[ -- Internship Proposals -- ]

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

wilfried.grangeu-paris.fr

Associate Professor at Université de Paris

ChangepointHypothesis_Testing
t-test

Change point detection. Part I : rolling *t*-test

In a time series, change point detection tries to identify abrupt changes. Different approaches have been proposed and here I show one of them based on a simple rolling *t*-test.

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

```
rm(list = ls())
if (!require(ggplot2)) install.packages('ggplot2')
```

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PowerHypothesis_Testing
t-test

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:

```
rm(list = ls())
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
```

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Confidence_IntervalsHypothesis_Testing
t-test

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

As usual, we check for some packages.

```
rm(list = ls())
if (!require(gridExtra)) install.packages('gridExtra')
```

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ANOVAHypothesis_Testing
graphs

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

As usual, we check for some packages

```
rm(list = ls())
# Check for Packages
if (!require(ggsignif)) install.packages('ggsignif')
```

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