研究方法の概論(research basics)

“Elementary my dear Fukuoka UX Study Group”「初歩だよ、福岡UX勉強会君」

クルッツ・クリスチャン

Basics definitions and common mistakes in research methodology 研究方法の基礎定義及び一般的な間違い

Cruz Christian

“Elementary my dear Fukuoka UX Study Group”

Basics definitions and common mistakes in research methodology74

�2

SEARCHRE



�3

Systematised effort to gain new knowledge 研究とは体制的に新しい知識を身につける事です。

1000 pt



�4

Precise Control over INNOVATION

イノベーションの正確な管理

Random decisions over CREATIVITY 創造力のランダムな決定

Systematised effort to gain new knowledge 研究とは体制的に新しい知識を身につける事です。

SEARCHRE



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‣ SYSTEMATIC体制的: Reject the use of guessing & intuition, but DOES NOT rule out creative thinking ‣ CONTROLLEDコントロール: Variables are identified & controlled, wherever possible ‣ LOGICAL論理的: Guided by rules of logical reasoning & logical process of induction& deduction

• Deduction (Aristotle)推論 - “From whole to part” • Induction (Francis Bacon) 帰納 - “From number of Observations”

‣ EMPIRICAL実証的: Provide a basis for external validity to results (validation)

‣ REPLICABLE重複: Verified by replicating the study ‣ SELF CORRECTING自ら修正: Built in mechanism & open to public scrutiny by fellow professionals

GOODA research is



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TYPES of research

Descriptive 叙述的

WHAT? 何？

Analytical 分解的

WHY? なぜ？

Applied 応用的

Problem 問題

Fundamental 理論的Theory 理論

Quantitative 数量的

How much, many, fast, heavy, long? etc.

いくつ、どのぐらい?など

Qualitative 質的

HOW? どう？

Conceptual 概念的

Abstract idea 抽象的アイデア

Empirical 実証的

Applied idea 応用的アイデア



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TYPES of research

Descriptive 叙述的

WHAT? 何？

Analytical 分解的

WHY? なぜ？

The major purpose of descriptive research is description of the state of affairs as it exists at present. The methods of research used in descriptive research are survey methods of all kinds, including comparative and correlational methods.

The analytical research usually concerns itself with cause-

effect relationships



�8

TYPES of research

Applied 応用的

Problem 問題

Fundamental 理論的Theory 理論

Applied research aims at finding a solution for an immediate problem facing a society or an industrial/business organisation. ”Discover a solution for some pressing practical problem"

Concerned with generalisations and with the

formulation of a theory.



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TYPES of research




Qualitative 質的

Why? なぜ？

Quantitative research is based on the measurement of quantity or amount.

Qualitative research, on the other hand, is concerned with qualitative phenomenon, i.e.,

phenomena relating to or involving quality or kind. This

type of research aims at discovering the underlying

motives and desires, using in depth interviews for the

purpose



�10

TYPES of research

Conceptual 概念的

Abstract idea 抽象的アイデア

Empirical 実証的

Applied idea 応用的アイデア

Empirical research relies on experience or observation

alone, often without due regard for system and theory. It is

data-based research, coming up with conclusions which are

capable of being verified by observation or experiment.

Conceptual research is that related to some abstract idea(s) or theory. It is generally used by philosophers and thinkers to develop new concepts or to reinterpret existing ones.



ResearchPROCESS

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1. Defining the research theme or idea 研究テーマを設立

2. Formulating the research problem 研究問題を明確化

3. Conceptual(or Theoretic) Framework 観念的枠組み

4. Development of working hypotheses 仮説を立てる

5. Preparing the research design 研究方法を立てる

6. Determining sample design 統計方法を立てる

7. Collecting the data データーを集計

8. Analysis of data データーを分析

9. Hypothesis-testing 仮説を検証

10. Generalisations and interpretation 結論とまとめ

11. Preparation of the report or the thesis 論文をまとめ

EMPHASISEMPHASIS

EMPHASISEMPHASIS

Execution of the project プロジェクトを実行



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Defining the research theme or idea 研究テーマを設立

A good idea is… 良いアイデアは…

Research PROCESS

Personal 個人的

Novel 新た

Useful 有意義

To think a good idea one must REVIEW THE EXISTING RESEARCH. 良いアイデア考える為に先行研究を調べなければなりません。



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Formulating the research problem 研究問題を明確化

The problem MUST express one or more relations between variables. 問題点は必ず変数の一つまたは一つ以上と関連する。

Research PROCESS

The Objectives MUST be measurable. 目標は必ず測定可能。!An objective MUST NOT contain moral or aesthetic judgments. 目標は必ず道徳または美感覚を含めない。!

