Running a One-Way ANOVA HW
Agnes Cao
2024-07-24
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':
##
## %+%, alphalibrary(expss) # for the cross_cases() command## Loading required package: maditr##
## To modify variables or add new variables:
## let(mtcars, new_var = 42, new_var2 = new_var*hp) %>% head()##
## Attaching package: 'maditr'## The following object is masked from 'package:base':
##
## sort_by##
## Attaching package: 'expss'## The following object is masked from 'package:ggplot2':
##
## varslibrary(car) # for the leveneTest() command## Loading required package: carData##
## Attaching package: 'car'## The following object is masked from 'package:expss':
##
## recode## The following object is masked from 'package:psych':
##
## 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':
##
## 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':
##
## 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: We predict that there will be a significant effect of relationship status on self-esteem, as measured by the Rosenberg Self-Esteem Inventory (rse).
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': 1337 obs. of 7 variables:
## $ sexual_orientation : chr "Heterosexual/Straight" "Heterosexual/Straight" "Heterosexual/Straight" "Heterosexual/Straight" ...
## $ relationship_status: chr "In a relationship/married and cohabiting" "Prefer not to say" "Prefer not to say" "In a relationship/married and cohabiting" ...
## $ big5_open : num 5.33 5.33 5 6 5 ...
## $ pswq : num 4.94 3.36 1.86 3.94 2.62 ...
## $ mfq_26 : num 4.2 3.35 4.65 4.65 4.5 4.3 5.25 5 4.7 4.05 ...
## $ rse : num 2.3 1.6 3.9 1.7 3.9 2.4 1.8 1.3 3.5 2.6 ...
## $ row_id : int 1 2 3 4 5 6 7 8 9 10 ...# make our categorical variables factors
#d$X <- as.factor(d$X)
#we'll actually use our ID variable for this analysis, so make sure it's coded as a factor
d$sexual_orientation <- as.factor(d$sexual_orientation)
d$relationship_status <- as.factor(d$relationship_status)
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
# Check the class of d$rse
class(d$rse)## [1] "numeric"# Convert factor to numeric
d$rse <- as.numeric(as.character(d$rse))
# Now try to describe it
describe(d$rse)## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1337 2.61 0.72 2.7 2.62 0.74 1 4 3 -0.17 -0.72 0.02# we'll use the describeBy() command to view skew and kurtosis across our IVs
describeBy(d$rse, group = d$relationship_status)##
## Descriptive statistics by group
## group: In a relationship/married and cohabiting
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 282 3.1 0.5 3.1 3.11 0.59 1.4 4 2.6 -0.39 -0.13 0.03
## ------------------------------------------------------------
## group: In a relationship/married but living apart
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 106 2.39 0.76 2.5 2.38 0.89 1 4 3 0.06 -0.97 0.07
## ------------------------------------------------------------
## group: Prefer not to say
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 104 2.45 0.7 2.4 2.44 0.82 1.1 3.9 2.8 0.1 -0.8 0.07
## ------------------------------------------------------------
## group: Single, divorced or widowed
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 44 2.94 0.54 2.9 2.94 0.52 1.2 4 2.8 -0.41 0.86 0.08
## ------------------------------------------------------------
## group: Single, never married
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 801 2.47 0.71 2.4 2.47 0.74 1 4 3 0.03 -0.7 0.03# also use histograms to examine your continuous variable
hist(d$rse)
# and cross_cases() to examine your categorical variables
cross_cases(d, relationship_status)|  #Total | |
|---|---|
|  relationship_status | |
|    In a relationship/married and cohabiting | 282 |
|    In a relationship/married but living apart | 106 |
|    Prefer not to say | 104 |
|    Single, divorced or widowed | 44 |
|    Single, never married | 801 |
|    #Total cases | 1337 |
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$relationship_status)##
## In a relationship/married and cohabiting
## 282
## In a relationship/married but living apart
## 106
## Prefer not to say
## 104
## Single, divorced or widowed
## 44
## Single, never married
## 8015.1.2 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(rse~relationship_status, data = d)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 4 15.654 1.596e-12 ***
## 1332
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 15.1.3 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(1108))
# 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(rse ~ relationship_status, 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
Our cell sizes are very 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 our relationship status variable (p<0.05). We are ignoring this and continuing with the analysis anyway, but in the real world this is something we would have to correct for.
