Running a One-Way or Two-Way/Factorial ANOVA HW
Josephine Allender
2024-07-23
1 Loading Libraries
library(psych) # for the describe() command
library(ggplot2) # to visualize our results##
## 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_rnotebook()' to display tables inside R Notebooks.
## 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 and plot results## 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(emmeans) # for posthoc tests## Welcome to emmeans.
## Caution: You lose important information if you filter this package's results.
## See '? untidy'2 Importing Data
# import the dataset you cleaned previously
# this will be the dataset you'll use throughout the rest of the semester
# use ARC data
d <- read.csv(file="Data/mydata.csv", header=T)
# new code! this adds a column with a number for each row. it makes it easier when we drop outliers later
d$row_id <- 1:nrow(d)3 State Your Hypothesis
Note: You can chose to run either a one-way ANOVA (a single IV with more than 3 levels) or a two-way/factorial ANOVA (at least two IVs) for the homework. You will need to specify your hypothesis and customize your code based on the choice you make. I will run both versions of the test here for illustrative purposes.
I predict that there will be a significant effect of education level on stress. Furthermore, I predict that individuals with a higher level of education will experience higher stress.
4 Check Your Variables
# you only need to check the variables you're using in the current analysis
# although 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': 3069 obs. of 7 variables:
## $ edu : chr "2 Currently in college" "5 Completed Bachelors Degree" "2 Currently in college" "2 Currently in college" ...
## $ marriage5 : chr "are currently divorced from one another" "are currently married to one another" "are currently married to one another" "are currently married to one another" ...
## $ moa_independence: num 3.67 3.67 3.5 3 3.83 ...
## $ moa_maturity : num 3.67 3.33 3.67 3 3.67 ...
## $ mindful : num 2.4 1.8 2.2 2.2 3.2 ...
## $ stress : num 3.3 3.3 4 3.2 3.1 3.5 3.3 2.4 2.9 2.7 ...
## $ row_id : int 1 2 3 4 5 6 7 8 9 10 ...# make our categorical variables factors
d$row_id <- as.factor(d$row_id) #we'll actually use our ID variable for this analysis, so make sure it's coded as a factor
d$edu <- as.factor(d$edu)
d$row_id <- as.factor(d$row_id)
# we're going to recode our race/ethnicity variable into two groups: poc and white
table(d$edu)##
## 1 High school diploma or less, and NO COLLEGE
## 53
## 2 Currently in college
## 2482
## 3 Completed some college, but no longer in college
## 34
## 4 Complete 2 year College degree
## 175
## 5 Completed Bachelors Degree
## 136
## 6 Currently in graduate education
## 133
## 7 Completed some graduate degree
## 56d$high_ed[d$edu == "2 Currently in college"] <- "high_ed"
d$high_ed[d$edu == "3 Completed some college, but no longer in college"] <- "standard_ed"
d$high_ed[d$edu == "4 Complete 2 year College degree"] <- "standard_ed"
d$high_ed[d$edu == "5 Completed Bachelors Degree"] <- "high_ed"
d$high_ed[d$edu == "6 Currently in graduate education"] <- "high_ed"
d$high_ed[d$edu == "7 Completed some graduate degree"] <- "high_ed"
d$high_ed[d$edu == "1 High school diploma or less, and NO COLLEGE"] <- "standard_ed"
table(d$high_ed)##
## high_ed standard_ed
## 2807 262d$high_ed <- as.factor(d$high_ed)
# you can use the describe() command on an entire dataframe (d) or just on a single variable
describe(d$stress)## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 3069 3.05 0.6 3 3.05 0.59 1.3 4.7 3.4 0.04 -0.16 0.01# we'll use the describeBy() command to view skew and kurtosis across our IVs
describeBy(d$stress, group = d$edu)##
## Descriptive statistics by group
## group: 1 High school diploma or less, and NO COLLEGE
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 53 3.27 0.7 3.2 3.27 0.74 1.6 4.6 3 0.01 -0.44 0.1
## ------------------------------------------------------------
## group: 2 Currently in college
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 2482 3.07 0.59 3.1 3.06 0.59 1.3 4.7 3.4 0.04 -0.15 0.01
## ------------------------------------------------------------
## group: 3 Completed some college, but no longer in college
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 34 3.01 0.62 3.05 3.01 0.59 1.4 4.3 2.9 -0.12 -0.05 0.11
## ------------------------------------------------------------
## group: 4 Complete 2 year College degree
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 175 2.96 0.65 2.9 2.95 0.59 1.4 4.6 3.2 0.16 -0.07 0.05
## ------------------------------------------------------------
## group: 5 Completed Bachelors Degree
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 136 2.88 0.64 2.8 2.88 0.74 1.3 4.4 3.1 0.07 -0.65 0.06
## ------------------------------------------------------------
## group: 6 Currently in graduate education
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 133 2.97 0.6 3 2.97 0.59 1.5 4.3 2.8 0 -0.54 0.05
## ------------------------------------------------------------
## group: 7 Completed some graduate degree
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 56 2.92 0.66 2.95 2.92 0.59 1.5 4.4 2.9 0.02 -0.19 0.09describeBy(d$stress, group = d$high_ed)##
## Descriptive statistics by group
## group: high_ed
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 2807 3.05 0.6 3 3.05 0.59 1.3 4.7 3.4 0.03 -0.18 0.01
## ------------------------------------------------------------
## group: standard_ed
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 262 3.03 0.66 3 3.02 0.59 1.4 4.6 3.2 0.13 -0.12 0.04# also use histograms to examine your continuous variable
hist(d$stress)
# and cross_cases() to examine your categorical variables
cross_cases(d, edu, high_ed)| high_ed | ||
|---|---|---|
| high_ed | standard_ed | |
| edu | ||
| 1 High school diploma or less, and NO COLLEGE | 53 | |
| 2 Currently in college | 2482 | |
| 3 Completed some college, but no longer in college | 34 | |
| 4 Complete 2 year College degree | 175 | |
| 5 Completed Bachelors Degree | 136 | |
| 6 Currently in graduate education | 133 | |
| 7 Completed some graduate degree | 56 | |
| #Total cases | 2807 | 262 |
5 Check Your Assumptions
5.1 ANOVA Assumptions
- DV should be normally distributed across levels of the IV
- 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 (increase change of Type II error)
- Homogeneity of variance should be assured
- Outliers should be identified and removed
- If you have confirmed everything about, the sampling distribution should be normal. (For a demonstration of what the sampling distribution is, go here.)
