Group Project
2024-04-17
Step 1: Examine Data
Create a table that indicates if we have “balanced” ANOVA
Each cell contains the same number of participants across our factors.
tbl_count_project <- table(Race_Ethnicity,Employment)
tbl_count_project## Employment
## Race_Ethnicity Employed_FT Employed_PT Self_Employed Unemployed
## American_Indian_Alaskan 5 5 5 5
## Asian 5 5 5 5
## Black_AA 5 5 5 5
## Hispanic_Latino 5 5 5 5
## Multi-Racial 5 5 5 5
## Nat_Hawaiian_PI 5 5 5 5
## White 5 5 5 5We can see in the output that there are 5 individuals in each possible cell, which means we DO have a balanced design and can run a standard Two-Way ANOVA.
Look at the proportion of individuals in each cell.
tbl_percent_project <- round(prop.table(tbl_count_project), digits=2)
tbl_percent_project## Employment
## Race_Ethnicity Employed_FT Employed_PT Self_Employed Unemployed
## American_Indian_Alaskan 0.04 0.04 0.04 0.04
## Asian 0.04 0.04 0.04 0.04
## Black_AA 0.04 0.04 0.04 0.04
## Hispanic_Latino 0.04 0.04 0.04 0.04
## Multi-Racial 0.04 0.04 0.04 0.04
## Nat_Hawaiian_PI 0.04 0.04 0.04 0.04
## White 0.04 0.04 0.04 0.04Add the sums for each factor level
tbl_cross_project <- table(Race_Ethnicity,Employment)
addmargins(tbl_cross_project)## Employment
## Race_Ethnicity Employed_FT Employed_PT Self_Employed Unemployed Sum
## American_Indian_Alaskan 5 5 5 5 20
## Asian 5 5 5 5 20
## Black_AA 5 5 5 5 20
## Hispanic_Latino 5 5 5 5 20
## Multi-Racial 5 5 5 5 20
## Nat_Hawaiian_PI 5 5 5 5 20
## White 5 5 5 5 20
## Sum 35 35 35 35 140Display summed table in Bar Chart
Examine variablity across factor levels using box/scatter plots
Mean comparison model for race_ethnicity
Scatter plot graph with the means and standard error bars.
Mean comparison model for employment
Scatter plot graph with the means and standard error bars.
Step 2: Running the 2-way ANOVA
project_2way <- aov(ASQ ~ Race_Ethnicity + Employment + Race_Ethnicity:Employment, data = project_data)
summary(project_2way)## Df Sum Sq Mean Sq F value Pr(>F)
## Race_Ethnicity 6 274591 45765 20.607 4.22e-16 ***
## Employment 3 196250 65417 29.456 4.37e-14 ***
## Race_Ethnicity:Employment 18 4606 256 0.115 1
## Residuals 111 246513 2221
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 1 observation deleted due to missingnessStep 3: Getting Descriptive Statistics
The following includes descriptive statistics needed for reporting results and/or creating a means table.
Race_Ethnicity Descriptives
## Race_Ethnicity count mean sd
## 1 American_Indian_Alaskan 20 99.7000 52.41344
## 2 Asian 20 175.5500 62.59097
## 3 Black_AA 20 94.3500 46.73697
## 4 Hispanic_Latino 20 152.1500 64.10622
## 5 Multi-Racial 20 105.1579 52.47990
## 6 Nat_Hawaiian_PI 20 109.6000 50.90900
## 7 White 20 221.2000 73.38980Employment Descriptives
## Employment count mean sd
## 1 Employed_FT 35 126.0000 60.45885
## 2 Employed_PT 35 114.3429 61.67893
## 3 Self_Employed 35 106.8857 64.63507
## 4 Unemployed 35 200.6286 62.87854Means Table
## Race_Ethnicity Employment count mean sd
## 1 American_Indian_Alaskan Employed_FT 5 89.6 44.76941
## 2 American_Indian_Alaskan Employed_PT 5 80.8 45.72417
## 3 American_Indian_Alaskan Self_Employed 5 71.2 50.72672
## 4 American_Indian_Alaskan Unemployed 5 157.2 25.66515
## 5 Asian Employed_FT 5 165.0 41.83898
## 6 Asian Employed_PT 5 148.2 59.12022
## 7 Asian Self_Employed 5 141.0 55.21322
## 8 Asian Unemployed 5 248.0 34.45287
## 9 Black_AA Employed_FT 5 85.0 38.43826
## 10 Black_AA Employed_PT 5 79.4 39.81583
## 11 Black_AA Self_Employed 5 68.4 45.03110
## 12 Black_AA Unemployed 5 144.6 29.97165
## 13 Hispanic_Latino Employed_FT 5 139.2 43.85430
## 14 Hispanic_Latino Employed_PT 5 126.8 57.63419
## 15 Hispanic_Latino Self_Employed 5 119.4 57.33934
## 16 Hispanic_Latino Unemployed 5 223.2 48.20996
## 17 Multi-Racial Employed_FT 5 88.5 40.68169
## 18 Multi-Racial Employed_PT 5 85.0 38.62642
## 19 Multi-Racial Self_Employed 5 78.0 40.36707
## 20 Multi-Racial Unemployed 5 165.8 41.55358
## 21 Nat_Hawaiian_PI Employed_FT 5 98.4 41.79474
## 22 Nat_Hawaiian_PI Employed_PT 5 90.0 43.84062
## 23 Nat_Hawaiian_PI Self_Employed 5 83.6 47.93537
## 24 Nat_Hawaiian_PI Unemployed 5 166.4 28.79757
## 25 White Employed_FT 5 208.8 56.63656
## 26 White Employed_PT 5 190.2 69.71513
## 27 White Self_Employed 5 186.6 76.73526
## 28 White Unemployed 5 299.2 33.65561Grand Mean for ANOVA model
describe(ASQ)## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 139 137.04 72.33 131 132.98 74.13 5 330 325 0.47 -0.17 6.13Step 4: Partial Eta-Squared
Calculate the partial eta-squared values that align to the various effects within our GLM 2-way ANOVA model.
Ensure we are specifying the correct model
m_2way_project <- aov(ASQ ~ Race_Ethnicity + Employment + Race_Ethnicity:Employment, data = project_data)Run the partial eta-squared estimates for our 2-way model effects.
eta_squared(car::Anova(m_2way_project, partial = TRUE, type = 2))## # Effect Size for ANOVA (Type II)
##
## Parameter | Eta2 (partial) | 95% CI
## ---------------------------------------------------------
## Race_Ethnicity | 0.53 | [0.41, 1.00]
## Employment | 0.44 | [0.33, 1.00]
## Race_Ethnicity:Employment | 0.02 | [0.00, 1.00]
##
## - One-sided CIs: upper bound fixed at [1.00].We can see from these results that interaction Race_Ethnicity:Employment has a small effect size (.02). Employment and Race_ethnicity have large effect sizes: (.44) and (.53) respectively.
Testing Assumptions
Homogeneity of Variance
leveneTest(ASQ ~ Race_Ethnicity*Employment, data = project_data)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 27 0.4086 0.9955
## 111The assumption is maintained here since the p-value of Levene’s test was > .05.