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R

April 6, 2023

Technical Team

Yan Luo, Arthur Ang

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Exercise

Lesson

Assignment

Agenda

Download R

Data Types

ggplot2

ANOVA

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Lesson

01

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Download R

Install R: https://cran.r-project.org/

Install RStudio: https://posit.co/download/rstudio-desktop/

Apps@Stern: https://apps.stern.nyu.edu/

TutorialsPoint: https://www.tutorialspoint.com/execute_r_online.php

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Hello World

Terminal: Rscript fileName.R

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Data Types

02

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Data Types - Vector Objects

Vectors

Lists

Matrices

Arrays

Factors

Data Frames

Data Type	Example	Syntax
Logical	TRUE, FLASE	v <- TRUE
Numeric	1, 3.14, -3/4	v <- 1
Integer	-2L, 0L, 2L	v <- -2L
Complex	3+2i	v <- 3.2i
Character	“ActSoc”, ‘b’, ‘3.14’	v <- “ActSoc”
Raw	“ActSoc” 41 63 74 53 6f 63	v <- charToRaw(‘ActSoc”)

class(v) to check data type, typeof(v) gives "logical", "integer", "double", "complex", "character", "raw" and "list", "NULL", "closure" (function), "special" and "builtin" (basic functions and operators)

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Data Types - Vectors

Vectors

Lists

Matrices

Arrays

Factors

Data Frames

# Create a vector.

apple <- c('red','green',"yellow")

print(apple)

# Get the class of the vector.

print(class(apple))

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Data Types - Lists

Vectors

Lists

Matrices

Arrays

Factors

Data Frames

# Create a list.

list1 <- list(c(2,5,3),21.3,sin)

# Print the list.

print(list1)

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Data Types - Matrices

Vectors

Lists

Matrices

Arrays

Factors

Data Frames

# Create a matrix.

M = matrix( c('a','a','b','c','b','a'), nrow = 2, ncol = 3, byrow = TRUE)

print(M)

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Data Types - Arrays

Vectors

Lists

Matrices

Arrays

Factors

Data Frames

# Create an array with one dimension with values ranging from 1 to 24.

thisarray <- c(1:24)

thisarray

# Create an array with more than one dimension.

multiarray <- array(thisarray, dim = c(4, 3, 2))

multiarray

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Data Types - Factors

Vectors

Lists

Matrices

Arrays

Factors

Data Frames

# Create a vector.

apple_colors <- c('green','green','yellow','red','red','red','green')

# Create a factor object.

factor_apple <- factor(apple_colors)

# Print the factor.

print(factor_apple)

print(nlevels(factor_apple))

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Data Types - Data Frames

Vectors

Lists

Matrices

Arrays

Factors

Data Frames

# Create the data frame.

BMI <- data.frame(

gender = c("Male", "Male","Female"),

height = c(152, 171.5, 165),

weight = c(81,93, 78),

Age = c(42,38,26)

)

print(BMI)

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ggplot2

03

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ggplot2

ggplot2 is an open-source data visualization package for the statistical programming language R
http://r-statistics.co/Top50-Ggplot2-Visualizations-MasterList-R-Code.html

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ANOVA

04

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ANOVA

Analysis of Variance

A statistical test to determine whether 2 or more population means are different

Assumptions

Check that your observations are independent.
Sample sizes:

In case of small samples, test the normality of residuals:

If normality is assumed, test the homogeneity of the variances:

If variances are equal, use ANOVA
If variances are not equal, use the Welch ANOVA

If normality is not assumed, use the Kruskal-Wallis test

In case of large samples normality is assumed, so test the homogeneity of the variances:

If variances are equal, use ANOVA
If variances are not equal, use the Welch ANOVA

Follow-Along: https ://statsandr.com/blog/anova-in-r/

homogeneity of the variances: an assumption of the independent samples t-test and ANOVA stating that all comparison groups have the same variance

Kruskal-Wallis test: is a non-parametric method for testing whether samples originate from the same distribution

�Welch’s ANOVA compares two means to see if they are equal. It is an alternative to the Classic ANOVA and can be used even if your data violates the assumption of homogeneity of variances

One way ANOVA is a hypothesis test, used to test the equality of three or more population means simultaneously using variance.

One Independent Variable

Three or more levels of one factor.

Need not to be same in each group.

Need to satisfy only two principles.

Two way Anova:

Two way ANOVA is a statistical technique wherein, the interaction between factors, influencing variable can be studied.

Two Independent Variable

Effect of multiple level of two factors.

Need to be equal in each group.

All three principles needs to be satisfied.

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One-Way Anova Results

F-statistic: The F-statistic measures the ratio of the between-group variability to the within-group variability. A larger F-statistic indicates that there is more variability between the groups than within the groups, which suggests that there is a significant difference between at least two of the groups being compared.
Degrees of freedom: The degrees of freedom represent the number of independent pieces of information used to estimate the variance in the data. In a one-way ANOVA, there are two degrees of freedom: one for the between-group variability and one for the within-group variability.
p-value: The p-value represents the probability of obtaining a result as extreme as the one observed, assuming that there is no difference between the groups being compared. A small p-value (typically less than 0.05) indicates that there is strong evidence to reject the null hypothesis of no difference between the groups and conclude that there is a significant difference.
Mean square: The mean square represents the sum of squares divided by the degrees of freedom. There are two mean squares in a one-way ANOVA: one for the between-group variability and one for the within-group variability.
Sum of squares: The sum of squares represents the total variability in the data. In a one-way ANOVA, there are two sums of squares: one for the between-group variability and one for the within-group variability.

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Post-Hoc Tests

A post hoc test is used only after we find a statistically significant result and need to determine where our differences truly came from.
Post-hoc tests are a family of statistical tests so there are several of them. The most common ones are:

Tukey HSD, used to compare all groups to each other (so all possible comparisons of 2 groups).
Dunnett, used to make comparisons with a reference group. For example, consider 2 treatment groups and one control group. If you only want to compare the 2 treatment groups with respect to the control group, and you do not want to compare the 2 treatment groups to each other, the Dunnett’s test is preferred.
Bonferroni correction if one has a set of planned comparisons to do.