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 aggregate data: take(mtcars, mean_mpg = mean(mpg), by = am)

## 
## Use 'expss_output_viewer()' to display tables in the RStudio Viewer.
##  To return to the console output, use 'expss_output_default()'.

## 
## 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/tt_clean_eammi2.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

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.

One-Way: We predict that there will be a significant effect of income on subjective well-being, as measured by the subjective well-being scale (SWB-6).

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':    3143 obs. of  8 variables:
##  $ ResponseId: chr  "R_BJN3bQqi1zUMid3" "R_2TGbiBXmAtxywsD" "R_12G7bIqN2wB2N65" "R_39pldNoon8CePfP" ...
##  $ edu_rc    : chr  "Currently in college" "Completed Bachelors Degree" "Currently in college" "Currently in college" ...
##  $ income_rc : chr  "20,000 - 39,999" "20,000 - 39,999" "Rather not say" "Rather not say" ...
##  $ stress    : num  3.3 3.3 4 3.2 3.1 3.5 3.3 2.4 2.9 2.7 ...
##  $ swb       : num  4.33 4.17 1.83 5.17 3.67 ...
##  $ 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 ...
##  $ 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$edu_rc <- as.factor(d$edu_rc)
d$income_rc <- as.factor(d$income_rc)
d$row_id <- as.factor(d$row_id)

# we're going to recode our income variable into two groups: under 60,000 and over 60,000
table(d$income_rc)

## 
##   100,000 - 199,999     20,000 - 39,999 200,000 - 1 million     40,000 - 59,999 
##                 388                 360                 139                 344 
##     60,000 - 79,999     80,000 - 99,999      Over 1 million      Rather not say 
##                 298                 236                   7                 854 
##        Under 20,000 
##                 517

d$under[d$income_rc == "Under 20,000"] <-"under"
d$under[d$income_rc == "20,000 - 39,999"] <- "under"
d$under[d$income_rc == "40,000 - 59,999"] <- "under"
d$under[d$income_rc == "60,000 - 79,999"] <- "over"
d$under[d$income_rc == "80,000 - 99,999"] <- "over"
d$under[d$income_rc == "100,000 - 199,999"] <- "over"
d$under[d$income_rc == "Over 1 million"] <- "over"
d$under[d$income_rc == "Rather not say"] <- NA
table(d$under)

## 
##  over under 
##   929  1221

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

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

##    vars    n mean   sd median trimmed  mad min max range  skew kurtosis   se
## X1    1 3143 4.47 1.32   4.67    4.53 1.48   1   7     6 -0.36    -0.45 0.02

# we'll use the describeBy() command to view skew and kurtosis across our IVs
describeBy(d$swb, group = d$income_rc)

## 
##  Descriptive statistics by group 
## group: 100,000 - 199,999
##    vars   n mean   sd median trimmed  mad min max range  skew kurtosis   se
## X1    1 388 4.81 1.28      5     4.9 1.24   1   7     6 -0.63     0.07 0.06
## ------------------------------------------------------------ 
## group: 20,000 - 39,999
##    vars   n mean   sd median trimmed  mad min max range  skew kurtosis   se
## X1    1 360  4.3 1.27   4.33    4.33 1.48   1   7     6 -0.21     -0.5 0.07
## ------------------------------------------------------------ 
## group: 200,000 - 1 million
##    vars   n mean   sd median trimmed  mad min max range  skew kurtosis   se
## X1    1 139 4.72 1.39      5     4.8 1.24   1   7     6 -0.57    -0.37 0.12
## ------------------------------------------------------------ 
## group: 40,000 - 59,999
##    vars   n mean   sd median trimmed  mad min max range  skew kurtosis   se
## X1    1 344 4.42 1.35    4.5     4.5 1.48   1   7     6 -0.42    -0.42 0.07
## ------------------------------------------------------------ 
## group: 60,000 - 79,999
##    vars   n mean   sd median trimmed  mad min max range  skew kurtosis   se
## X1    1 298 4.62 1.31   4.83    4.69 1.24   1   7     6 -0.45    -0.47 0.08
## ------------------------------------------------------------ 
## group: 80,000 - 99,999
##    vars   n mean   sd median trimmed  mad  min max range  skew kurtosis   se
## X1    1 236 4.82 1.25      5     4.9 1.24 1.17   7  5.83 -0.55    -0.18 0.08
## ------------------------------------------------------------ 
## group: Over 1 million
##    vars n mean  sd median trimmed  mad  min  max range skew kurtosis   se
## X1    1 7  5.1 1.9   5.83     5.1 1.48 2.33 6.83   4.5 -0.4    -1.83 0.72
## ------------------------------------------------------------ 
## group: Rather not say
##    vars   n mean   sd median trimmed  mad min max range  skew kurtosis   se
## X1    1 854 4.39 1.28    4.5    4.43 1.48   1   7     6 -0.28    -0.53 0.04
## ------------------------------------------------------------ 
## group: Under 20,000
##    vars   n mean   sd median trimmed  mad min max range  skew kurtosis   se
## X1    1 517  4.2 1.35   4.33    4.23 1.48   1   7     6 -0.22     -0.5 0.06

