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(Upload on June 16 2023) [ 日本語 | English ]

Statistical test (統計的検定)






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

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

Types of statistical tests (検定の種類)

= parameter test + goodness-of-fit test

Parameter test

Goodness-of-fit test

Ex. Uniformity test (一様性の検定)
Sun 17.  Mon 6.  Tue 8.  Wed 12.  Thu 11.  Fri 16.  Sat 14  = Total 84

H: pi = 1/7(I = 1 … 7) mi = mpi → 84 × 1/7 = 12 (> 5)
χ2 = 1/12{(17 - 12)2 + (6 - 12)2 + (8 - 12)2 + (12 - 12)2

+ (11 - 12)2 + (16 - 12)2 + (14 - 12)2} ≈ 82

χ20.05(df = n - 1 = 6) = 12.592 → D = [12.592, ∞],
accept H (= accept uniformity)

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]

Covariance structure analysis (共分散構造分析)

≈ structural equation model (構造方程式モデル) (with latent variable), SEM/LV
considering a model representing how various aspects of some phenomenon are thought to causally connect to one another

System dynamics, SD (システムダイナミクス)

Forrester, Jay Wright (1918-2016, MIT)
1944 started to develop a flight simulator, by a digital computer, Whirlwind
1956 develped system dynamics - to analyze social systems
1961 "Industrial Dynamics": business behavior simulation (early stage) ⇒
1969 "Urban Dynamics": diversified applications, e.g., urban planning
⇒ consolidation and integration = SD
1971 "World dynamics": affected The Limits to Growth (LTG, 成長の限界)
Advantages and applications
Diagrammatically describe causal relationships between model elements

→ automatic generation of numerical simulation models

convenient to understand relationships between elements

→ directly model individual problem phenomena and causal relationships

∴ suitable for simulation models for systems (society, business, policy, etc.) that are difficult to conduct experiment with or to oversee in a broad range
System (システム)
The concept of system for using system dynamics

system has the objective(s) (目的)
present broundary (システム境界) enclosing components

= the components within the system →

the components are connected logically to each other
input from the outsides (environments) →

[negative feedback] → output from the inside

System = natural system + human system

human system = social system* + physical system

*: present decision-making step (意思決定点) - real system

Optner, Stanford L (1920-2017)
Def. problem: defined as a situation in which there are two states: one is characterized by the present state, the other by a proposed state. The present state is exemplified by the existing system; the proposed state is exemplified by the system that is hypothesized (desired) or proposed (1965)
System analysis ≈ problem resolution

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
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