#### Institut de Physique et Chimie des Matériaux de Strasbourg

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A blog for physicists or biologists. Mainly for experimentalists interested in Statistics. R scripts detailed and explained.

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wilfried.grangeu-paris.fr

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# Statistical Power

Posted 2020-10-30 by Wilfried. Post 8 of 8.
PowerHypothesis Testing

What is Statiscal Power? Why should I mention it when comparing means of 2 samples?

We have previously performed some 2-sample t-tests. When the p-value was smaller than 0.05, we have concluded that the 2 samples originate from 2 populations with equal means. Obviously the probability to conclude that 2 samples (originating from populations with different means) have equal means depends on the sample size, the actual difference in means and the type-I error. That is what we will investigate here.

Let us define some parameters:

delta<-0.5 # difference in means
sd<-1.5 # standard deviation in populations
mu1<-20 # mean of 1st population
mu2<-mu1+delta # mean of 2nd population
n<-40 # number (n) of elements in each sample


# t-tests and Confidence Intervals

Posted 2020-10-25 by Wilfried. Post 7 of 8.
CIHypothesis Testing

Calculating 0.84 confidence intervals and performing a two-sample t-test

As usual, we check for some packages.

if (!require(gridExtra)) install.packages('gridExtra')

# ANOVA (ANalysis Of VAriance) Part II

Posted 2020-10-20 by Wilfried. Post 6 of 8.
ANOVAHypothesis Testing

P i m p my ANOVA Graph. Display FDR values for multiple comparisons

As usual, we check for some packages

# Check for Packages
if (!require(ggsignif)) install.packages('ggsignif')

# ANOVA (ANalysis Of VAriance) Part I

Posted 2020-10-13 by Wilfried. Post 5 of 8.
ANOVAHypothesis Testing

A step by step guide to perform a single-factor ANOVA

Family-Wise Error Rate (FWER)

Let's first have a look at the code below:

n<-2:20
m<-factorial(n)/(factorial(n-2)*factorial(2))
p<- 1- (1-0.05)^m
plot(n,p, main='Probability to observe at least 1 false discovery', xlab='Number of samples')
grid()

# Non-Linear Fitting (lots of points)

Posted 2020-10-09 by Wilfried. Post 4 of 8.
FittingChi^2

Non-linear fitting with R (lots of points, with error bars). I also discuss how some parameters can give statistical information regarding the quality of the fit

For this example, I use ggplot2 and so you need to enter:

if (!require(ggplot2)) install.packages('ggplot2')

# Fitting multiple data at once

Posted 2020-10-08 by Wilfried. Post 3 of 8.
BeginnerFitting

Here, I demonstrate how to fit multiple data at once using an easy script

For this example, I use ggplot2 and so you need to enter:

if (!require(ggplot2)) install.packages('ggplot2')

# Non-Linear Fitting

Posted 2020-10-07 by Wilfried. Post 2 of 8.
FittingChi^2

Non-linear fitting with R (few points, with error bars). I also discuss how some parameters can give statistical information regarding the quality of the fit

As an example of non-linear fitting, I will perform a Michaelis Menten fit on some synthetic data. I am using 3 vectors, which represent the Substrate concentration (S), the rate of product formation (v) as well as the error on v (dv).

# data (use c to create a vector and combine elements of identical types)
v<-c(0.004507692,0.004192308,0.00355384,0.002576923,0.001661538,0.001064286)
S<-c(3.6000,1.8000,0.9000,0.4800,0.2250,0.1125)
dv<-c(0.00012, 0.00008,  0.00012, 0.00010, 0.00007, 0.00005)

# Simple Linear Regression

Posted 2020-10-06 by Wilfried. Post 1 of 8.
BeginnerFitting

How to make a very simple linear fit with R (few points, no error bars)

myX<-1:10
myY<-jitter(1:10)
adjust<-lm(myY ~ myX)  # Use adjust<-lm(myY ~ 0 + myX) to force the intercept at 0
plot(myX,myY,abline(adjust))