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':
## 
##     %+%, alpha

library(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: '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 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':
## 
##     lmer

library(emmeans) # for posthoc tests

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/eammi2_finalREAL.csv", header=T)

# for the HW, you may or may not need to use the code below this comment
# check to see if you have a variable called 'X' or 'ResponseId' in your data
names(d)

## [1] "gender"       "marriage5"    "support"      "belong"       "moa_role"    
## [6] "moa_maturity"

# if you do have 'X' or 'ResponseId' (aka your ID variable) then DELETE THE CODE BELOW
# if you don't have those variables, keep the code and run it
d$row_id <- 1:nrow(d)

3 State Your Hypothesis

Note: You can chose to run either a one-way ANOVA (a single IV with more than 3 levels) or a two-way/factorial ANOVA (at least two IVs) for the homework. You will need to specify your hypothesis and customize your code based on the choice you make. I will run both versions of the test here for illustrative purposes.

Two-Way: We predict that there will significant effects of gender identity (gender) and parent’s marriage status (marriage5) on percieved social support (support). We also predict that gender and parent’s marriage status will interact and that women with parents who are anything except currently married will report significantly lower levels of percieved social support.

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':    3075 obs. of  7 variables:
##  $ gender      : chr  "f" "m" "m" "f" ...
##  $ 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" ...
##  $ support     : num  6 6.75 5.17 5.58 6 ...
##  $ belong      : num  2.8 4.2 3.6 4 3.4 4.2 3.9 3.6 2.9 2.5 ...
##  $ moa_role    : num  3 2.67 2.5 2 2.67 ...
##  $ moa_maturity: num  3.67 3.33 3.67 3 3.67 ...
##  $ row_id      : int  1 2 3 4 5 6 7 8 9 10 ...

# make our categorical variables factors
#recoding our variables as factors overriding current one withg 
d$row_id <- as.factor(d$row_id) #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$marriage5 <- as.factor(d$marriage5)

# check your categorical variables
#table(d$VARIABLE)
table(d$gender)

## 
##    f    m   nb 
## 2252  770   53

table(d$marriage, useNA = "always")

## 
##             are currently divorced from one another 
##                                                 712 
##                are currently married to one another 
##                                                2084 
##       never married each other and are not together 
##                                                 235 
## never married each other but are currently together 
##                                                  44 
##                                                <NA> 
##                                                   0

# also use histograms to examine your continuous variable
#hist(YOUR DV)
hist(d$support)

5 Check Your Assumptions

5.1 ANOVA Assumptions

Assumptions checked below:

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 else…

The sampling distribution should be normal. (For a demonstration of what the sampling distribution is, go here.)

5.1.1 Check levels of IVs

# check your categorical variables and make sure they have decent cell sizes
# they should have at least 5 participants in each cell
# but larger numbers are always better
#table(IV1)
#table(IV2)
#cross_cases(d, IV1, IV2)

table(d$gender)

## 
##    f    m   nb 
## 2252  770   53

table(d$marriage5)

## 
##             are currently divorced from one another 
##                                                 712 
##                are currently married to one another 
##                                                2084 
##       never married each other and are not together 
##                                                 235 
## never married each other but are currently together 
##                                                  44

cross_cases(d, gender, marriage5)

	marriage5
	are currently divorced from one another	are currently married to one another	never married each other and are not together	never married each other but are currently together
gender
f	529	1518	173	32
m	170	532	56	12
nb	13	34	6
#Total cases	712	2084	235	44

# we're going to recode our race/ethnicity variable into two groups: poc and white
# you may or may not need to combine and/or drop groups for the HW
table(d$marriage5)

## 
##             are currently divorced from one another 
##                                                 712 
##                are currently married to one another 
##                                                2084 
##       never married each other and are not together 
##                                                 235 
## never married each other but are currently together 
##                                                  44

d$marriage_rc[d$marriage5 == "are currently divorced from one another"] <- "not married"
d$marriage_rc[d$marriage5 == "never married each other and are not together"] <- "not married"
d$marriage_rc[d$marriage5 == "never married each other but are currently together"] <- "not married"
d$marriage_rc[d$marriage5 == "prefer_not"] <- NA
d$marriage_rc[d$marriage5 == "are currently married to one another"] <- "married"
table(d$marriage_rc)

## 
##     married not married 
##        2084         991

d$marriage_rc <- as.factor(d$marriage_rc)

# our number of small nb participants 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 d2
d2 <- subset(d, gender == "m" | gender == "f")
d2$gender <- droplevels(d2$gender)

# to double-check any changes we made
#table(IV1)
#table(IV2)
#cross_cases(d2, IV1, IV2)
table(d2$gender)

## 
##    f    m 
## 2252  770

table(d2$marriage_rc)

## 
##     married not married 
##        2050         972

cross_cases(d2, gender, marriage_rc)

	marriage_rc
	married	not married
gender
f	1518	734
m	532	238
#Total cases	2050	972

