Statistical test

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Statistical test (統計的検定)

Mount Usu / Sarobetsu post-mined peatland
From left: Crater basin in 1986 and 2006. Cottongrass / Daylily

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Terminology

zero-inflated model = hurdle model = two-part model

Softwares

SAS
SPSS (statistical packages for social sciences)
Systat
Statistica
MVSP (multi-variate statistical package)
JMP: good for biostatistics

R (package): freeware

1997 Ihaka R & Gentleman: proposed R → open source (⇔ S)
CRAN (The comprehensive R archive network): mega-infromation source on R

Python: freeware

Cpython

Analysis of variance (ANOVA, 分散分析)

an analysis tool used in statistics that splits an observed aggregate variability found inside a data set into two parts: systematic factors and random factors

systematic factors: a statistical influence on the given data set
random factors: … do not

One-way analysis of variance (one-way ANOVA, 1元配置分散分析)

used to determine whether there are any statistically significant differences between the means of three or more independent (unrelated) groups

Two-way analysis of variance (two-way ANOVA, 2元配置分散分析)

an extension of the one-way ANOVA that reveals the results of two independent variables on a dependent variable

[ ordination ]

Multivariate analysis (多変量解析)

Univariate analysis, which looks at just one variable
Bivariate analysis, which analyzes two variables
Multivariate analysis, which looks at more than two variables

[cluster analysis, meta-analysis, ordination]

Factor analysis, FA (因子分析)

A part of general linear model
Assumpstion:

data: interval
linear relationship with no outlier and without multicollinearity

sample size: number of cases > number of factors

including relevant variables
true correlation between variables and factors

Exploratory factor analysis ≈ FA
Confirmatory factor analysis (CFA)

≈ PCA

Factor model (因子モデル)
Fixed (effect) model (固定モデル) = parametric model (母数モデル), FM: type I

The way to obtain common factors (共通因子)

• principal factor analysis (PFA) or principal axis factoring (PAF)
• centroid method
• varimax rotation for obtaining varimax solution

Discriminant analysis, DFA (判別分析)

= discriminant function analysis, DFA