WHAT? 何？

WHO? 誰？

WHEN? いつ？

WHY? なぜ？

HOW? どうやって？

ETC… など・・・

ETC… など・・・

The problem 問題点

Objectives 目標

Research Questions 研究質問

Viability 実行可能性

Relevance 重要

Consequences 結果

Convenience 利便 !Social relevance 社会的関連 !Practical Implications 具体的結果 !Theoretical value 理論的価値 !Methodological value 方法論的価値


Basics definitions and common mistakes in research methodology74Collecting the data データーを集計 Research PROCESS

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Qualitative 質的

HOW? どう？

Measuring sets of variables or quantities and their relationship to one another

Understanding the qualities of a

specific field of inquiry

ETHNOGRAPHY !Interviewインタビュー Focus Groupフォーカスグループ

ETCなど

MEASUREMENT !

態度測定Attitude measurement

アンケートQuestionnaire

一定試験と目録Standardised test and inventories

Research PROCESS



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Measure 測定

To assign empiric(quantifiable) indicators to abstract concepts 抽象概念を量的指標化する

Hypotheses relation 仮説関係 Answer

結果

Observable Data 観測可能なデータ



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knowledge 知識

Our personal map/model of the World 世界の個人的なモデル。

Data is raw and unorganised fundamental facts. Numerical values !データとは、未処理あるいは未組織な基礎的事実のことです。「数値」

A property which can change and its variations can be measured.

変化する特徴、この特徴が計る事が出来る。

Variable 変数

information 情報

data データ

When data is processed,

organised, structured or presented in a

given context so as to make it useful, it is called Information.

Meaning

データが処理、整理、構造化されると、役立つデータになり、情報と呼ばれています。「意味」



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KEEP CALM

AND

LOVE Evangelion

information 情報

Watch timesmonth A B C D E F G

January 2 4 31 6 8 1 8February 3 7 28 3 5 1 3

March 1 4 31 8 3 1 3April 4 8 30 4 4 4 4May 5 3 31 5 2 1 5June 12 3 30 6 1 2 1July 5 14 31 5 4 5 3

August 6 6 31 7 1 2 3September 8 8 30 8 4 2 3

October 3 6 31 5 5 2 1November 5 4 30 5 7 2 2December 1 0 31 12 8 1 1

Variable 変数

A property which can change and its variations can be measured.

変化する特徴、この特徴が計る事が出来る。

Variable 変数

Watch timesmonth times

JanuaryFebruary

MarchAprilMayJuneJuly

AugustSeptember

OctoberNovemberDecember

data データ



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Collection Instrument 手法

RELIABILITY 確実性The degree in which the repeated application produces the same results. 繰り返す適用の程度は同じ結果を生成している

VALIDITY 妥当性

The degree in which an instrument really

measures what is intended to be measured. 本当に測定する手法の程度は

意図している測定です。



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Collection Instrument 手法

RELIABILITY 確実性

VALIDITY 妥当性

Factors that affect Validity and Reliability 妥当性と確実性に影響を与える要因

Cultural Context and Time 文化的文脈と時間

Morphology 形態論

e.g. Not enough space for writing e.g. Too small characters

Improvisation 即興 e.g. Intelligence measurement e.g. Behaviour measurement

Environment 環境 e.g. Weather e.g. Lunch time

Empathy 共感

e.g. Complicated language e.g. economical background e.g. educational background



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Category 部門

Quantity 分量

Interval 間隔

ratio 比率

Ordinal 順序

Measurement 測定

Discrete 個別

Type(Mountain bike, Tourer, Road Racer, etc.) タイプ

Components Maker(Shimano, Campagnolo, etc.) 要素のメーカ

Age 期間

Condition (Excellent, Acceptable, Poor) 状態（良い, まあまあ, 悪い)

Price 値段

Size of frame フレームのサイズ

Number of gears(2, 4, 6, 8, 10, 12…) 変速の数量

Maker(Trek, Peugeot, Hammer, etc.) メーカ

Nominal 名義

What is measuring the instrument? (items scales) 手法は何を測定するのか？

USED BICYCLE 中古自転車

Qualitative

HOW good?

