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Advanced Statistics and 'R' - lecture - up to week 5

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These are the notes taken during the Continuing Statistics and “R” lectures. The course is taught at Utrecht University.

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Uploaded on
November 16, 2024
File latest updated on
January 14, 2025
Number of pages
40
Written in
2024/2025
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Class notes
Professor(s)
Erika tsingosi & yann hautier
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LECTURE 1 – WEEK 1: about this course + R and RStudio VSR

SEMESTER 1 | ERIKA TSINGOSI + YANN HAUTIER




ABOUT THIS COURSE


●​ learning goals
○​ expand statistics toolbox
○​ reason about appropriate experimental approaches
and statistical tools
○​ critically evaluate analyses and outputs
○​ learn the basics of data science
○​ master the tools for creating a reproducible analysis
in R
●​ final grade must be ≥ 5.5
○​ attend all computer sessions ●​ ?lm or help(lm) gives you help on the lm function
○​ complete weekly quizzes ●​ helpful sources
○​ complete all 4 hand-in assignments (30%) ○​ http://tryr.codeschool.com/
○​ pass the exam with a grade ≥ 5.5 (70%) ○​ http://www.cookbook-r.com/
○​ https://thecrashcourse.com/courses/what-is%20stat
istics-crash-course-statistics-1/
R AND RSTUDIO
●​ outlier has a huge impact on linear regression

●​ statistics are done in R not RStudio; Rstudio is the tool
○​ RStudio is an IDE for R
●​ you have to annotate your script using #
●​ R automatically creates a code when you click on Import
Dataset which you need to paste in the script and save
●​ library() #get a list of all installed packages
●​ install.packages("ggplot2") #to install a package
●​ library(‘’ggplot2’’) #to load a package
○​ no need to install a package again after it has been
installed, but it’s important to load it again
●​ hand in assignments need to be in pdf




●​ ggplot2 = grammar of graphics
○​ https://ggplot2.tidyverse.org/
○​ http://www.cookbook-r.com/Graphs/




1

, LECTURE 2 – WEEK 1: fundamentals of statistics VSR

SEMESTER 1 | ERIKA TSINGOSI + YANN HAUTIER


○​ n – 1 is used because you might get outliers by chance
FUNDAMENTALS OF STATISTICS when you take a sample
⎯​ sample measurements are on average closer to their
own mean than to the true mean of the population;
SAMPLING
subtracting by 1 can correct for that bias when the
sample size is small
●​ flowchart of a study ○​ Ȳ is a random variable
○​ execution; while you're collecting data, you should already
make plots to see if the data makes sense




●​ to find the distribution of Ȳ we sample multiple times
○​ when you add the different samples, you get the sampling
distribution of the sample mean Ȳ
○​ sampling distribution of Ȳ is a t-distribution
⎯​ t-distribution has a lower peak and fatter tails than the
normal distribution
●​ statistics quantifies uncertainty; statistics is about making sense
of the variation (in samples)
○​ descriptive statistics quantify
⎯​ location or central tendency of data; mean, median
⎯​ spread of the data; range, standard deviation
○​ comparative statistics
⎯​ compare different groups
⎯​ based on location and spread
⎯​ How likely is the sample compatible with our
expectation?
●​ population distribution; ideal value we’d know if we’d have
perfect knowledge of measured individuals (almost always
impossible to measure)
○​ most common measures for location and spread for a
population distribution are mean (μ) and standard
deviation (σ)
⎯​ μ: sum of each individual measurement divided by the ○​ mu hat: mean of the sampling distribution of Ȳ
total number of measurements which is an estimate for the population mean (μ)
⎯​ σ: you square each measurement subtracted from the ⎯​ you sum the sample means and divide it by the
mean → sum the squares → divide it by the total
number of samples
number of measurements → take square root;
○​ σȲ = standard deviation of the population / square
standard deviation is the square root of the variance
⎯​ population μ and σ are constant (they are not random root of the sample size
and don’t change, because the population is always ○​ we usually don’t have the population standard
the same) deviation σ → that's why we estimate the spread of
Ȳ (standard error of the mean) with the sample
standard deviation s
⎯​ the estimate is the standard error of the mean =
sample standard deviation / square root of the
sample size

●​ sample distribution; random subset of the population
○​ sample mean (Ȳ) and sample standard deviation (s)


2

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