Running a One-Way ANOVA HW
Sophie Sabo
2023-06-17
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 aggregate data: take(mtcars, mean_mpg = mean(mpg), by = am)##
## 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 tests2 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="eammi2_final.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 gender on stress, as measured by the perceived stress scale (PSS).
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': 3182 obs. of 8 variables:
## $ ResponseId: chr "R_BJN3bQqi1zUMid3" "R_2TGbiBXmAtxywsD" "R_12G7bIqN2wB2N65" "R_39pldNoon8CePfP" ...
## $ gender : chr "f" "m" "m" "f" ...
## $ race_rc : chr "white" "white" "white" "other" ...
## $ swb : num 4.33 4.17 1.83 5.17 3.67 ...
## $ stress : num 3.3 3.6 3.3 3.2 3.5 2.9 3.2 3 2.9 3.2 ...
## $ belong : num 3.4 3.4 3.6 3.6 3.2 3.4 3.5 3.2 3.5 2.7 ...
## $ SocMedia : num 4.27 2.09 3.09 3.18 3.36 ...
## $ row_id : int 1 2 3 4 5 6 7 8 9 10 ...# make our categorical variables factors
d$ResponseId <- as.factor(d$ResponseId) #we'll actually use our ID variable for this analysis, so make sure it's coded as a factor
d$gender <- as.factor(d$gender)
d$race_rc <- as.factor(d$race_rc)
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$stress)## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 3175 3.27 0.41 3.3 3.26 0.44 1 5 4 -0.16 2.67 0.01# we'll use the describeBy() command to view skew and kurtosis across our IVs
describeBy(d$stress, group = d$gender)##
## Descriptive statistics by group
## group: f
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 2326 3.29 0.4 3.3 3.29 0.44 1 5 4 -0.06 2.16 0.01
## ------------------------------------------------------------
## group: m
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 791 3.18 0.41 3.2 3.18 0.44 1 5 4 -0.2 3.41 0.01
## ------------------------------------------------------------
## group: nb
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 54 3.36 0.37 3.4 3.36 0.3 2 4.4 2.4 -0.37 2.26 0.05# also use histograms to examine your continuous variable
hist(d$stress)
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$gender)##
## f m nb
## 2332 792 545.1.2 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~gender, data = d)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 2 0.4129 0.6617
## 31685.1.3 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(stress ~ gender, 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 especially because we’ve kept our low amount of non-binary participants (because we need 3+ cells for one-way ANOVA). 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 not significant for our three-level gender variable.
We identified our highest outliers but did not remove any because there was a straight red line already when displaying residuals vs leverage.
6 Run an ANOVA
aov_model <- aov_ez(data = d,
id = "ResponseId",
between = c("gender"),
dv = "stress",
anova_table = list(es = "pes"))## Warning: Missing values for 11 ID(s), which were removed before analysis:
## R_1EihKePhUenEL9L, R_1oBJ33zLPm5Lusa, R_2tbf8FyKp1Dg0wV, R_3PZvgQSzbXD8PG5, R_3QXfRHzrQr2VUE1, R_6sO4a1z8iDHY1kV, R_77J1rfMXuRJR5vP, R_9EPStPMnugteJXn, R_9n2p79F9uUrbMpH, R_Y69XOURBCDXZd0R, ... [showing first 10 only]
## Below the first few rows (in wide format) of the removed cases with missing data.
## ResponseId gender .
## # 215 R_1EihKePhUenEL9L <NA> 2.8
## # 587 R_1oBJ33zLPm5Lusa f NA
## # 1313 R_2tbf8FyKp1Dg0wV f NA
## # 2211 R_3PZvgQSzbXD8PG5 f NA
## # 2256 R_3QXfRHzrQr2VUE1 m NA
## # 2414 R_6sO4a1z8iDHY1kV <NA> 3.5## Contrasts set to contr.sum for the following variables: gender7 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 gender 2, 3168 0.16 25.09 *** .016 <.001
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 18 Visualize Results
afex_plot(aov_model, x = "gender")
9 Run Posthoc Tests (One-Way)
emmeans(aov_model, specs="gender", adjust="tukey")## Note: adjust = "tukey" was changed to "sidak"
## because "tukey" is only appropriate for one set of pairwise comparisons## gender emmean SE df lower.CL upper.CL
## f 3.294 0.008359 3168 3.274 3.314
## m 3.180 0.014334 3168 3.146 3.215
## nb 3.359 0.054859 3168 3.228 3.490
##
## Confidence level used: 0.95
## Conf-level adjustment: sidak method for 3 estimatespairs(emmeans(aov_model, specs="gender", adjust="tukey"))## contrast estimate SE df t.ratio p.value
## f - m 0.1141 0.0166 3168 6.878 <.0001
## f - nb -0.0648 0.0555 3168 -1.169 0.4721
## m - nb -0.1790 0.0567 3168 -3.157 0.0046
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## P value adjustment: tukey method for comparing a family of 3 estimates10 Write Up Results
10.1 One-Way ANOVA
To test our hypothesis that there would be a significant effect of gender on stress, we used a one-way ANOVA. Our data was unbalanced, with many more women participating in our survey (n = 2326) than men (n = 791) or non-binary participants (n = 54). This significantly reduces the power of our test and increases the chances of a Type II error. We also identified our highest outliers but did no removing since they looked like they were giving us no issues. An insignificant Levene’s test (p = .66) also indicates that our data does not violate the assumption of homogeneity of variance.
We found a significant effect of gender, F(2,3168) = 25.09, p < .001, ηp2 = .016 (large effect size; Cohen, 1988). Posthoc tests using Tukey’s HSD revealed that women reported more stress than men but less stress than non-binary participants, while non-binary participants reported the highest amount of stress overall (see Figure 1 for a comparison).
References
Cohen J. (1988). Statistical Power Analysis for the Behavioral Sciences. New York, NY: Routledge Academic.
Cohen, S, Kamarck, T and Mermelstein, R 1983 A global measure of perceived stress. Journal of Health and Social Behavior, 24: 385–396. DOI: https://doi.org/10.2307/2136404