Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Content-how the chapters fit together
- 1 A brief introduction to R
- 2 Styles of data analysis
- 3 Statistical models
- 4 A review of inference concepts
- 5 Regression with a single predictor
- 6 Multiple linear regression
- 7 Exploiting the linear model framework
- 8 Generalized linear models and survival analysis
- 9 Time series models
- 10 Multi-level models and repeated measures
- 11 Tree-based classification and regression
- 12 Multivariate data exploration and discrimination
- 13 Regression on principal component or discriminant scores
- 14 The R system – additional topics
- 15 Graphs in R
- Epilogue
- References
- Index of R symbols and functions
- Index of terms
- Index of authors
- Plate Section
4 - A review of inference concepts
Published online by Cambridge University Press: 05 October 2013
- Frontmatter
- Dedication
- Contents
- Preface
- Content-how the chapters fit together
- 1 A brief introduction to R
- 2 Styles of data analysis
- 3 Statistical models
- 4 A review of inference concepts
- 5 Regression with a single predictor
- 6 Multiple linear regression
- 7 Exploiting the linear model framework
- 8 Generalized linear models and survival analysis
- 9 Time series models
- 10 Multi-level models and repeated measures
- 11 Tree-based classification and regression
- 12 Multivariate data exploration and discrimination
- 13 Regression on principal component or discriminant scores
- 14 The R system – additional topics
- 15 Graphs in R
- Epilogue
- References
- Index of R symbols and functions
- Index of terms
- Index of authors
- Plate Section
Summary
A random sample is a set of values drawn independently from a larger population. A (uniform) random sample has the characteristic that all members of the population have an equal chance of being drawn. In the previous chapter, we discussed the implications of drawing repeated random samples from a normally distributed population, where the probability that a value lies in a given interval is governed by the normal density. This chapter will expand upon that discussion by using the idea of a sampling distribution, with its associated standard error, to assess estimation accuracy. Confidence intervals and tests of hypotheses offer a formal basis for inference, based on the sampling distribution. We will comment on weaknesses in the hypothesis testing framework.
Basic concepts of estimation
This section will introduce material that is fundamental to inference.
Population parameters and sample statistics
Parameters, such as the mean (μ) or standard deviation (σ), numerically summarize various aspects of a population. Such parameters are usually unknown and are estimated using statistics calculated using a random sample taken from the population. The sample mean is an example of a statistic, and it is used to estimate the population mean.
Other commonly used statistics are the proportion, standard deviation, variance, median, the quartiles, the slope of a regression line, and the correlation coefficient. Each may be used as an estimate of the corresponding population parameter.
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- Data Analysis and Graphics Using RAn Example-Based Approach, pp. 102 - 141Publisher: Cambridge University PressPrint publication year: 2010