Variable 変数



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Learned predisposition to react in favor or against to objects or symbols 態度は物がシンボルに対する賛成か反対かを反映する学習の偏向です。

attitude 態度


MEASUREMENT 態度測定Attitude measurement



�22



Learned predisposition to react in favor or against to objects or symbols

!態度は物がシンボルに対する賛成か反対かを反映す

る学習の偏向です。

Attitudes are INDICATORS of conduct but NOT the conduct itself.

!態度は、行動ではなく、行動の指標です。

Attitudes are symptoms only. !

態度は兆候だけです。

?態度ATTITUDE



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Attitude measurement 態度測定

Attitude Scales 態度スケール

Semantic Differential ＳＤ法

Likert Scale リッカート尺度



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Statement

陳述

Scoring 得点

Reaction 反応

1.Strongly disagree 1.全く同意できない 1 -2 5

2. Disagree 2.同意できない 2 -1 4

3. Neither agree nor disagree 3.どちらともいえない 3 0 3

4. Agree 4.同意できる 4 1 2

5.Strongly agree 5.非常に同意できる 5 2 1




�25



Variable 変数

Item アイテム

Category カテゴリー

Codes コード化

Column 列

What is being measured 何を測定するのか？

Statement 1 陳述１

1.Strongly disagree 1.全く同意できない 1

12. Disagree 2.同意できない 2

3. Neither agree nor disagree 3.どちらともいえない 3

4. Agree 4.同意できる 4

5.Strongly agree 5.非常に同意できる 5

Statement 2 陳述２


22. Disagree 2.同意できない 2




Statement n 陳述 n


n2. Disagree 2.同意できない 2




Codebook (Likert Scale) コードブック (リッカート尺度)



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Data Matrix データー行列

Subject 回答者

Column 1 列1

Column 2 列２

Column 3 列３

Column 4 列４

Column n 列 n

1 1 2 5 1 3

2 2 3 4 2 3

3 3 2 5 3 2

4 4 5 4 3 2

5 5 3 3 3 4

6 1 2 2 2 2

7 2 1 3 1 1

8 4 2 4 2 2

n o p q r s



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Subject回答者

Column 1列1

Column 2列2

Column 3列3

Column 4列4

Average平均

1 1 2 5 1 2.25

2 2 3 4 2 2.75

3 3 2 5 3 3.25

4 4 5 4 3 4

5 5 3 3 3 3.5

6 1 2 2 2 1.75

7 2 1 3 1 1.75

8 4 2 4 2 3

Level of Agreement (per Subject)

Agre

emen

t Lev

el

0

1

3

4

5

Subject 1 Subject 2 Subject 3 Subject 4 Subject 5 Subject 6 Subject 7 Subject 8

3

1.751.75

3.5

4

3.25

2.75

2.25

Column 1 Column 2 Column 3 Column 4 AverageSubject回答者

Column 1列1

Column 2列2

Column 3列3

Column 4列4

1 1 2 5 1

2 2 3 4 2

3 3 2 5 3

4 4 5 4 3

5 5 3 3 3

6 1 2 2 2

7 2 1 3 1

8 4 2 4 2

Average平均 2.75 2.5 3.75 2.125

Level of Agreement Average (per Statement)Ag

reem

ent L

evel

0

1

2

3

4

5

Statements

2.125

3.75

2.52.75

Column 1 Column 2 Column 3 Column 4




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Percentage of Selections (Total)

30%

17%11%

23%

20%

1.Strongly disagree 2. Disagree 3. Neither agree nor disagree4. Agree 5.Strongly agree

Percentage of Selections (Statement 1)

18%

5%3%

50%

25%

1.Strongly disagree 2. Disagree 3. Neither agree nor disagree4. Agree 5.Strongly agree



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Comparission of the Agreement Level Average and Best Possible Selection

Leve

l of A

gree

men

t

012345

Column 1 Column 2 Column 3 Column 4

Average Best Possible

5

3.75

2.52.752.75 2.5

3.75

5

Comparission of the Agreement Level for Each Statement (Number of selections)

Num

ber o

f Peo

ple

0

10

20

30

40

Statement 1 Statement 2 Statement 3 Statement 4 Statement 5 Statement 6

21

27

20

14

710

1

10107

2

20

21121

5

13

1

5

10

20

3

23

14

710

1.Strongly disagree 2. Disagree 3. Neither agree nor disagree 4. Agree5.Strongly agree