describeBy(d$swb, group = d$under
           )

## 
##  Descriptive statistics by group 
## group: over
##    vars   n mean   sd median trimmed  mad min max range  skew kurtosis   se
## X1    1 929 4.75 1.29   4.83    4.83 1.24   1   7     6 -0.55    -0.19 0.04
## ------------------------------------------------------------ 
## group: under
##    vars    n mean   sd median trimmed  mad min max range  skew kurtosis   se
## X1    1 1221 4.29 1.33   4.33    4.34 1.48   1   7     6 -0.28    -0.48 0.04

# also use histograms to examine your continuous variable
hist(d$swb)

# and cross_cases() to examine your categorical variables
cross_cases(d, income_rc, swb
            )

	swb
	1	1.16666666666667	1.33333333333333	1.5	1.66666666666667	1.83333333333333	2	2.16666666666667	2.33333333333333	2.5	2.66666666666667	2.83333333333333	3	3.16666666666667	3.33333333333333	3.5	3.66666666666667	3.83333333333333	4	4.16666666666667	4.33333333333333	4.5	4.66666666666667	4.83333333333333	5	5.16666666666667	5.33333333333333	5.5	5.66666666666667	5.83333333333333	6	6.16666666666667	6.33333333333333	6.5	6.66666666666667	6.83333333333333	7
income_rc
100,000 - 199,999	3		2	2	4		1	5	3	5	5	3	7	9	14	4	10	7	15	7	17	26	17	26	24	14	22	17	16	20	28	14	11	6	8	7	9
20,000 - 39,999	1	2	2	3		5	2	7	9	9	10	9	9	9	13	7	14	16	24	20	17	16	21	18	8	18	18	15	10	9	13	6	6	6	2	4	2
200,000 - 1 million	1	1	1		1	1	1	2	1	3	2	5	2	4	4	4	2	3	2	4	4	5	5	6	9	11	9	6	3	10	5	7	4	1	4	1	5
40,000 - 59,999	3	2	2	2	5	3	8	6	1	5	4	11	4	6	14	15	10	16	11	17	13	20	11	13	13	25	18	12	15	14	15	7	7	5	3	5	3
60,000 - 79,999	1		2	1	1	3	2	6	9	1	3	4	12	9	8	2	11	9	9	11	16	8	18	13	12	19	15	18	13	16	11	8	9	6	5	1	6
80,000 - 99,999		3			1			3	2	3	5	4	3	6	5	6	6	6	12	10	6	8	13	11	9	16	10	13	15	10	15	10	7	6	4	3	5
Over 1 million									1			1										1								1				1		2
Rather not say	2	3	3	5	10	7	14	8	13	10	19	29	31	26	16	30	36	32	46	34	41	34	40	42	54	30	37	36	35	30	36	19	16	7	8	6	9
Under 20,000	6	4	6	4	5	5	6	9	12	9	16	13	10	29	16	21	16	19	21	22	34	18	24	23	27	24	17	16	20	17	10	8	10	8	1	3	8
#Total cases	17	15	18	17	27	24	34	46	51	45	64	79	78	98	90	89	105	108	140	125	148	136	149	152	156	157	146	133	127	127	133	79	70	46	35	32	47