# you can use the describe() command on an entire dataframe (d) or just on a single variable
#describe(YOUR DV)
describe(d$support)

##    vars    n mean   sd median trimmed  mad min max range  skew kurtosis   se
## X1    1 3075 5.54 1.13   5.75    5.66 0.99   0   7     7 -1.11     1.48 0.02

# we'll use the describeBy() command to view skew and kurtosis across our IVs
#describeBy(YOUR DV, group = YOUR IV 1)
describeBy(d2$support, group = d2$gender)

## 
##  Descriptive statistics by group 
## group: f
##    vars    n mean   sd median trimmed  mad min max range  skew kurtosis   se
## X1    1 2252  5.6 1.11   5.83    5.72 0.99   0   7     7 -1.18     1.74 0.02
## ------------------------------------------------------------ 
## group: m
##    vars   n mean   sd median trimmed  mad min max range  skew kurtosis   se
## X1    1 770 5.41 1.16   5.58    5.52 1.11   1   7     6 -0.98     1.06 0.04

#doing the two way anova
describeBy(d2$support, group = d2$gender)

## 
##  Descriptive statistics by group 
## group: f
##    vars    n mean   sd median trimmed  mad min max range  skew kurtosis   se
## X1    1 2252  5.6 1.11   5.83    5.72 0.99   0   7     7 -1.18     1.74 0.02
## ------------------------------------------------------------ 
## group: m
##    vars   n mean   sd median trimmed  mad min max range  skew kurtosis   se
## X1    1 770 5.41 1.16   5.58    5.52 1.11   1   7     6 -0.98     1.06 0.04

#also do across levels of second IV which is race 
#for the two anova 
describeBy(d2$support, group = d2$marriage_rc)

## 
##  Descriptive statistics by group 
## group: married
##    vars    n mean  sd median trimmed  mad min max range  skew kurtosis   se
## X1    1 2050 5.62 1.1   5.83    5.75 0.99   0   7     7 -1.22     1.92 0.02
## ------------------------------------------------------------ 
## group: not married
##    vars   n mean   sd median trimmed  mad min max range  skew kurtosis   se
## X1    1 972  5.4 1.16   5.58    5.51 1.11   1   7     6 -0.96     0.94 0.04

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
#leveneTest(DV~IV1, data = d)
#leveneTest(DV~IV1*IV2, data = d2)


leveneTest(support~gender*marriage_rc, data = d2)

## Levene's Test for Homogeneity of Variance (center = median)
##         Df F value  Pr(>F)  
## group    3  2.3846 0.06737 .
##       3018                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#this one came out to not significant !

5.1.3 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, where y is our DV, x1 is our first IV and x2 is our second IV
reg_model2 <- lm(support~gender*marriage_rc, data = d2) #for two-way

5.1.3.2 Check for outliers (Two-Way)

# Cook's distance
plot(reg_model2, 4)

# Residuals vs Leverage
plot(reg_model2, 5)

5.2 Issues with My Data

We are way below the 0.5 cutoff for the cook’s distance test.

leveneTest came out as not significant so that’s all good.

In the residual vs leverage the red line hugged the dotted line well.

Our cell sizes are very unbalanced especially for gender. A small sample size for one of the levels of our variable limits our power and increases our Type II error rate.

6 Run an ANOVA

#two way anova
aov_model2 <- aov_ez(data = d2,
                    id = "row_id",
                    between = c("gender","marriage_rc"),
                    dv = "support",
                    anova_table = list(es = "pes"))

## Contrasts set to contr.sum for the following variables: gender, marriage_rc

7 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_model2)

## Anova Table (Type 3 tests)
## 
## Response: support
##               Effect      df  MSE         F   pes p.value
## 1             gender 1, 3018 1.25 15.45 ***  .005   <.001
## 2        marriage_rc 1, 3018 1.25 22.34 ***  .007   <.001
## 3 gender:marriage_rc 1, 3018 1.25      0.24 <.001    .627
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1

8 Visualize Results

#need to use post hoc test to figure out whats significantly diff
#for the two way anova
#afex_plot(aov_model2, x = "IV1", trace = "IV2")
#swap order of variable 
#afex_plot(aov_model2, x = "IV2", trace = "IV1")
afex_plot(aov_model2, x = "gender", trace = "marriage_rc")

afex_plot(aov_model2, x = "marriage_rc", trace = "gender")

9 Run Posthoc Tests (Two-Way)

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

#emmeans(aov_model2, specs="IV1", adjust="tukey")
#pairs(emmeans(aov_model2, specs="IV1", adjust="tukey"))
#pairs sees if comparison is signif, get p value 
emmeans(aov_model2, specs="gender", adjust="tukey")

