By Rafael A. Irizarry, Michael I. Love

ISBN-10: 1315367009

ISBN-13: 9781315367002

ISBN-10: 1498775675

ISBN-13: 9781498775670

ISBN-10: 1498775683

ISBN-13: 9781498775687

This publication covers numerous of the statistical innovations and information analytic abilities had to reach data-driven existence technological know-how learn. The authors continue from fairly uncomplicated suggestions on the topic of computed p-values to complex subject matters on the topic of studying highthroughput facts. They comprise the R code that plays this research and attach the traces of code to the statistical and mathematical recommendations defined

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**Sample text**

Thus we can compute p-values using the function pnorm. The t-distribution The CLT relies on large samples, what we refer to as asymptotic results. When the CLT does not apply, there is another option that does not rely on asymptotic results. When the original population from which a random variable, say Y , is sampled is normally distributed with mean 0, then we can calculate the distribution of: √ Y¯ N sY This is the ratio of two random variables so it is not necessarily normal. The fact that the denominator can be small by chance increases the probability of observing large values.

8 Populations, Samples and Estimates Now that we have introduced the idea of a random variable, a null distribution, and a p-value, we are ready to describe the mathematical theory that permits us to compute p-values in practice. We will also learn about confidence intervals and power calculations. Population parameters A first step in statistical inference is to understand what population you are interested in. In the mouse weight example, we have two populations: female mice on control diets and female mice on high fat diets, with weight being the outcome of interest.

We will use the replicate to observe 10,000 realizations of this random variable. Set the seed at 1, generate these 10,000 averages. Make a histogram and qq-plot of these 10,000 numbers against the normal distribution. We can see that, as predicted by the CLT, the distribution of the random variable is very well approximated by the normal distribution. y <- filter(dat, Sex=="M" & Diet=="chow") %>% select(Bodyweight) %>% unlist avgs <- replicate(10000, mean( sample(y, 25))) mypar(1,2) hist(avgs) qqnorm(avgs) qqline(avgs) What is the average of the distribution of the sample average?

### Data analysis for the life sciences with R by Rafael A. Irizarry, Michael I. Love

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