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$income_rc)

## 
##   100,000 - 199,999     20,000 - 39,999 200,000 - 1 million     40,000 - 59,999 
##                 388                 360                 139                 344 
##     60,000 - 79,999     80,000 - 99,999      Over 1 million      Rather not say 
##                 298                 236                   7                 854 
##        Under 20,000 
##                 517

# 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, income_rc != "Over 1 million")
d2$income_rc <- droplevels(d2$income_rc)

# to double-check any changes we made
cross_cases(d2, income_rc, swb)

	swb
	1	1.16666666666667	1.33333333333333	1.5	1.66666666666667	1.83333333333333	2	2.16666666666667	2.33333333333333	2.5	2.66666666666667	2.83333333333333	3	3.16666666666667	3.33333333333333	3.5	3.66666666666667	3.83333333333333	4	4.16666666666667	4.33333333333333	4.5	4.66666666666667	4.83333333333333	5	5.16666666666667	5.33333333333333	5.5	5.66666666666667	5.83333333333333	6	6.16666666666667	6.33333333333333	6.5	6.66666666666667	6.83333333333333	7
income_rc
100,000 - 199,999	3		2	2	4		1	5	3	5	5	3	7	9	14	4	10	7	15	7	17	26	17	26	24	14	22	17	16	20	28	14	11	6	8	7	9
20,000 - 39,999	1	2	2	3		5	2	7	9	9	10	9	9	9	13	7	14	16	24	20	17	16	21	18	8	18	18	15	10	9	13	6	6	6	2	4	2
200,000 - 1 million	1	1	1		1	1	1	2	1	3	2	5	2	4	4	4	2	3	2	4	4	5	5	6	9	11	9	6	3	10	5	7	4	1	4	1	5
40,000 - 59,999	3	2	2	2	5	3	8	6	1	5	4	11	4	6	14	15	10	16	11	17	13	20	11	13	13	25	18	12	15	14	15	7	7	5	3	5	3
60,000 - 79,999	1		2	1	1	3	2	6	9	1	3	4	12	9	8	2	11	9	9	11	16	8	18	13	12	19	15	18	13	16	11	8	9	6	5	1	6
80,000 - 99,999		3			1			3	2	3	5	4	3	6	5	6	6	6	12	10	6	8	13	11	9	16	10	13	15	10	15	10	7	6	4	3	5
Rather not say	2	3	3	5	10	7	14	8	13	10	19	29	31	26	16	30	36	32	46	34	41	34	40	42	54	30	37	36	35	30	36	19	16	7	8	6	9
Under 20,000	6	4	6	4	5	5	6	9	12	9	16	13	10	29	16	21	16	19	21	22	34	18	24	23	27	24	17	16	20	17	10	8	10	8	1	3	8
#Total cases	17	15	18	17	27	24	34	46	50	45	64	78	78	98	90	89	105	108	140	125	148	135	149	152	156	157	146	133	127	126	133	79	70	45	35	30	47

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(swb~income_rc, data = d)

## Levene's Test for Homogeneity of Variance (center = median)
##         Df F value Pr(>F)
## group    8  1.0061  0.429
##       3134

5.1.3 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())

# 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)& row_id!=c(220))

# 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(swb ~ income_rc, 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)

# Cook's distance
# plot(reg_model2, 4)

# Residuals vs Leverage
# plot(reg_model2, 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 two-level income variable. We are ignoring this and continuing with the analysis anyway.

We did not remove any outliers.