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Dimension 次元

Positive adjective 積極的形容詞

Scoring 得点

Negative Adjective 消極的形容詞

GOOD3 2 1 0 -1 -2 -3

BAD2 1 0 -1 -27 6 5 4 3 2 1

○




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Dimension 次元

Bipolar Adjectives Pair 正反対的形容詞双

Codes コード化

Column 列

What is being measured 何を測定するのか？

Positive adjective 1 積極的形容詞１

Negative Adjective 1 消極的形容詞

2

11

0

-1

-2

Positive adjective 2 積極的形容詞２

Negative Adjective 2 消極的形容詞２

2

21

0

-1

-2

Positive adjective n 積極的形容詞 n

Negative Adjective n 消極的形容詞

2

n1

0

-1

-2

Codebook(Semantic Differential) コードブック (ＳＤ法)



�32



Data Matrix データー行列

Subject 回答者

Column 1 列1

Column 2 列２

Column 3 列３

Column 4 列４

Column n 列 n

1 1 2 5 1 3

2 2 3 4 2 3

3 3 2 5 3 2

4 4 5 4 3 2

5 5 3 3 3 4

6 1 2 2 2 2

7 2 1 3 1 1

8 4 2 4 2 2

n o p q r s



�33



Dimension 1 Dimension 2 Dimension 3 Dimension 4 Average

+ / - 1 4 1 3 1 2.25

+ / - 2 4 1 2 2 2.25

+ / - 3 4 1 3 3 2.75

+ / - 4 5 2 2 4 3.25

+ / - 5 3 3 2 4 3

+ / - 6 4 4 2 4 3.5

+ / - 7 2 5 2 4 3.25

+ / - 8 3 5 2 4 3.5

+ / - 9 4 5 2 4 3.75

+ / - 10 5 4 2 4 3.75

+ / - 11 3 3 3 3 3

+ / - 12 2 4 4 2 3

+ / - 13 3 3 5 2 3.25

+ / - 14 2 4 3 2 2.75

+ / - 15 2 3 2 2 2.25

+ / - 16 2 2 2 2 2

+ / - 17 3 1 3 1 2

+ / - 18 4 4 4 1 3.25

+ / - 19 3 5 5 1 3.5

+ / - 20 2 2 5 2 2.75




�34

a set of questions about a certain variable 特定の変数についての質問のセット

questionnaire アンケート


MEASUREMENT アンケートQuestionnaire



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OPENCLOSEDANSWER 1

ANSWER 2

ANSWER 3

ANSWER 4

Delimited Categories or Alternatives of answers 限定するカテゴリーの自由な答えあるいは提供された選択

肢からの答え



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CLOSEDANSWER 1

ANSWER 2

ANSWER 3

ANSWER 4

Advantages メリット

Disadvantages デメリット

Easy to answer (effortless) 答えやすい !Faster 早い !Easy to Codify コード化しやすい !Easy to analyse 分析しやすい

Due to their nature, these questions might limit the number of options and not really represent the respondents' point of view. 限定された選択肢からの答えのため、参加者の本当の見解が見つからない可能性がある。



�37




OPEN

Advantages メリット

Disadvantages デメリット

These questions allow the gathering of more detailed data about the measured topic これらの質問は、測定されたトピックに関するより詳細なデータの収集を可能にする

Slower 遅い !Difficult to Codify コード化しづらい !Difficult to analyse 分析しづらい



�38



OPEN

Questions must… 質問は必ず…


CLOSEDANSWER 1

ANSWER 2

ANSWER 3

ANSWER 4

!BE Clear and Easy to understand わかりやすい、理解しやすい !NOT be uncomfortable or disturbing 不快なことは与えない !BE oriented toward a UNIQUE logical aspect. 固有の論理の側面に行 !NOT contain the answers or elements which negate the free will of the respondent 全く自由意志否定ません !Be according to the social, cultural, and intellectual characteristics of the respondent 回答者の社会的・文化的・知的特性に応じたこと !NOT express ideas supported by institutions, organisations, or groups. 組織やグループなどの考えを表現しない !Include clear and easy to understand INSTRUCTIONS. わかりやすい、理解しやすい説明があり



