In Planning Stage
Preface
0.1
Target
0.2
Topics/textbooks
0.3
Regression from the outset
0.4
Parameters first, data later
0.5
Let's switch to "y-bar", and drop "x-bar".
0.6
Computing from the outset
0.7
Appendix:
1
Introduction
1.1
Goals
1.2
Structure
1.3
Attitudes, etc....
I Part I
2
Statistical Parameters
2.1
Parameters
2.2
Parameter Contrasts
2.2.1
Parameter relations in numbers and words
2.2.2
Parameter relations in symbols, and with the help of an index-category indicator
2.3
Parameter functions
2.4
Phraseology to avoid
2.5
SUMMARY
2.6
Exercises
2.7
References
3
Statistical Inference
3.1
The Bayesian Approach
3.1.1
Example: parameter is 2-valued: yes or no
3.1.2
Example: parameter is a proportion
3.1.3
Examples: parameter is a personal number or population mean
3.1.4
The Bayesian Bottom Line
3.2
Frequentist approach
3.2.1
(Frequentist) Test of a Null Hypothesis
3.2.2
Ingredients and methods of procedure in a statistical test
3.3
Does the approach matter?
4
Parameter Intervals
4.1
'100% confidence' intervals
4.2
More-nuanced intervals
4.3
SUMMARY
5
The 'mean' parameter
\(\mu\)
5.1
Two genres
5.2
Fitting these to data / Estimating them from data
6
The (proportion) parameter
6.1
Example one
6.2
Example two
7
The (event rate) parameter
7.1
Etc
7.2
ETC
8
Contrast: 2 mean parameters
8.1
Estimand, estimator, estimate
9
Contrast: 2 proportion parameters
9.1
Estimand, estimator, estimate
10
Contrast: 2 speed parameters
10.1
Estimand, estimator, estimate
II Part II
11
Probability
11.1
Objectives
11.2
Probability Scales
11.3
Basic rules for probability calculations
11.4
Conditional probabilities, and (in)dependence
11.5
Changing the Conditioning: the direction matters
11.6
Summary Slides
11.7
Exercises:
12
Random Variables/Variation
12.1
Objectives
12.2
Random Variables
12.3
Expectation (mean) of a Random Variable
12.4
Expected value of a FUNCTION of a random variable
12.5
Variance (and thus, SD) of a random variable
12.5.1
Definitions
12.5.2
Some (good) reasons for using variance, which averages the squares of the deviations from the mean.
12.5.3
But, for end-users today ....
12.5.4
Example of Variance-calculation using one-pass formula
12.6
Variance and SD of a FUNCTION of a random variable
12.7
Sums/means/differences of RVs
12.7.1
A sum (of 2 or
\(n\)
)
12.7.2
Measurement Errors
12.7.3
Mean (of 2 or
\(n\)
RVs)
12.7.4
Difference of 2 RVs
12.8
Linear combinations of RVs (regression slopes)
12.9
Exercises
12.10
Summary Slides
13
Distributions
13.1
Objectives
13.2
Named Distributions
13.2.1
Bernoulli
13.2.2
Binomial
13.2.3
Poisson
13.2.4
Normal
13.2.5
Hypergeometric
13.2.6
Chi-square
13.3
Exercises
13.3.1
Clusters of Miscarriages [based on article by L Abenhaim]
13.3.2
'Prone-ness' to Miscarriages ?
13.3.3
Automated Chemistries (from Ingelfinger et al)
13.3.4
Binomial or Opportunistic? (Capitalization on chance... multiple looks at data)
13.3.5
Can one influence the sex of a baby?
13.3.6
It's the 3rd week of the course: it must be Binomial
13.3.7
Tests of intuition
13.3.8
CI for proportion when observe 0/n or n/n
13.3.9
neg. correlations ... under-binomial variation
13.3.10
weights of offspring (pups/twins)
13.3.11
suicides
13.3.12
horsekicks
13.3.13
Visits to dentists (Cochran)
13.3.14
JH's steps per day
13.3.15
CD4 counts
13.3.16
tweets
13.3.17
accidents
13.3.18
bootstrap
13.3.19
no. of seats / doors / cyclinders in cars
13.3.20
sex ratio in accidents (FARS)
III Part III
14
Mathematics
14.1
Notation
14.2
Powers, Logarithms and Anti–logarithms
15
Computing Session 1
15.1
Objectives
15.2
Background to two datasets
15.2.1
Climate
15.2.2
Ages of Cars
15.3
Statistical/Computing Tasks
15.3.1
Guesses re Date of Ice Breakup
15.3.2
How old are UK cars?
15.4
The p and q functions: an orientation
15.5
Shapes of Distributions
15.6
Exercises
15.6.1
Guesses in Nenana Ice Classic
15.6.2
Exercise: Ages of UK Cars
15.7
SUMMARY
15.7.1
Computing
15.7.2
Statistical Concepts and Principles
16
Computing: Session No. 2
16.1
Objectives
16.2
Scientific background
16.3
Random Variation
16.3.1
Measurement errors
16.3.2
Biological variation
16.3.3
Example 2
16.4
When these Laws don't apply
16.5
SUMMARY
16.5.1
Computing
16.5.2
Statistical Concepts and Principles
17
Computing: Session No. 3
17.1
Objectives
17.2
Exercises
17.2.1
Pooled Blood
17.2.2
Life Tables [1990]
17.2.3
Life Tables [2018]
17.2.4
A simplified epidemic
17.2.5
Screening for HIV
17.2.6
Duplicate Birthdays
17.2.7
Chevalier de Méré
17.3
Other Exercises (under construction)
17.3.1
HIV transmission
17.3.2
The 2018 Book of Guesses
17.3.3
Trends over the last 100 years
18
Computing: Session No. 4
18.1
Objectives
18.2
Exercises
18.2.1
Ages of UK cars
18.2.2
Lengths of Babies' Names
18.2.3
Life Tables [2018]
18.2.4
Variable-length (parallel) parking spaces
18.2.5
Galton's data on family heights
18.2.6
Height differences of random M-F pairs
18.2.7
Same-sex or opposite-sex?
18.2.8
Box minus bowl
18.2.9
car parking fixed and variable
18.2.10
Correcting length-biased sampling
18.3
Other Exercises (under construction)
18.3.1
The 2018 Book of Guesses
18.3.2
Trends over the last 100 years
19
DALITE
19.1
Aim
19.2
How it works
Published with bookdown
Introduction to Statistical Analysis: a regression-from-the-outset approach
Chapter 9
Contrast: 2 proportion parameters
9.1
Estimand, estimator, estimate