## NOTE: Results may be misleading due to involvement in interactions

## 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        5.56 0.0251 3018     5.50     5.61
##  m        5.36 0.0436 3018     5.26     5.46
## 
## Results are averaged over the levels of: marriage_rc 
## Confidence level used: 0.95 
## Conf-level adjustment: sidak method for 2 estimates

pairs(emmeans(aov_model2, specs="gender", adjust="tukey"))

## NOTE: Results may be misleading due to involvement in interactions

##  contrast estimate     SE   df t.ratio p.value
##  f - m       0.198 0.0503 3018   3.931  0.0001
## 
## Results are averaged over the levels of: marriage_rc

#emmeans(aov_model2, specs="IV2", adjust="tukey")
#pairs(emmeans(aov_model2, specs="IV2", adjust="tukey"))
emmeans(aov_model2, specs="marriage_rc", adjust="tukey")

## NOTE: Results may be misleading due to involvement in interactions
## Note: adjust = "tukey" was changed to "sidak"
## because "tukey" is only appropriate for one set of pairwise comparisons

##  marriage_rc emmean     SE   df lower.CL upper.CL
##  married       5.58 0.0282 3018     5.52     5.64
##  not married   5.34 0.0417 3018     5.25     5.43
## 
## Results are averaged over the levels of: gender 
## Confidence level used: 0.95 
## Conf-level adjustment: sidak method for 2 estimates

pairs(emmeans(aov_model2, specs="marriage_rc", adjust="tukey"))

## NOTE: Results may be misleading due to involvement in interactions

##  contrast              estimate     SE   df t.ratio p.value
##  married - not married    0.238 0.0503 3018   4.727  <.0001
## 
## Results are averaged over the levels of: gender

#emmeans(aov_model2, specs="IV1", by="IV2", adjust="sidak")
#pairs(emmeans(aov_model2, specs="IV2", by="IV1", adjust="sidak"))
#looking at interaction 
emmeans(aov_model2, specs="gender", by="marriage_rc", adjust="sidak")

## marriage_rc = married:
##  gender emmean     SE   df lower.CL upper.CL
##  f        5.66 0.0287 3018     5.60     5.73
##  m        5.49 0.0485 3018     5.38     5.60
## 
## marriage_rc = not married:
##  gender emmean     SE   df lower.CL upper.CL
##  f        5.45 0.0413 3018     5.36     5.54
##  m        5.23 0.0725 3018     5.07     5.39
## 
## Confidence level used: 0.95 
## Conf-level adjustment: sidak method for 2 estimates

pairs(emmeans(aov_model2, specs="marriage_rc", by="gender", adjust="sidak"))

## gender = f:
##  contrast              estimate     SE   df t.ratio p.value
##  married - not married    0.214 0.0503 3018   4.246  <.0001
## 
## gender = m:
##  contrast              estimate     SE   df t.ratio p.value
##  married - not married    0.262 0.0872 3018   3.008  0.0026

emmeans(aov_model2, specs="marriage_rc", by="gender", adjust="sidak")

## gender = f:
##  marriage_rc emmean     SE   df lower.CL upper.CL
##  married       5.66 0.0287 3018     5.60     5.73
##  not married   5.45 0.0413 3018     5.36     5.54
## 
## gender = m:
##  marriage_rc emmean     SE   df lower.CL upper.CL
##  married       5.49 0.0485 3018     5.38     5.60
##  not married   5.23 0.0725 3018     5.07     5.39
## 
## Confidence level used: 0.95 
## Conf-level adjustment: sidak method for 2 estimates

pairs(emmeans(aov_model2, specs="marriage_rc", by="gender", adjust="sidak"))

## gender = f:
##  contrast              estimate     SE   df t.ratio p.value
##  married - not married    0.214 0.0503 3018   4.246  <.0001
## 
## gender = m:
##  contrast              estimate     SE   df t.ratio p.value
##  married - not married    0.262 0.0872 3018   3.008  0.0026

10 Write Up Results

```

10.1 Two-Way ANOVA

#summerize hypothesis To test our hypothesis that gender and parent’s marriage status would impact support and would interact significantly, we used a two-way/factorial ANOVA. Our data met most of the assumptions of the test, although our data was unbalanced, with many more women participating in our survey (n = 1004) than men (n = 195). There were no noticable outliers on the residuals vs leverage plots.

As predicted, we found a significant main effect for gender, REPORT STUFF FROM ANOVA- F(1, 3018) = 15.45, p < .001, η_p² .01 (small effect size; Cohen, 1988). As predicted, women reported significantly more support than men. As predicted, people with married parents reported significantly more support than people with not married parents- F(1, 3018) = 22.34, p < .001, η_p² .01 (small effect size; Cohen, 1988)

Lastly, we did not find a significant interaction between gender and parent’s marriage (p=.627).

References

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

Running a One-Way or Two-Way/Factorial ANOVA

Nora Barth

2024-04-18