1 Loading Libraries

#install.packages("afex")
#install.packages("emmeans")
#install.packages("ggbeeswarm")

library(psych) # for the describe() command
library(ggplot2) # to visualize our results
## 
## Attaching package: 'ggplot2'
## The following objects are masked from 'package:psych':
## 
##     %+%, alpha
library(expss) # for the cross_cases() command
## Loading required package: maditr
## 
## To aggregate all non-grouping columns: take_all(mtcars, mean, by = am)
## 
## Attaching package: 'expss'
## The following object is masked from 'package:ggplot2':
## 
##     vars
library(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':
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##     logit
library(afex) # to run the ANOVA 
## 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':
## 
##     lmer
library(ggbeeswarm) # to run plot results
library(emmeans) # for posthoc tests
## 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

Note: For your HW, you will choose to run EITHER a one-way ANOVA (a single IV with at least 3 levels) OR a two-way ANOVA (two IVs, each with 2 levels). You will need to specify your hypothesis and customize your code based on the choice you make (i.e., delete code that is not relevant). We will run BOTH versions in the lab for illustrative purposes.

One-Way Hypothesis: We predict that there will be a significant difference in perceived social support based on age group (between ages 18 and 25, between ages 26 and 35, over age 45).

IV = age group DV = perceived social support

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':    2163 obs. of  8 variables:
##  $ ResponseID: chr  "R_BJN3bQqi1zUMid3" "R_2TGbiBXmAtxywsD" "R_12G7bIqN2wB2N65" "R_39pldNoon8CePfP" ...
##  $ age       : chr  "1 between 18 and 25" "1 between 18 and 25" "1 between 18 and 25" "1 between 18 and 25" ...
##  $ edu       : chr  "2 Currently in college" "5 Completed Bachelors Degree" "2 Currently in college" "2 Currently in college" ...
##  $ swb       : num  4.33 4.17 1.83 5.17 3.67 ...
##  $ support   : num  6 6.75 5.17 5.58 6 ...
##  $ efficacy  : num  3.4 3.4 2.2 2.8 3 2.4 2.3 3 3 3.7 ...
##  $ 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 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$age <- as.factor(d$age) 
d$row_id <- as.factor(d$row_id)

#Dropping Level

d <- subset(d, age != "3 between 36 and 45")
table(d$age, useNA = "always")
## 
## 1 between 18 and 25 2 between 26 and 35 3 between 36 and 45           4 over 45 
##                1991                 116                   0                  18 
##                <NA> 
##                   0
d$age <- droplevels(d$age)
table(d$age, useNA = "always")
## 
## 1 between 18 and 25 2 between 26 and 35           4 over 45                <NA> 
##                1991                 116                  18                   0
# For your HW, you can choose to combine levels like we did here, OR you can simply choose which existing levels you want to compare/test -- to do this option, you'll need to copy/paste the "drop levels" code from the t-test lab/HW and delete the recoding code line above.


# check that all our categorical variables of interest are now factors
str(d)
## 'data.frame':    2125 obs. of  8 variables:
##  $ ResponseID: chr  "R_BJN3bQqi1zUMid3" "R_2TGbiBXmAtxywsD" "R_12G7bIqN2wB2N65" "R_39pldNoon8CePfP" ...
##  $ age       : Factor w/ 3 levels "1 between 18 and 25",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ edu       : chr  "2 Currently in college" "5 Completed Bachelors Degree" "2 Currently in college" "2 Currently in college" ...
##  $ swb       : num  4.33 4.17 1.83 5.17 3.67 ...
##  $ support   : num  6 6.75 5.17 5.58 6 ...
##  $ efficacy  : num  3.4 3.4 2.2 2.8 3 2.4 2.3 3 3 3.7 ...
##  $ stress    : num  3.3 3.3 4 3.2 3.1 3.5 3.3 2.4 2.9 2.7 ...
##  $ row_id    : Factor w/ 2163 levels "1","2","3","4",..: 1 2 3 4 5 6 7 8 9 10 ...
# check our DV skew and kurtosis
describe(d$support)
##    vars    n mean   sd median trimmed  mad min max range  skew kurtosis   se
## X1    1 2125 5.53 1.14   5.75    5.65 0.99   0   7     7 -1.09     1.32 0.02
# we'll use the describeBy() command to view our DV's skew and kurtosis across our IVs' levels
describeBy(d$support, group = d$age)
## 
##  Descriptive statistics by group 
## group: 1 between 18 and 25
##    vars    n mean   sd median trimmed  mad min max range skew kurtosis   se
## X1    1 1991 5.54 1.13   5.75    5.66 0.99   0   7     7 -1.1     1.38 0.03
## ------------------------------------------------------------ 
## group: 2 between 26 and 35
##    vars   n mean   sd median trimmed mad  min max range  skew kurtosis   se
## X1    1 116 5.38 1.27   5.67     5.5 1.3 1.08   7  5.92 -0.83     0.36 0.12
## ------------------------------------------------------------ 
## group: 4 over 45
##    vars  n mean   sd median trimmed  mad min max range  skew kurtosis   se
## X1    1 18 5.35 1.53   5.38    5.48 1.61 1.5   7   5.5 -1.01     0.18 0.36
# also use histograms to examine your continuous variable
hist(d$support)

