Running a One-Way ANOVA
Allie Burton
2024-06-11
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 drop variable use NULL: let(mtcars, am = NULL) %>% head()##
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## sort_by##
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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
One-Way: I predict that there will be a significant effect of education level on independence, as measured by the Markers of Adulthood- Importance scale (MoA- Importance).
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': 3045 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_role : num 3 2.67 2.5 2 2.67 ...
## $ mindful : num 2.4 1.8 2.2 2.2 3.2 ...
## $ efficacy : num 3.4 3.4 2.2 2.8 3 2.4 2.3 3 3 3.7 ...
## $ row_id : int 1 2 3 4 5 6 7 8 9 10 ...# make our categorical variables factors
d$edu <- as.factor(d$edu)
d$row_id <- as.factor(d$row_id)
# you can use the describe() command on an entire dataframe (d) or just on a single variable
describe(d$moa_independence)## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 3045 3.54 0.46 3.67 3.61 0.49 1 4 3 -1.43 2.47 0.01# we'll use the describeBy() command to view skew and kurtosis across the IV
describeBy(d$moa_independence, group = d$edu)##
## Descriptive statistics by group
## group: 1 High school diploma or less, and NO COLLEGE
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 53 3.51 0.54 3.67 3.6 0.49 2 4 2 -1.34 1.03 0.07
## ------------------------------------------------------------
## group: 2 Currently in college
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 2460 3.54 0.46 3.67 3.61 0.49 1 4 3 -1.48 2.71 0.01
## ------------------------------------------------------------
## group: 3 Completed some college, but no longer in college
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 35 3.56 0.45 3.67 3.62 0.49 2.5 4 1.5 -0.9 -0.15 0.08
## ------------------------------------------------------------
## group: 4 Complete 2 year College degree
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 174 3.6 0.42 3.67 3.66 0.49 2.17 4 1.83 -1.14 0.79 0.03
## ------------------------------------------------------------
## group: 5 Completed Bachelors Degree
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 135 3.51 0.48 3.67 3.58 0.49 1.5 4 2.5 -1.33 2.12 0.04
## ------------------------------------------------------------
## group: 6 Currently in graduate education
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 132 3.48 0.46 3.5 3.53 0.49 2 4 2 -0.99 0.75 0.04
## ------------------------------------------------------------
## group: 7 Completed some graduate degree
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 56 3.4 0.45 3.5 3.44 0.49 1.67 4 2.33 -1.25 2.41 0.06# also use histograms to examine your continuous variable
hist(d$moa_independence)
5 Check Your Assumptions
5.1 ANOVA Assumptions
- DV should be normally distributed across levels of the IV (skew and kurtosis)
- 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 (levene’s)
- 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
# One-way ANOVA:
table(d$edu)##
## 1 High school diploma or less, and NO COLLEGE
## 53
## 2 Currently in college
## 2460
## 3 Completed some college, but no longer in college
## 35
## 4 Complete 2 year College degree
## 174
## 5 Completed Bachelors Degree
## 135
## 6 Currently in graduate education
## 132
## 7 Completed some graduate degree
## 565.1.2 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(moa_independence~edu, data = d)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 6 0.2866 0.9436
## 30385.1.3 Check for outliers using Cook’s distance and Residuals vs Leverage plot
5.1.3.1 Run a Regression
# 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(moa_independence ~ edu, 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)
5.2 Issues with My Data
The kurtosis for the group of those currently in college and those who have completed some graduate degree are above the cut-off.This means that the DV is not evenly distributed, so the data is slightly skewed.
The cell sizes are very unbalanced, with the majority of participants being currently in college. A small sample size for one of the levels of the variable limits the power and increases the Type II error rate.
6 Run an ANOVA
aov_model <- aov_ez(data = d,
id = "row_id",
between = c("edu"),
dv = "moa_independence",
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: moa_independence
## Effect df MSE F pes p.value
## 1 edu 6, 3038 0.21 1.95 + .004 .070
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 18 Visualize Results
afex_plot(aov_model, x = "edu")
9 Write Up Results
9.1 One-Way ANOVA
To test the hypothesis that there will be a significant effect of education level on independence, as measured by the Markers of Adulthood- Importance scale (MoA- Importance), I used a one-way ANOVA. The data was unbalanced, with many more current college students participating in the survey (n = 2460) than the number of other participants combined (n = 585). The smallest group was those who completed some college, but were no longer in college (n = 35). This significantly reduces the power of the test and increases the chances of a Type II error.
No outliers were deemed necessary to remove following visual analysis of a Residuals vs Leverage plot. Levene’s test produced an insignificant result (p = .94), indicating that the data does not violate the assumption of homogeneity of variance, and no adhoc tests were necessary. I did not find a significant effect of education, F(6,3038) = 1.95, p = .07, ηp2 = .004 (negligible effect size; Cohen, 1988) on independence.(see Figure 1 for a comparison).
1 = High school diploma or less, and NO COLLEGE; 2 = Currently in college; 3 = Completed some college, but no longer in college; 4 = Complete 2 year College degree; 5 = Completed Bachelors Degree; 6 = Currently in graduate education; 7 = Completed some graduate degree
References
Cohen J. (1988). Statistical Power Analysis for the Behavioral Sciences. New York, NY: Routledge Academic.