5.1.1 Check levels of IVs
table(d$edu)##
## 1 High school diploma or less, and NO COLLEGE
## 53
## 2 Currently in college
## 2482
## 3 Completed some college, but no longer in college
## 34
## 4 Complete 2 year College degree
## 175
## 5 Completed Bachelors Degree
## 136
## 6 Currently in graduate education
## 133
## 7 Completed some graduate degree
## 56cross_cases(d, edu, high_ed)| high_ed | ||
|---|---|---|
| high_ed | standard_ed | |
| edu | ||
| 1 High school diploma or less, and NO COLLEGE | 53 | |
| 2 Currently in college | 2482 | |
| 3 Completed some college, but no longer in college | 34 | |
| 4 Complete 2 year College degree | 175 | |
| 5 Completed Bachelors Degree | 136 | |
| 6 Currently in graduate education | 133 | |
| 7 Completed some graduate degree | 56 | |
| #Total cases | 2807 | 262 |
# our number of small nb participants is going to hurt us for the two-way anova, but it should be okay for the one-way anova
# so we'll create a new dataframe for the two-way analysis and call it d2
d2 <- subset(d, edu != "nb")
d2$edu <- droplevels(d2$edu)
# to double-check any changes we made
cross_cases(d2, edu, high_ed)| high_ed | ||
|---|---|---|
| high_ed | standard_ed | |
| edu | ||
| 1 High school diploma or less, and NO COLLEGE | 53 | |
| 2 Currently in college | 2482 | |
| 3 Completed some college, but no longer in college | 34 | |
| 4 Complete 2 year College degree | 175 | |
| 5 Completed Bachelors Degree | 136 | |
| 6 Currently in graduate education | 133 | |
| 7 Completed some graduate degree | 56 | |
| #Total cases | 2807 | 262 |
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
leveneTest(stress~edu, data = d)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 6 1.2895 0.2584
## 3062leveneTest(stress~edu*high_ed, data = d)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 6 1.2895 0.2584
## 30625.1.3 Check for outliers using Cook’s distance and Residuals vs Leverage plot
5.1.3.1 Run a Regression
# use this commented out section only if you need to remove outliers
# to drop a single outlier, remove the # at the beginning of the line and use this code:
d <- subset(d, row_id!=c(1246))
# to drop multiple outliers, remove the # at the beginning of the line and 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, and c is our covariate
reg_model <- lm(stress ~ edu, data = d) #for one-way
reg_model2 <- lm(stress ~ edu*high_ed, data = d) #for two-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)
# Cook's distance
plot(reg_model2, 4)
# Residuals vs Leverage
plot(reg_model2, 5)
5.2 Issues with My Data
Our cell sizes are somewhat unbalanced. 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 is significant for my two-level education variable. I am ignoring this and continuing with the analysis anyway, but in the real world this is something I would have to correct for.
I identified and removed a single outlier.
6 Run an ANOVA
aov_model <- aov_ez(data = d,
id = "row_id",
between = c("edu"),
dv = "stress",
anova_table = list(es = "pes"))## Contrasts set to contr.sum for the following variables: edu7 View Output
Effect size cutoffs from Cohen (1988):
- η2 = 0.01 indicates a small effect
- η2 = 0.06 indicates a medium effect
- η2 = 0.14 indicates a large effect
nice(aov_model)## Anova Table (Type 3 tests)
##
## Response: stress
## Effect df MSE F pes p.value
## 1 edu 6, 3059 0.36 4.84 *** .009 <.001
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1# Visualize Resultsafex_plot(aov_model, x = "edu")
8 Run Posthoc Tests (One-Way)
Only run posthocs if the test is significant! E.g., only run the posthoc tests on gender if there is a main effect for education.
9 Write Up Results
9.1 One-Way ANOVA
To test my hypothesis that there would be a significant effect of education level on stress, I used a one-way ANOVA. I identified and removed a single outlier following visual analysis of a Residuals vs Leverage plot. A significant Levene’s test also indicates that our data violates the assumption of homogeneity of variance. This suggests that there is an increased chance of Type I error. I continued with my analysis for the purpose of this class.
I found an insignificant effect of gender, F(6,3061) = 4.85, p < .001, ηp2 = .009 (insignificant effect size; Cohen, 1988). Posthoc tests using Tukey’s HSD were not used for this analysis, due to insignificant effect size.
References
Cohen J. (1988). Statistical Power Analysis for the Behavioral Sciences. New York, NY: Routledge Academic.