# and cross_cases() to examine your categorical variables' cell count
cross_cases(d, age)
 #Total 
 age 
   1 between 18 and 25  1991
   2 between 26 and 35  116
   4 over 45  18
   #Total cases  2125 
# REMEMBER your test's level of POWER is determined by your SMALLEST subsample

5 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 an equal number of cases and there should be no empty cells. Cells with low numbers decreases 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$age)
## 
## 1 between 18 and 25 2 between 26 and 35           4 over 45 
##                1991                 116                  18
# REMEMBER your test's level of POWER is determined by your SMALLEST subsample

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

# One-Way
leveneTest(support~age, data = d)
## Levene's Test for Homogeneity of Variance (center = median)
##         Df F value  Pr(>F)  
## group    2  2.5945 0.07492 .
##       2122                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

5.1.3 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:
 #d <- subset(d, row_id!=c(1108))

# 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(support~age, data = d) #for One-Way

5.1.3.2 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 unbalanced between the age group levels. 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 was not significant for our three-level age group variable with the One-Way ANOVA which is ideal.

We did not identify any outliers that surpassed the cutoff for Cook’s Distance or any that were pulling significantly on the Residuals vs Leverage plot, so none were removed.

6 Run an ANOVA

# One-Way
aov_model <- aov_ez(data = d,
                    id = "ResponseID",
                    between = c("age"),
                    dv = "support",
                    anova_table = list(es = "pes"))
## Contrasts set to contr.sum for the following variables: age
# FOR your HW, the id variable in this code will be "X" for the ARC data and "ResponseID" for the EAMMi2 data

7 View Output

nice(aov_model)
## Anova Table (Type 3 tests)
## 
## Response: support
##   Effect      df  MSE    F  pes p.value
## 1    age 2, 2122 1.30 1.26 .001    .283
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1

ANOVA Effect Size [partial eta-squared] cutoffs from Cohen (1988): * η^2 < 0.01 indicates a trivial effect * η^2 >= 0.01 indicates a small effect * η^2 >= 0.06 indicates a medium effect * η^2 >= 0.14 indicates a large effect

8 Visualize Results

# One-Way
afex_plot(aov_model, x = "age")

9 Run Posthoc Tests (One-Way)

ONLY run posthoc IF the ANOVA test is SIGNIFICANT!

#emmeans(aov_model, specs="age", adjust="sidak")
#pairs(emmeans(aov_model, specs="age", adjust="sidak"))

10 Write Up Results

10.1 One-Way ANOVA

To test our hypothesis that there will be a significant difference in perceived social support based on age group (between ages 18 and 25, between ages 26 and 35, over age 45), we used a one-way ANOVA. Our data was unbalanced, with many more people who were between ages 18 and 25 participating in our survey (n = 1991) than who were between ages 26 and 35 (n = 116) or who were over age 45 (n = 18). This significantly reduces the power of our test and increases the chances of a Type II error. No outliers were removed, and our Levene’s test was not significant (p = 0.075), indicating that our data does not violate the assumption of homogeneity of variance.

We did not find a significant effect of age group, F(2, 2122) = 1.26, p = 0.283, ηp2 = .001 (trivial effect size; Cohen, 1988). Posthoc tests were not conducted because the ANOVA test was not significant (see Figure 1).

References

Cohen J. (1988). Statistical Power Analysis for the Behavioral Sciences. New York, NY: Routledge Academic.