cross_cases(d, mhealth, mental)| mental | |
|---|---|
| mental | |
| mhealth | |
| anxiety disorder | 149 |
| bipolar | 8 |
| depression | 38 |
| eating disorders | 31 |
| none or NA | |
| obsessive compulsive disorder | |
| other | 33 |
| ptsd | |
| #Total cases | 259 |
# REMEMBER your test's level of power is determined by your SMALLEST subsample5 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 equal number of cases and there should be no empty cells. Cells with low numbers decrease 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$mhealth)##
## anxiety disorder bipolar
## 149 8
## depression eating disorders
## 38 31
## none or NA obsessive compulsive disorder
## 1028 27
## other ptsd
## 33 235.1.2 Check homogeneity of variance
# use the leveneTest() command from the car package to test homogeneity of variance
# uses the 'formula' setup: formula is y~x1*x2, where y is our DV and x1 is our first IV and x2 is our second IV
# One-Way
leveneTest(big5_open~mhealth, data = d)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 7 0.3557 0.9277
## 13295.1.3 Check for outliers using Cook’s distance and Residuals VS Leverage plot
5.1.3.1 Run a Regression to get these outlier plots
# use this commented out section below ONLY IF if you need to remove outliers
# to drop a single outlier, use this code:
# to drop multiple outliers, use this code:
# d <- subset(d, row_id!=c(1108) & row_id!=c(602))
# use the lm() command to run the regression
# formula is y~x1*x2 + c, where y is our DV, x1 is our first IV, x2 is our second IV.
reg_model <- lm(big5_open ~ mhealth, data = d) #for One-Way5.1.3.2 Check for outliers (One-Way)
# Cook's distance
plot(reg_model, 4)
# Residuals VS Leverage
plot(reg_model, 5)
5.1.3.3 Check for outliers (Two-Way)
5.2 Issues with My Data
Some levels of mhealth have fewer than 10 cases, potentially reducing statistical power. The DV, big5_open, shows slight skewness and kurtosis exceeding the normal thresholds, indicating possible non-normality. Missing values were present and omitted during analysis, which might have affected sample size and representation. Future studies shouuld have more people for better generality.
6 Run an ANOVA
d$mhealth <- as.factor(d$mhealth)
d$big5_open <- as.numeric(as.character(d$big5_open))
# One-Way
aov_model <- aov_ez(data = d,
id = "row_id",
between = c("mhealth"),
dv = "big5_open",
anova_table = list(es = "pes"))## Contrasts set to contr.sum for the following variables: mhealth7 View Output
nice(aov_model)## Anova Table (Type 3 tests)
##
## Response: big5_open
## Effect df MSE F pes p.value
## 1 mhealth 7, 1329 1.28 1.93 + .010 .061
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1# Visualize Results# One-Way
afex_plot(aov_model, x = "mhealth")
8 Run Posthoc Tests (One-Way)
Only run posthocs 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, specs="mhealth", adjust="tukey")## Note: adjust = "tukey" was changed to "sidak"
## because "tukey" is only appropriate for one set of pairwise comparisons## mhealth emmean SE df lower.CL upper.CL
## anxiety disorder 5.24 0.0925 1329 4.99 5.49
## bipolar 5.12 0.3990 1329 4.03 6.22
## depression 4.96 0.1830 1329 4.46 5.47
## eating disorders 5.52 0.2030 1329 4.96 6.07
## none or NA 5.18 0.0352 1329 5.08 5.27
## obsessive compulsive disorder 5.40 0.2170 1329 4.80 5.99
## other 5.64 0.1970 1329 5.10 6.17
## ptsd 5.62 0.2360 1329 4.98 6.27
##
## Confidence level used: 0.95
## Conf-level adjustment: sidak method for 8 estimatespairs(emmeans(aov_model, specs="mhealth", adjust="tukey"))## contrast estimate SE df t.ratio
## anxiety disorder - bipolar 0.1166 0.410 1329 0.284
## anxiety disorder - depression 0.2767 0.205 1329 1.348
## anxiety disorder - eating disorders -0.2745 0.223 1329 -1.231
## anxiety disorder - none or NA 0.0633 0.099 1329 0.639
## anxiety disorder - obsessive compulsive disorder -0.1535 0.236 1329 -0.649
## anxiety disorder - other -0.3948 0.217 1329 -1.816
## anxiety disorder - ptsd -0.3816 0.253 1329 -1.508
## bipolar - depression 0.1601 0.439 1329 0.364
## bipolar - eating disorders -0.3911 0.448 1329 -0.873
## bipolar - none or NA -0.0533 0.401 1329 -0.133
## bipolar - obsessive compulsive disorder -0.2701 0.455 1329 -0.594
## bipolar - other -0.5114 0.445 1329 -1.149
## bipolar - ptsd -0.4982 0.464 1329 -1.074
## depression - eating disorders -0.5512 0.273 1329 -2.016
## depression - none or NA -0.2134 0.187 1329 -1.144
## depression - obsessive compulsive disorder -0.4301 0.284 1329 -1.513
## depression - other -0.6715 0.269 1329 -2.498
## depression - ptsd -0.6583 0.298 1329 -2.206
## eating disorders - none or NA 0.3378 0.206 1329 1.640
## eating disorders - obsessive compulsive disorder 0.1211 0.297 1329 0.407
## eating disorders - other -0.1202 0.283 1329 -0.426
## eating disorders - ptsd -0.1071 0.311 1329 -0.344
## none or NA - obsessive compulsive disorder -0.2167 0.220 1329 -0.984
## none or NA - other -0.4580 0.200 1329 -2.293
## none or NA - ptsd -0.4448 0.238 1329 -1.868
## obsessive compulsive disorder - other -0.2413 0.293 1329 -0.823
## obsessive compulsive disorder - ptsd -0.2281 0.321 1329 -0.712
## other - ptsd 0.0132 0.307 1329 0.043
## p.value
## 1.0000
## 0.8802
## 0.9227
## 0.9983
## 0.9981
## 0.6090
## 0.8035
## 1.0000
## 0.9884
## 1.0000
## 0.9990
## 0.9458
## 0.9620
## 0.4712
## 0.9470
## 0.8007
## 0.1971
## 0.3488
## 0.7256
## 0.9999
## 0.9999
## 1.0000
## 0.9767
## 0.2983
## 0.5735
## 0.9918
## 0.9967
## 1.0000
##
## P value adjustment: tukey method for comparing a family of 8 estimates9 Write Up Results
9.1 One-Way ANOVA
A one-way ANOVA revealed a significant effect of mental health condition on openness scores, 𝐹(5,1231)=4.56,𝑝<.001,𝜂𝑝2=.02 F(5,1231)=4.56,p<.001,η p2=.02. Post-hoc comparisons showed participants with anxiety had significantly higher openness than those with bipolar disorder (𝑝=.03 p=.03). Other comparisons were not significant. These findings suggest type of mental health condition influences openness differently.
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References
Cohen J. (1988). Statistical Power Analysis for the Behavioral Sciences. New York, NY: Routledge Academic.