6 Run an ANOVA

aov_model <- aov_ez(data = d,
                    id = "ResponseId",
                    between = c("income_rc"),
                    dv = "swb",
                    anova_table = list(es = "pes"))

## Contrasts set to contr.sum for the following variables: income_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_model)

## Anova Table (Type 3 tests)
## 
## Response: swb
##      Effect      df  MSE         F  pes p.value
## 1 income_rc 8, 3134 1.70 10.86 *** .027   <.001
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1

#nice(aov_model2)

8 Visualize Results

afex_plot(aov_model, x = "income_rc")

9 Run Posthoc Tests (One-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_model, specs="income_rc", adjust="tukey")

## Note: adjust = "tukey" was changed to "sidak"
## because "tukey" is only appropriate for one set of pairwise comparisons

##  income_rc           emmean     SE   df lower.CL upper.CL
##  100,000 - 199,999     4.81 0.0662 3134     4.63     4.99
##  20,000 - 39,999       4.30 0.0687 3134     4.11     4.49
##  200,000 - 1 million   4.72 0.1106 3134     4.41     5.03
##  40,000 - 59,999       4.42 0.0703 3134     4.23     4.62
##  60,000 - 79,999       4.62 0.0756 3134     4.41     4.83
##  80,000 - 99,999       4.82 0.0849 3134     4.59     5.06
##  Over 1 million        5.10 0.4929 3134     3.73     6.46
##  Rather not say        4.39 0.0446 3134     4.26     4.51
##  Under 20,000          4.20 0.0574 3134     4.04     4.35
## 
## Confidence level used: 0.95 
## Conf-level adjustment: sidak method for 9 estimates

pairs(emmeans(aov_model, specs="income_rc", adjust="tukey"))

##  contrast                                    estimate     SE   df t.ratio
##  (100,000 - 199,999) - (20,000 - 39,999)       0.5089 0.0954 3134   5.332
##  (100,000 - 199,999) - (200,000 - 1 million)   0.0890 0.1289 3134   0.690
##  (100,000 - 199,999) - (40,000 - 59,999)       0.3840 0.0966 3134   3.976
##  (100,000 - 199,999) - (60,000 - 79,999)       0.1882 0.1005 3134   1.873
##  (100,000 - 199,999) - (80,000 - 99,999)      -0.0122 0.1077 3134  -0.113
##  (100,000 - 199,999) - Over 1 million         -0.2868 0.4974 3134  -0.577
##  (100,000 - 199,999) - Rather not say          0.4228 0.0798 3134   5.295
##  (100,000 - 199,999) - Under 20,000            0.6131 0.0876 3134   6.998
##  (20,000 - 39,999) - (200,000 - 1 million)    -0.4199 0.1302 3134  -3.224
##  (20,000 - 39,999) - (40,000 - 59,999)        -0.1249 0.0983 3134  -1.270
##  (20,000 - 39,999) - (60,000 - 79,999)        -0.3207 0.1021 3134  -3.140
##  (20,000 - 39,999) - (80,000 - 99,999)        -0.5211 0.1092 3134  -4.770
##  (20,000 - 39,999) - Over 1 million           -0.7957 0.4977 3134  -1.599
##  (20,000 - 39,999) - Rather not say           -0.0861 0.0820 3134  -1.051
##  (20,000 - 39,999) - Under 20,000              0.1042 0.0895 3134   1.164
##  (200,000 - 1 million) - (40,000 - 59,999)     0.2950 0.1311 3134   2.251
##  (200,000 - 1 million) - (60,000 - 79,999)     0.0992 0.1340 3134   0.740
##  (200,000 - 1 million) - (80,000 - 99,999)    -0.1012 0.1394 3134  -0.726
##  (200,000 - 1 million) - Over 1 million       -0.3758 0.5052 3134  -0.744
##  (200,000 - 1 million) - Rather not say        0.3338 0.1193 3134   2.798
##  (200,000 - 1 million) - Under 20,000          0.5241 0.1246 3134   4.206
##  (40,000 - 59,999) - (60,000 - 79,999)        -0.1958 0.1032 3134  -1.897
##  (40,000 - 59,999) - (80,000 - 99,999)        -0.3962 0.1102 3134  -3.594
##  (40,000 - 59,999) - Over 1 million           -0.6708 0.4979 3134  -1.347
##  (40,000 - 59,999) - Rather not say            0.0388 0.0833 3134   0.466
##  (40,000 - 59,999) - Under 20,000              0.2291 0.0907 3134   2.524
##  (60,000 - 79,999) - (80,000 - 99,999)        -0.2004 0.1136 3134  -1.763
##  (60,000 - 79,999) - Over 1 million           -0.4750 0.4987 3134  -0.952
##  (60,000 - 79,999) - Rather not say            0.2346 0.0877 3134   2.674
##  (60,000 - 79,999) - Under 20,000              0.4249 0.0949 3134   4.479
##  (80,000 - 99,999) - Over 1 million           -0.2746 0.5002 3134  -0.549
##  (80,000 - 99,999) - Rather not say            0.4350 0.0959 3134   4.535
##  (80,000 - 99,999) - Under 20,000              0.6253 0.1025 3134   6.103
##  Over 1 million - Rather not say               0.7096 0.4950 3134   1.434
##  Over 1 million - Under 20,000                 0.8999 0.4963 3134   1.813
##  Rather not say - Under 20,000                 0.1903 0.0727 3134   2.618
##  p.value
##   <.0001
##   0.9989
##   0.0023
##   0.6325
##   1.0000
##   0.9997
##   <.0001
##   <.0001
##   0.0347
##   0.9400
##   0.0449
##   0.0001
##   0.8058
##   0.9808
##   0.9639
##   0.3730
##   0.9982
##   0.9984
##   0.9981
##   0.1161
##   0.0009
##   0.6157
##   0.0100
##   0.9169
##   0.9999
##   0.2206
##   0.7066
##   0.9898
##   0.1576
##   0.0003
##   0.9998
##   0.0002
##   <.0001
##   0.8849
##   0.6734
##   0.1793
## 
## P value adjustment: tukey method for comparing a family of 9 estimates

