In A-Farina/pl462: Data package and Templates for PL462

knitr::opts_chunk$set(echo = TRUE, 
                      include = TRUE, 
                      message = FALSE, 
                      warning = FALSE)
# Loading required packages
if (!require("pacman")) install.packages("pacman")
pacman::p_load(tidyverse, ggpubr, rstatix, palmerpenguins)
pacman::p_load_gh("A-Farina/pl462")

Today we will discuss the Analysis of Variance (ANOVA) in its simplest form.

What is a One-Way ANOVA?

What are the statistical assumptions of an ANOVA?

What is a One-Way Repeated Measures ANOVA?

Analysis Framework

1. Load the Data

2. Understand the data (Distribution, Variability, Outliers)
  * Summary Statistics
  * Data Visualization
  * Outliers

3. Check Assumptions
  * Normality of Residuals or DV by group
  * Homogeneity (Equality) of Variance or Sphericity
  * Independent Samples

4. Conduct the Statistical Test
  * Run ANOVA

5. Conduct Post-Hoc Analyses as needed
  * Pairwise *t*-tests
  * One-Way ANOVAs

One-Way ANOVA (Between-Subjects)

1. Load the Data

# Loading the Data
penguins <- palmerpenguins::penguins # Loads the dataset called 'penguins' from the palmerpengins package and assigns it the name "penguins"
?penguins # Loads the help menu giving some descriptive information for the dataset
glimpse(penguins) # Gives a quick view of the structure of the dataset.

Research Question: We are interested in determining if different species of penguins have different flipper lengths.

What is the DV?

What is/are the IV(s)? How many levels do they have?

2. Understand the data (Distribution, Variability, Outliers)

• Summary Statistics

penguins %>% 
  group_by(species) %>% 
  get_summary_stats(flipper_length_mm)

What are your observations given the descriptive statistics?

• Data Visualization

# Boxplot
penguins %>% 
  ggplot() + 
  aes(x = species, y = flipper_length_mm) + 
  geom_boxplot() +
  geom_jitter(alpha = 0.2, width = .1)

# Continuous Density Plot
penguins %>% ggplot() + 
  aes(x = flipper_length_mm, fill = species) + 
  geom_density() + 
  facet_grid(species ~ .)

What are your observations (distribution, variability) given these data visualizations?

• Outliers

penguins %>% 
  group_by(species) %>% 
  rstatix::identify_outliers(flipper_length_mm) # Produces a table of outliers and extreme cases.

Are there any outliers in these data?

3. Check Assumptions

• Normality of Residuals or DV by group

a. Analyzing the ANOVA model residuals. This approach is generally easier to do and helpful if there are many groups. This is the approach we will take.

# Assumption testing- Normality of Residuals- QQ Plot
model <- lm(flipper_length_mm ~ species, data = penguins)
ggqqplot(residuals(model)) # Graphically depicts the correlation of these data and a normal distribution.

# Shapiro-Wilkes Test
shapiro_test(residuals(model)) # Statistically determines normality of these data.

b. Checking Normality for each group separately. This might be helpful if you have only a few groups.

# Assumption testing- Normality DV by groups

ggqqplot(penguins, "flipper_length_mm", facet.by = "species") # Graphically depicts the correlation of these data and a normal distribution.

# Shapiro-Wilkes Test
penguins %>%
  group_by(species) %>%
  shapiro_test(flipper_length_mm) # Statistically determines normality of these data. 

Note: may be overly sensitive if data is more than 50. In that case, the qq plot is preferred.

Are these data normally distributed?

If the data are not normally distributed, a Kruskal-Wallis test is a non-parametric alternative to the One-Way ANOVA.

• Homogeneity (Equality) of Variance

# Residuals vs Fitted Plot
plot(model, 1) # Graphically compares the residuals to fitted values (mean of each group)

# Assumption testing- Homogeneity of Variance
penguins %>% levene_test(flipper_length_mm ~ species) # Statistically shows homogeneity of variance.

If the data do not have homogeneity of variance, a welch one way ANOVA test can be performed (welch_anova_test())

Do these data meet the assumption of homogeneity of variance?

• Independent Samples

Are these independent samples?

4. Conduct the Statistical Test

• Run ANOVA

# One-Way ANOVA- Tests of Between-Subject with equal variance
penguins %>% 
  anova_test(flipper_length_mm ~ species)

Interpret the results

5. Conduct Post-Hoc Analyses as needed

• Pairwise t-tests

penguins %>% 
  pairwise_t_test(flipper_length_mm ~ species)

Interpret the results

---

One-Way Repeated-Measures ANOVA (Within-Subjects)

1. Load the Data

# Loading the Data
grit <- pl462::grit # Loads the dataset called 'grit' from the pl462 package and assigns it the name "penguins"
?grit # Loads the help menu giving some descriptive information for the dataset
glimpse(grit) # Gives a quick view of the structure of the dataset.

Research Question: We are interested in determining whether grit changes based on when the measure is taken (matriculation, freshmen year, sophmore year)

What is the DV?

What is/are the IV(s)? How many levels do they have?

2. Understand the data (Distribution, Variability, Outliers)

• Summary Statistics

grit %>% 
  group_by(class) %>% 
  get_summary_stats(grit)

What are your observations given the descriptive statistics?

• Data Visualization

# Boxplot
grit %>% 
  ggplot() + 
  aes(x = class, y = grit) + 
  geom_boxplot() +
  geom_jitter(alpha = 0.2, width = .1)

# Continuous Density Plot
grit %>% ggplot() + 
  aes(x = grit, fill = class) + 
  geom_density() + 
  facet_grid(class ~ .)

What are your observations (distribution, variability) given these data visualizations?

• Outliers

grit %>% 
  group_by(class) %>% 
  rstatix::identify_outliers(grit) # Produces a table of outliers and extreme cases.

Are there any outliers in these data?

3. Check Assumptions

• Normality of Residuals or DV by group

a. Analyzing the ANOVA model residuals. This approach is generally easier to do and helpful if there are many groups. This is the approach we will take.

# Assumption testing- Normality of Residuals- QQ Plot
model <- lm(grit ~ class, data = grit)
ggqqplot(residuals(model)) # Graphically depicts the correlation of these data and a normal distribution.

# Shapiro-Wilkes Test
shapiro_test(residuals(model)) # Statistically determines normality of these data.

b. Checking Normality for each group separately. This might be helpful if you have only a few groups.

# Assumption testing- Normality DV by groups

ggqqplot(grit, "grit", facet.by = "class") # Graphically depicts the correlation of these data and a normal distribution.

# Shapiro-Wilkes Test
grit %>%
  group_by(class) %>%
  shapiro_test(grit) # Statistically determines normality of these data. 

Note: may be overly sensitive if data is more than 50. In that case, the qq plot is preferred.

Are these data normally distributed?

If the data are not normally distributed, a Kruskal-Wallis test is a non-parametric alternative to the One-Way ANOVA (kruskal_test()).

• Sphericity variance of the differences between groups should be equal. This can be checked using the Mauchly’s test of sphericity. This is automatically reported and adjusted with anova_test()

4. Conduct the Statistical Test

• Run ANOVA

# One-Way Repeated Measures ANOVA- Tests of Within-Subject.
grit %>% 
  anova_test(wid = id, dv = grit, within = class)

Interpret the results

5. Conduct Post-Hoc Analyses as needed

• Pairwise t-tests

grit %>% 
  pairwise_t_test(grit ~ class,
                  paired = TRUE)

Interpret the results

A-Farina/pl462 documentation built on May 9, 2022, 1:52 p.m.