6 Run an ANOVA
aov_model <- aov_ez(data = d,
id = "row_id",
between = c("relationship_status"),
dv = "rse",
anova_table = list(es = "pes"))## Contrasts set to contr.sum for the following variables: relationship_status7 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: rse
## Effect df MSE F pes p.value
## 1 relationship_status 4, 1332 0.45 52.54 *** .136 <.001
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 18 Visualize Results
afex_plot(aov_model, x = "relationship_status")
9 Run Posthoc Tests (One-Way)
Only run posthocs if the test is significant! E.g., only run the posthoc tests on relationship status if there is a main effect for relationship status.
emmeans(aov_model, specs="relationship_status", adjust="tukey")## Note: adjust = "tukey" was changed to "sidak"
## because "tukey" is only appropriate for one set of pairwise comparisons## relationship_status emmean SE df lower.CL
## In a relationship/married and cohabiting 3.10 0.0399 1332 2.99
## In a relationship/married but living apart 2.39 0.0650 1332 2.23
## Prefer not to say 2.45 0.0657 1332 2.28
## Single, divorced or widowed 2.94 0.1009 1332 2.68
## Single, never married 2.47 0.0237 1332 2.41
## upper.CL
## 3.20
## 2.56
## 2.61
## 3.20
## 2.53
##
## Confidence level used: 0.95
## Conf-level adjustment: sidak method for 5 estimatespairs(emmeans(aov_model, specs="relationship_status", adjust="tukey"))## contrast
## (In a relationship/married and cohabiting) - (In a relationship/married but living apart)
## (In a relationship/married and cohabiting) - Prefer not to say
## (In a relationship/married and cohabiting) - Single, divorced or widowed
## (In a relationship/married and cohabiting) - Single, never married
## (In a relationship/married but living apart) - Prefer not to say
## (In a relationship/married but living apart) - Single, divorced or widowed
## (In a relationship/married but living apart) - Single, never married
## Prefer not to say - Single, divorced or widowed
## Prefer not to say - Single, never married
## Single, divorced or widowed - Single, never married
## estimate SE df t.ratio p.value
## 0.7016 0.0763 1332 9.198 <.0001
## 0.6498 0.0768 1332 8.460 <.0001
## 0.1587 0.1085 1332 1.462 0.5874
## 0.6236 0.0464 1332 13.451 <.0001
## -0.0518 0.0924 1332 -0.560 0.9806
## -0.5430 0.1201 1332 -4.522 0.0001
## -0.0780 0.0692 1332 -1.127 0.7921
## -0.4912 0.1204 1332 -4.079 0.0005
## -0.0262 0.0698 1332 -0.376 0.9958
## 0.4650 0.1037 1332 4.485 0.0001
##
## P value adjustment: tukey method for comparing a family of 5 estimates10 Write Up Results
10.1 One-Way ANOVA
To test our hypothesis that there would be a significant effect of relationship status on self-esteem, we used a one-way ANOVA. Our data was unbalanced, with many more single, never married participating in our survey (n = 800), and small group of single, divorced or widowed participants (n = 44). This significantly reduces the power of our test and increases the chances of a Type II error. There was no outlier based on the Cook’s distance and Residuals vs Leverage plots. A significant Levene’s test (p = 1.551e-12) 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 gender, F(4,1331) = 52.55, p < .001, ηp2 = .136 (large effect size; Cohen, 1988). Posthoc tests using sidak’s test revealed that participants who are in a relationship/married and cohabiting reported higher self-esteem than other groups, followed by single/divorced or widowed, single/never married, prefer not to say, and participants who are in a relationship/married but living apart reported the lowest self-esteem. (see Figure 1 for a comparison).
References
Cohen J. (1988). Statistical Power Analysis for the Behavioral Sciences. New York, NY: Routledge Academic.