Cover

Title

Copyright

Contents

Acknowledgments

1 Introduction

1.1 About the book

Purpose

Intended readers

Why use computation

Prerequisites

How to use this book

Brief overview

1.2 Basic principles

Applicability

Argument style

Structure and variation

Example of a probability distribution

Other argument styles

1.3 Scientific argument

Ingredients of statistical argument

Intellectual foundation

Structure

Test statistic

What is a statistical hypothesis?

Summary

2 Programming and statistical concepts

2.1 Computer programming

History

The two parts of a computer program

Places

Service berry example

Instructions

Leading spaces

Spreadsheet I/O

Procedures

Errors

2.2 You start programming

Experienced programmers

Getting started with EXCEL macro programming

How to read and write a spreadsheet from your macro

2.3 Completing the service berry example

Fruit-ripening phenology

Mechanisms of variation in fruit-ripening date

The data

Hypothesis and statistic

A macro to calculate the predicted probability distribution

Calculate the test statistic

Remember the four ingredients

Name vs content

2.4 Sub CARPEL

2.5 You practice

More about the EXCEL macro editor

A real exercise problem

How to solve it

Remember lawyers

3 Choosing a test statistic

3.1 Significance of what

Data from fossil marine organisms

The controversy

Relevance of precision

Two irrelevant statistics

Relevant statistics

Freedom to choose any statistic

3.2 Implement the program

Hypotheses of non-periodicity

Computational overview

Sample the chosen hypothesis with computation

Calculate a relevant statistic

Discover inter-peak intervals

Testing the macro

Estimate realized significance

Using significance to argue

3.3 Sub PERIOD

4 Random variables and distributions

4.1 Random variables

At random

Random process

Continuous distributions

Random variable

4.2 Distributions

Computation eliminates calculus

Bar graph

Practice writing a macro

Interpret the bar graph

Randomize

Accuracy vs precision

Pseudo-random

4.3 Arithmetic with random variables

Hypotheses make statistics into random variables

Arithmetic with a random variable and numbers

A macro to convert u to another continuous uniform distribution

Sum of independent samples of the same binary random variable

Pascal’s triangle

A macro to estimate s3

Macros to estimate other density distributions

4.4 Expected value and variance

The middle of a distribution

Theoretical properties of expected value

Variance

Variance of the sum, f + g

The variance of u

5 More programming and statistical concepts

5.1 Re-sampling data

A question

Choose a test statistic

Design the macro

Not different mean same random process

Re-sampling data

Overview

Style

Efron

5.2 Procedures

Why write procedures?

How to write a procedure

Access to places

Sub SORT

BIGDIF3

5.3 Testing procedures

Testing SORT

Test data

Infinite loop

The watch window

Testing PERMUTE

6 Parametric distributions

6.1 Basic concepts

Binary distributions

Binomial distributions

Parametric distributions arise from specific processes

6.2 Poisson distribution

Trees in a savanna

An approximation of e

Birds at a feeder

The secret parameter

How to sample a Poisson distribution in a macro

Ancient anthropology with genetic markers

Stable population

6.3 Normal distribution

Standardization

Increase number of samples

Quick estimates

What is so normal?

How to sample a normal distribution in a macro

6.4 Negative binomial, Chi Square, and F distributions

Negative binomial

Chi Square and F

6.5 Percentiles

Why percentiles?

Interpreting percentiles

A macro to calculate percentiles

Quit while you are ahead

7 Linear model

7.1 Linear model

The classical approach

7.2 Quantifying error

Ways to quantify error

Sum of squared error

Choose a linear model with SSE

7.3 Linear model in matrix form

SSE(B0,B1)

A look at some matrices

Solve the matrix equation

Use the solution

Why bother with matrices?

7.4 Using a linear model

Use Equation 7.3

Plot the linear model

Sub LINMO

Test Sub LINMO

7.5 Hypotheses of random for a linear model

Statistical hypotheses include a concept of random

Null hypothesis

Test statistics for a linear model

Concepts of random for linear models

Examples are instructive

ANOVA

A macro to calculate the predicted distribution of B1

7.6 Two-way analysis of variance

Example data

Calculate sum of squared error

Two-way ANOVA

Interaction

No interaction

Re-coding

Sub INVERSE

Test Sub INVERSE

8 Fitting distributions

8.1 Estimation of parameters

Estimators are random variables

Bias

Accuracy

Consistent

Error as a random variable

Variance/covariance matrix

Maximum likelihood

Normal distribution

Confidence interval

Re-using data

8.2 Goodness of fit

Test statistic

Derive Chi Square

Use Chi Square

Accuracy of Chi Square

Calculate the predicted distribution

Iberian demography

9 Dependencies

9.1 Interpreting mixtures

Variablers

Use the null hypothesis

Effect of test statistic on your argument

Catalpa speciosa

9.2 Series of dependent random variables

Dependency

Random walk

Auto-regressive series

Markov process

Test for a Markov process

Absorbing Markov process

Describe spatial distribution

Condor demography

9.3 Analysis of covariance

Example

Are the rates equal?

A null hypothesis

Simulated reality

9.4 Confounding dependencies

The problem

Size-independent units

Design a macro

Exponential size difference

Size difference is part of your hypothesis

9.5 Sub SEXDIMO

10 How to get away with peeking at data

Examples

The problem

Legitimate peeking

Include peeking in your hypothesis

Goodness-of-fit

11 Contingency

11.1 What is contingency?

Examples

Contingency table

Independence

Goodness-of-fit

Useful statistics

ACTUS

11.2 ACTUS2

Analysis of contingency tables using simulation

Exvotos example

SMALL and BIG arrays

Important questions

Significance of the whole contingency

Interpret significance

Another hypothesis of independence

Hypotheses of dependence

11.3 Spreadsheet ACTUS

Design the spreadsheet

Report results

How to run ACTUS.XLS

11.4 Sub ACTUS

References

Index