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Mastering Scientific Computing with R

Employ professional quantitative methods to answer scientific questions with a powerful open source data analysis environment

Book Description
With this book, you will learn not just about R, but how to use R to answer conceptual, scientific, and experimental questions.

Beginning with an overview of fundamental R concepts, you'll learn how R can be used to achieve the most commonly needed scientific data analysis tasks: testing for statistically significant differences between groups and model relationships in data. You will delve into linear algebra and matrix operations with an emphasis not on the R syntax, but on how these operations can be used to address common computational or analytical needs. This book also covers the application of matrix operations for the purpose of finding structure in high-dimensional data using the principal component, exploratory factor, and confirmatory factor analysis in addition to structural equation modeling. You will also master methods for simulation and learn about an advanced analytical method.

Book Details
Publisher:        Packt Publishing
By:        Paul Gerrard, Radia M. Johnson
ISBN:        978-1-78355-525-3
Year:        2015
Pages:        432
Language:        English
File size:        5.3 MB
File format:        PDF
Download:   

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关键词：Scientific Mastering computing Comput Master conceptual scientific overview concepts testing

1. Proportion tests
   
2. 
   
3. Sometimes we want to evaluate proportions instead of individual measurements. Several statistical tests are used to determine whether the proportion observed in your dataset is significantly different from some theoretical value. Two useful statistical tests used in hypothesis testing for proportions are the traditional Z-test and the binomial exact test. Say we wanted to test that 50 percent of patients have to wait more than 4 hours to see a doctor. We can record the waiting period for 11 patients and store that information in a numerical vector as follows:
   
4. 
   
5. > waiting.period <- c(3, 5, 4, 5.5, 3.5, 2.5, 3, 5, 4.5, 3, 3.5)
   
6. Next, we can count the number of patients who waited for more than 4 hours by creating a table using the following commands:
   
7. 
   
8. > above4.hrs <- ifelse(waiting.period > 4, "yes", "no")
   
9. > above4hs.table <- table(above4.hrs)
   
10. > above4hs.table
    
11. above4.hrs
    
12. no yes
    
13.   7   4
    
14. Now, if we can assume the waiting period to see a doctor is indeed 50 percent, then we can use a Z-test to this hypothesis using the prop.test() function:
    
15. 
    
16. > prop.test(4, n=11, p=0.5, alternative="two.sided", correct=FALSE)
    
17.   1-sample proportions test without continuity correction
    
18. data:  4 out of 11, null probability 0.5
    
19. X-squared = 0.8182, df = 1, p-value = 0.3657
    
20. alternative hypothesis: true p is not equal to 0.5
    
21. 95 percent confidence interval:
    
22. 0.1516647 0.6461988
    
23. sample estimates:
    
24.         p
    
25. 0.3636364

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1. Two sample hypothesis tests
   
2. 
   
3. So far, we have covered how to use statistical tests for hypothesis testing on a single sample distribution. However, these statistical tests can also be applied to compare two sample distributions. For example, we could test whether the mean of the probeA sample distribution was significantly different from the probeB sample distribution. If we can assume that the error of both samples are normally distributed, then we can use a t-test to compare the mean of both samples by entering t.test(probeA, probeB), as follows:
   
4. 
   
5. > t.test(probeA, probeB)
   
6.   Welch Two Sample t-test
   
7. data:  probeA and probeB
   
8. t = -35.8398, df = 58.92, p-value < 2.2e-16
   
9. alternative hypothesis: true difference in means is not equal to 0
   
10. 95 percent confidence interval:
    
11. -3.486162 -3.117460
    
12. sample estimates:
    
13. mean of x mean of y
    
14. 4.773866  8.075677
    
15. If the errors are not normally distributed for these samples, we can run the Wilcoxon rank-sum test, as follows:
    
16. 
    
17. > wilcox.test(probeA, probeB)
    
18.   Wilcoxon rank sum test
    
19. data:  probeA and probeB
    
20. W = 0, p-value < 2.2e-16
    
21. alternative hypothesis: true location shift is not equal to 0

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ding!!!!!!!!!!!

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good book

不错的书