�39



OPEN

A questionnaire should… アンケートは…すべき


CLOSEDANSWER 1

ANSWER 2

ANSWER 3

ANSWER 4

Contain introductory questions of a neutral nature (age, sex, job, etc.) so the respondent can get accustomed to the situation. 回答者は慣れるためにニュートラル質問があります（年齢、性別、仕事、など） !Include (depending on the necessity) verification questions 検証質問があり（必要性による）

Depend on wether the answers really reveal the necessary information. 答えは本当に必要な情報を表示しているかどうか

!Not ask unnecessary or unjustified questions in order to keep the answer time on a "comfortable scope" 不必要な質問が含まれていない



�40

Category 部門

Quantity 分量

Interval 間隔

ratio 比率

Ordinal 順序

Measurement 測定

Discrete 個別

Type(Mountain bike, Tourer, Road Racer, etc.) タイプ

Components Maker(Shimano, Campagnolo, etc.) 要素のメーカ

Age 期間

Condition (Excellent, Acceptable, Poor) 状態（良い, まあまあ, 悪い)

Price 値段

Size of frame フレームのサイズ

Number of gears(2, 4, 6, 8, 10, 12…) 変速の数量

Maker(Trek, Peugeot, Hammer, etc.) メーカ

Nominal 名義

What is measuring the instrument? (items scales) 手法は何を測定するのか？

USED BICYCLE 中古自転車

Qualitative

HOW good?

Variable 変数


Basics definitions and common mistakes in research methodology74Analysis of data データーを分析 Research PROCESS

�41

Measurement Scales 測定スケール

Calculation 計算

Category 部門

Quantity 分量

Nominal 名義

Ordinal 順序

Interval 間隔

ratio 比率

Frequency Distribution

度数分布 ○ ○ ○ ○Median and Percentiles 中央値、パーセンタイル X ○ ○ ○

Add or Subtract 足し算、減算 X X ○ ○

Arithmetic Mean, standard deviation, standard error of the mean

平均、標準偏差、標準誤差X X ○ ○

Ratio, coefficient of variation 比率、微系数 X X X ○

Likert Scale !Semantic Differential

Likert Scale !Semantic Differential



�42

age 年齢

gender 性別

income 給料

health 健康

Cross-Breaks | Cross-Tabulations クロス集計



�43

“Statistical Thinking” 統計的な考え



�44

Summarising our experience so that we and other people can understand its essential features. 皆が分かるために我々の経験をまとめます !Using the summary to make estimates or predictions about what is likely to be the case in other (perhaps future) situations. 未来を予測するためにその経験を使います

2010 18歳

2011 19歳

2012 20歳

2013 21歳 ?



�45

Statistics 統計

A set of methods used to collect or process or interpret quantitative data. 統計とは数量的なデータを集計し、手順を整理する及び判断する手法。

Descriptive Statistics 要約統計量Methods to summarise or describe our observations

Inferential Statistics 推計統計量Using those observations as a basis for making estimates or predictions, i.e. inferences about a situation that has not been observed.



�46

Population 母集団 !Refers to ALL the finite or infinite collection of items under consideration. 母集団とは、調査対象のとなる数値，属性等の源となる集合全体を意味する。

Representatively generalise from a Sample to the population 標本は母集団を代表する

Sampling 標本調査

Sample 標本 !A portion from a population 標本とは、母集団の部分集合のこと



�47


n =((e2×(N-1))+((k2)×p×q))

((k2)×N×p×q)

n =((N-1)e2+σ2×k2)

(N×σ2×k2)



�48

p: subjects proportion which posses the studied characteristic.!

q: subjects proportion which DOES NOT posses the studied characteristic, that is to say, 1-p.! p = q = 0.5

k:confidence value [constant不変量]!

信憑性

1.15 1.28 1.44 1.65 1.96 2 2.58

k 75% 80% 85% 90% 95% 95.5% 99% 信憑性

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

e 1% 2% 3% 4% 5% 6% 7% 8% 9% 誤差

e:error margin [constant不変量](difference between the results that might be obtained applying the survey or experiment to the total population and the sample)!誤差

N:Total Population"母集団

n:Sample size"標本サイズ

n =((e2×(N-1))+((k2)×p×q))

((k2)×N×p×q)



�49

k:confidence value [constant不変量]!

