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
## 
## Use magrittr pipe '%>%' to chain several operations:
##              mtcars %>%
##                  let(mpg_hp = mpg/hp) %>%
##                  take(mean(mpg_hp), by = am)
## 
## 
## Attaching package: 'maditr'
## The following object is masked from 'package:base':
## 
##     sort_by
## 
## 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':
## 
##     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 more than 2 levels) OR a two-way/factorial ANOVA (at least two IVs). You will need to specify your hypothesis and customize your code based on the choice you make. We will run both versions of the test in the lab for illustrative purposes.

One-Way: We predict that there will be a significant effect of gender on people’s narcissistic personality inventory.

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':    2132 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" ...
##  $ gender      : chr  "f" "m" "m" "f" ...
##  $ moa_maturity: num  3.67 3.33 3.67 3 3.67 ...
##  $ belong      : num  2.8 4.2 3.6 4 3.4 4.2 3.9 3.6 2.9 2.5 ...
##  $ efficacy    : num  3.4 3.4 2.2 2.8 3 2.4 2.3 3 3 3.7 ...
##  $ npi         : num  0.6923 0.1538 0.0769 0.0769 0.7692 ...
##  $ 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$CATVARIABLE <- as.factor(d$CATVARIABLE) 
d$gender <- as.factor(d$gender)
d$row_id <- as.factor(d$row_id) 

# we're going to recode our race variable into two groups: poc and white
# in doing so, we are creating a new variable "poc" that has 2 levels
d <- subset(d, gender != "nb")

table(d$gender, useNA = "always")
## 
##    f    m   nb <NA> 
## 1562  539    0    0
d$gender <- droplevels(d$gender) # use droplevels() to drop the empty factor

table(d$gender, useNA = "always")
## 
##    f    m <NA> 
## 1562  539    0
table(d$gender)
## 
##    f    m 
## 1562  539
d$gender <- as.factor(d$gender)

# check that all our categorical variables of interest are now factors
str(d)
## 'data.frame':    2101 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" ...
##  $ gender      : Factor w/ 2 levels "f","m": 1 2 2 1 2 1 1 1 1 1 ...
##  $ moa_maturity: num  3.67 3.33 3.67 3 3.67 ...
##  $ belong      : num  2.8 4.2 3.6 4 3.4 4.2 3.9 3.6 2.9 2.5 ...
##  $ efficacy    : num  3.4 3.4 2.2 2.8 3 2.4 2.3 3 3 3.7 ...
##  $ npi         : num  0.6923 0.1538 0.0769 0.0769 0.7692 ...
##  $ row_id      : Factor w/ 2132 levels "1","2","3","4",..: 1 2 3 4 5 6 7 8 9 10 ...
# check our DV skew and kurtosis
describe(d$npi)
##    vars    n mean  sd median trimmed  mad min max range skew kurtosis   se
## X1    1 2101 0.27 0.3   0.15    0.23 0.23   0   1     1 0.99    -0.57 0.01
# we'll use the describeBy() command to view our DV's skew and kurtosis across our IVs' levels
describeBy(d$npi, group = d$gender)
## 
##  Descriptive statistics by group 
## group: f
##    vars    n mean  sd median trimmed  mad min max range skew kurtosis   se
## X1    1 1562 0.25 0.3   0.15    0.21 0.23   0   1     1  1.1    -0.32 0.01
## ------------------------------------------------------------ 
## group: m
##    vars   n mean   sd median trimmed  mad min max range skew kurtosis   se
## X1    1 539 0.32 0.32   0.15    0.29 0.23   0   1     1 0.71    -1.08 0.01
# also use histograms to examine your continuous variable
hist(d$npi)

# and cross_cases() to examine your categorical variables' cell count
cross_cases(d, gender)
 #Total 
 gender 
   f  1562
   m  539
   #Total cases  2101 
# 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 equal number of cases and there should be no empty cells. Cells with low numbers decrease 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$gender)
## 
##    f    m 
## 1562  539
# our small number of participants owning rabbits 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 d_tw

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(npi~gender, data = d)
## Levene's Test for Homogeneity of Variance (center = median)
##         Df F value    Pr(>F)    
## group    1  13.319 0.0002692 ***
##       2099                      
## ---
## 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(npi ~ gender, 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)

5.1.3.3 Check for outliers (Two-Way)

5.2 Issues with My Data

The DV was not normally distributed across the IV

All levels of the IV are not equal, there are almost 3 times the amount of female participants than male participants.

Levene’s test was significant. We are ignoring this and continuing with the analysis anyway for this class.

We identified 3 outliers but ultimately determined that the outliers weren’t going to have a significant impact on the results of the ANOVA.

[UPDATE this section in your HW.]

6 Run an ANOVA

# One-Way
aov_model <- aov_ez(data = d,
                    id = "row_id",
                    between = c("gender"),
                    dv = "npi",
                    anova_table = list(es = "pes"))
## Contrasts set to contr.sum for the following variables: gender

7 View Output

nice(aov_model)
## Anova Table (Type 3 tests)
## 
## Response: npi
##   Effect      df  MSE         F  pes p.value
## 1 gender 1, 2098 0.09 18.51 *** .009   <.001
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1

ANOVA Effect Size cutoffs from Cohen (1988): * η2 < 0.01 indicates a trivial effect * η2 >= 0.01 indicates a small effect * η2 >= 0.06 indicates a medium effect * η2 >= 0.14 indicates a large effect

8 Visualize Results

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

# NOTE: for the Two-Way, you will need to decide which plot version makes the most sense based on your data / rationale when you make the nice Figure 2 at the end

9 Run Posthoc Tests (One-Way)

Only run posthocs IF the ANOVA test is significant! E.g., only run the posthoc tests on pet type if there is a main effect for pet type

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       0.255 0.00764 2098    0.238    0.272
##  m       0.320 0.01300 2098    0.291    0.349
## 
## Confidence level used: 0.95 
## Conf-level adjustment: sidak method for 2 estimates
pairs(emmeans(aov_model, specs="gender", adjust="tukey"))
##  contrast estimate     SE   df t.ratio p.value
##  f - m     -0.0649 0.0151 2098  -4.302  <.0001

10 Run Posthoc Tests (Two-Way)

Only run posthocs IF the ANOVA test is significant! E.g., only run the posthoc tests on pet type if there is a main effect for pet type.

11 Write Up Results

11.1 One-Way ANOVA

To test our hypothesis that there would be a significant effect of type of gender on narcissitic personality inventory, we used a one-way ANOVA. Our data was unbalanced, with many more females (n = 1562) than males(n = 539). This significantly reduces the power of our test and increases the chances of a Type II error. We had 3 outliers but did not remove any as we determined they would not have a significant impact on the results of the ANOVA. A significant Levene’s test (p = .0002) 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(1, 2099) = 18.50, p < .001, ηp2 = .009 (trivial effect size; Cohen, 1988). Posthoc tests using Sidak’s adjustment revealed that male participants (M = 0.320, SE = .013) reported more narcissitic personality than female participants (M = 0.255, SE = .007).

11.2 Two-Way ANOVA

References

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