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E-raamat: Statistical Inference and Probability

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Statistical Inference and ProbabilitySuurem pilt
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An experienced author in the field of data analytics and statistics, John Macinnes has produced a straight-forward text that breaks down the complex topic of inferential statistics with accessible language and detailed examples. It covers a range of topics, including:

·       Probability and Sampling distributions

·       Inference and regression

·       Power, effect size and inverse probability

Part of The SAGE Quantitative Research Kit, this book will give you the know-how and confidence needed to succeed on your quantitative research journey.



Part of The SAGE Quantitative Research Kit, this concise text breaks down the complex topic of inferential statistics with accessible language and detailed examples. Covering a range of topics, it provides you with the know-how and confidence needed for a successful quantitative research journey.

List of Figures and Tables
xi
About the Author xv
1 The Challenge and Promise of Inference
1(20)
What Is Inference?
2(1)
Informal Inference: The Tyranny of Causal Narratives
2(2)
Cognitive Illusions
4(1)
Scientific Inference
5(1)
Statistical Inference
6(4)
Exploration and Inference: Detectives and Lawyers
10(1)
The NHST Wars
11(4)
Inference, Reproducibility and Replication
15(1)
Inference in Action: The Salk Vaccine Trial
15(2)
Inference in Action: Fertility and Development
17(1)
The World Before Statistics
18(1)
What Knowledge I Assume
19(1)
The Structure of This Book
19(2)
2 Probability, Randomness, Probability Distributions and Sampling Distributions
21(38)
What is Probability?
22(2)
Some Elementary Descriptive Statistics and Notations
24(5)
Trials and Sample Spaces
29(2)
The Law of Large Numbers
31(1)
Bernoulli Trials
32(5)
The Probability Distribution
37(3)
Bar Charts and Histograms
40(2)
Heights of Union Soldiers
42(2)
Probability Distributions and Variables
44(1)
Conditional Probability With Categorical Variables
45(5)
Conditional Probability With Continuous Variables
50(1)
Pearson's r
51(3)
Conditional Probabilities With a Continuous and Categorical Distribution
54(1)
What Have We Done?
55(1)
Appendix: Simulating Coin Flips With Excel
56(3)
3 Bernoulli, Coke and Pepsi
59(20)
A Series of 10 Trials
60(1)
Statistical Inference and Research Design
60(1)
The Null Hypothesis
61(1)
Short Run Probabilities: The Binomial Distribution
62(5)
The Sampling Distribution and p-Values
67(2)
Alpha, Significance, Confidence and Type I Errors
69(1)
Improbable Expectations, Definite Results
70(1)
Why the Double Negative and All the Bother?
71(1)
The Logic of NHST
71(2)
From Statistical Inference to Scientific Inference
73(1)
What Does Significant Mean?
73(1)
Appendix: A Famous Experiment: Milk First or Tea First?
74(5)
4 Samples and Populations
79(40)
The Difficulty of Measurement
80(1)
The Illusion of Representative Samples
81(1)
The Sampling Distribution, Samples and Populations
82(4)
Flipping the Logic: One Sample From a Distribution
86(3)
Standard Errors
89(1)
Confidence Intervals for Point Estimates
90(2)
The r-Distribution
92(1)
Examining Differences in Means and Proportions
93(2)
Calculating Standard Errors for Categorical Variables
95(4)
The Binomial Formula in Action: Stop and Search
99(2)
Chi-Square and Contingency Tables
101(8)
Chi-Square and Goodness of Fit
109(4)
Fisher's Exact Test
113(3)
Appendix: Degrees of Freedom
116(3)
5 Inference and Regression
119(34)
Introduction
120(1)
The Analysis of Variance
120(4)
The Regression Equation
124(2)
Regression as the Analysis of Unconditional and Conditional Variance
126(5)
Correlation and Regression
131(2)
Regression and ANOVA
133(1)
Multiple Regression
134(1)
Inference in Regression: The F-Statistic and Standard Errors
135(2)
An Example of Multiple OLS Regression
137(4)
What Can Go Wrong With Multiple Regression?
141(1)
Transformation
142(2)
Appendix: A Refresher on Powers and Logarithms
144(9)
Powers
144(2)
Arithmetic Rules of Powers
146(1)
Powers Can Be Negative
147(1)
Powers Need Not Be Whole Numbers
147(1)
Logarithms
148(1)
The Logit
149(4)
6 Power, Effect Size and Inverse Probability
153(20)
Introduction
154(2)
Thomas Bayes: Prior and Posterior Probabilities
156(9)
Taxi for Kahneman and Tversky
165(2)
A More Substantial Application: Medical Tests
167(1)
Covid-19
168(1)
Breast Cancer Screening
169(4)
7 What Does Sound Inference Comprise?
173(20)
The ASA Debate
174(1)
Ten Steps of Inference
175(8)
The Six Principles of the ASA
183(3)
From the Six Principles to ATOM
186(3)
Contemporary Scientific Research
189(4)
Glossary 193(4)
References 197(4)
Index 201
From 2009 to 2014 John was the Strategic Advisor to the Economic and Social Research Council (ESRC) on quantitative methods training overseeing the genesis and launch of the Q-Step programme. From 2015 to 2020 he was Strategic Advisor to the British Academy on Quantitative skills and a member of the British Academys High Level Strategy group on Quantitative Skills. John is a Chartered Statistician and was Vice President (Professional Affairs) of the Royal Statistical Society 2019-20. He has held research grants from the European Commission, UK ESRC, British Academy, Leverhulme trust and British, Spanish and Catalan government departments.
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