10 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_model, specs="gender_rc", adjust="tukey")
# pairs(emmeans(aov_model, specs="gender_rc", adjust="tukey"))
 
# emmeans(aov_model2, specs="poc", adjust="tukey")
# pairs(emmeans(aov_model2, specs="poc", adjust="tukey"))
 
# emmeans(aov_model2, specs="gender_rc", by="poc", adjust="sidak")
# pairs(emmeans(aov_model2, specs="gender_rc", by="poc", adjust="sidak"))

# emmeans(aov_model2, specs="poc", by="gender_rc", adjust="sidak")
# pairs(emmeans(aov_model2, specs="poc", by="gender_rc", adjust="sidak"))

11 Write Up Results

11.1 One-Way ANOVA

To test our hypothesis that there would be a significant effect of income on subjective well-being (swb), we used a one-way ANOVA. Our data was slightly unbalanced, with participants who make 60,000 dollars or less participating in our survey (n = 1,221) than participants who make 60,000 dollars of more (n = 1,068). This reduces the power of our test and increases the chances of a Type II error. We also identified single outlier, but did not remove it following visual analysis of a Residuals vs Leverage plot. A significant Levene’s test (p = <.001) 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 income, F(8,3,133) = 11.19, p < .001, η_p² = .028 (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 and other gender participants, while non-binary and other gender participants reported the highest amount of stress overall (see Figure 1 for a comparison).

11.2 Two-Way ANOVA

To test our hypothesis that gender and race would impact stress 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). We identified and removed a single outlier following visual analysis of a Residuals vs Leverage plot.

As predicted, we found a significant main effect for gender, F(1,1195) = 28.31, p < .001, η_p² .023 (small effect size; Cohen, 1988). As predicted, women reported significantly more stress than men. Contrary to our expectations, we did not find a significant main effect for race (p = .453).

Lastly, we found a significant interaction between gender and race (see Figure 2), F(1,1195) = 3.43, p = .064, η_p² = .003 (trivial effect size; Cohen, 1988). When comparing by race, women of color (M = 3.16, SE = .07) reported significantly more stress than men of color (M = 2.52, SE = .14; p < .001), as did white women (M = 2.93, SE = .03) compared to white men (M = 2.62, SE = .08; p < .001). When comparing by gender, women of color reported significantly more stress than white women (p = .002), while men of color and white men reported similar levels of stress (p = .546).

References

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

Running a One-Way ANOVA HW

Taylor Todd

2023-06-10