How to Perform
One-Way ANOVA
Test in R

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What is the One-Way ANOVA Test?

One-way ANOVA is a parametric statistical technique applied when we have one continuous dependent variable (e.g. level of anxiety, stress, etc.) and one categorical independent variable with three or more groups (e.g. level of education, marital status, etc.). This method examines the effect of one independent categorical variable on one quantitative dependent variable.

When Should a One-Way ANOVA be Used?

The One-Way ANOVA is used when you have three or more separate groups of individuals or cases in an among-participants design. It is used when you want to evaluate whether differences among 3 or more group means are statistically significant.

Why do we need ANOVA, when we already have the t-test as a way to compare group means?

Suppose you have 5 groups. You could assess the differences among the 5 means by doing all possible t-tests (group 1 vs 2, 1 vs 3, 2 vs 3, etc.). However, this would require a large number of tests (10 t-tests in this example), and that would be tedious to calculate. Doing a large number of significance tests also increases the risk of obtaining at least one Type I error (decision to reject the null hypothesis when it is true).

An Example Of One-Way ANOVA

For example, if we are examining the effect of the level of education (a categorical variable with three groups: High School, Bachelor’s degree, and Master’s Degree) on the level of anxiety at work (a quantitative variable that has a range of 1 to 10), then we will perform a one-way ANOVA to determine the effect of level education to the level of anxiety.

Therefore, we test the following hypotheses:

Null hypothesis: There is no significant effect of education (High School, Bachelor’s degree, Master’s Degree) on anxiety level.

Alternative hypothesis: There is a significant effect of education (High School, Bachelor’s degree, Master’s Degree) on anxiety levels.

R function to Compute One-Way ANOVA

The code to run a One-Way ANOVA using R is as follows:

aov (DV~ IV, var.equal=TRUE, data = dataframe)
TukeyHSD (#model)

DV: dependent variable

IV: Independent variable

model: Results of the One-way ANOVA model that we obtained for the first function

Running One-Way ANOVA in Rstudio

In this section, we will show you how to run the one-way ANOVA using the r studio program and how to interpret the test results after we obtain the result of the test. In the first part, we present the r program code and function for the one-way ANOVA test. Next, you will see the outputs as a result of running the r codes. In the last section, you can find the interpretation of the One-Way ANOVA in APA format.

# LOAD DATA
library(readxl)
Data <- read_excel(“Data.xlsx“)
# VIEW DATA
View(Data)
# NAME VARIABLES
data <- Data
education <- data$education
anxiety <- data$anxiety
# SHOW LEVELS OF CATEGORICAL VARIABLE
levels(education)

# SHOW MEANS AND STANDARD DEVIATIONS OF DEPENDENT VARIABLE BY CATEGORICAL VARIABLE
library(dplyr)
group_by(data, education) %>% summarise(count = n(), mean = mean(anxiety, na.rm = TRUE), sd = sd(stress, na.rm = TRUE))

# PERFORM ONE-WAY ANOVA
res.aov <- aov(anxiety ~ education, data = data)
summary(res.aov)

# PERFORM POST HOC TEST

TukeyHSD(res.aov)

> group_by(data, education) %>% summarise(count = n(), mean = mean(anxiety, na.rm = TRUE), sd = sd(stress, na.rm = TRUE))

## # A tibble: 3 × 4
##   education         count  mean    sd
##   <chr>             <int> <dbl> <dbl>
## 1 Bachelor's Degree    33  5.58  2.69
## 2 High school          33  5.82  2.79
## 3 Master's Degree      33  5.39  2.90

> res.aov <- aov(anxiety ~ education, data = data)
> summary(res.aov)

##             Df Sum Sq Mean Sq F value Pr(>F)
## education    2    3.0   1.495   0.191  0.826
## Residuals   96  750.8   7.821

> TukeyHSD(res.aov)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = anxiety ~ education, data = data)
## 
## $education
##                                         diff       lwr      upr     p adj
## High school-Bachelor's Degree      0.2424242 -1.396603 1.881452 0.9339920
## Master's Degree-Bachelor's Degree -0.1818182 -1.820845 1.457209 0.9623009
## Master's Degree-High school       -0.4242424 -2.063270 1.214785 0.8116300

Reporting One-Way ANOVA in R

One-way ANOVA was conducted to determine the effect of education level (High School, Bachelor’s Degree, Master’s Degree) on anxiety level at work for a sample of 99 employees. The results indicate a non-significant effect of education level on anxiety level at work, F(2, 96) = 0.191, p = 0.826. We, therefore, fail to reject the null hypothesis that there is no significant effect of education (High School, Bachelor’s degree, Master’s Degree) on anxiety level. The mean anxiety level for employees who completed High school is 5.58 (M = 5.58; SD = 2.69), for employees who have Bachelor’s Degree is 5.82 (M = 5.82; SD = 2.79), and for employees who have Master’s Degree is 5.39 (M = 5.39; SD = 2.90)

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How to Perform One-Way ANOVA Test in R