信憑性

1.15 1.28 1.44 1.65 1.96 2 2.58

k 75% 80% 85% 90% 95% 95.5% 99% 信憑性

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

e 1% 2% 3% 4% 5% 6% 7% 8% 9% 誤差

e:error margin [constant不変量](difference between the results that might be obtained applying the survey or experiment to the total population and the sample)!誤差

N:Total Population"母集団


n =((N-1)e2+σ2×k2)

(N×σ2×k2)

σ:standard deviation = 0.5!標準偏差



�50

!STRATUM(h)

層化

1st year"students

2nd year"students

3rd year"students

4th year"students


Stratified Sampling 層化抽出法

Total Population"母集団

Sample"標本

N n

Total Population STRATUM!母集団の層化"

(Nh)

Nh1Nh2Nh3Nh4

Sub-sample!標本の層化"

(nh)

nh1nh2nh3nh3



�51

fh = n/N [constant 不変量]

Total Population STRATUM!母集団の層化"

(Nh)fh Calculation"

計算

Sub-sample!標本の層化"

(nh)

1st year!students Nh1 fh Nh1 x fh nh12nd year!students Nh2 fh Nh2 x fh nh23rd year!students Nh3 fh Nh3 x fh nh34th year!students Nh4 fh Nh4 x fh nh4Total!

students N n




�52

Every item has the same chance of being selected 各アイテムが選ばれる可能性は同じ

I = N/n

Random ランダム

Systematic 体制的

I:Approximate integer!近似整数!

N:Total Population!母集団!





�53

Every important characteristic of the population is likely to have one or more

representative in the sample

?

The probability that a one-time-in-twenty phenomenon will not appear

at all in a simple random sample of size 60 is 0.46

Representatively generalise from a Sample to the population 標本は母集団を代表する




�54

Asuka LangleyAyanami Rei

80 points 点

Eva Units combat tactics 汎用人型決戦兵器の技術

History of the Second Impact セカンドインパクトの歴史

Standard Deviation(SD) = 5 標準偏差

Arithmetic mean = 60 相加平均

90 points 点





�55

A

Helvetica Regular 20 pts5 mts

5 mts Helvetica regular 20 pts

50% 50%

○X



�56

A

Helvetica Regular 20 pts5 mts

2.35% 0.15%

M-1SD +1SD

34% 34%13.5% 13.5%2.35%0.15%

-2SD-3SD +2SD +3SD

68%

95%99.7%

Normal Curve of Distribution 正規分布曲線



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Whatever the height or width of the normal curve, the distribution of the area under it, is always the same. 正規分布曲線の高さまたは巾がいろいろあっても、曲線の下にある分布の面積はいつも同じです。




89 68 92 74 76 65 77 83 75 87

85 64 79 77 96 80 70 85 80 80

82 81 86 71 90 87 71 72 62 78

77 90 83 81 73 80 78 81 81 75

82 88 79 79 94 82 66 78 74 72

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Pulse-rate (beats per minute) of 50 students ５０人学生の心拍数

Cross-Breaks | Cross-Tabulations クロス集計

Look for patterns! パターンを探そう！



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62 64 65 66 68 70 71 71 72 7273 74 74 75 75 76 77 77 77 7878 78 79 79 79 80 80 80 80 8181 81 81 82 82 82 83 83 85 8586 87 87 88 89 90 90 92 94 96


Frequency Distribution 度数分布



�60

62 64 65 66 68 70 71 71 72 72

73 74 74 75 75 76 77 77 77 78

78 78 79 79 79 80 80 80 80 81

81 81 81 82 82 82 83 83 85 85

86 87 87 88 89 90 90 92 94 96

90 BPM：2

69 BPM：0

Frequency is the count of the occurrences of values within a particular group or interval 度数とは各階級に属する資料の個数のこと


Frequency Distribution 度数分布



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Pulse-rate 心拍数

Nº students 学生人数

60-64 265-69 370-74 875-79 12

80-84 13

85-89 7

90-94 495-99 1

50

Grouped Frequency Distribution

グループ化された度数分布

Gro

uped

Fre

quen

cy d

istrib

utio

n 度数（各グループの人数）

0

4

7

11

14

Pulse-rate 心拍数（BPM）62 67 72 77 82 87 92 97 102

01

4

7

1312

8

32

60-64 65-69 70-74 75-79 80-84 85-89 90-94 95-99

62 64 65 66 68 70 71 71 72 72

73 74 74 75 75 76 77 77 77 78

78 78 79 79 79 80 80 80 80 81

81 81 81 82 82 82 83 83 85 85

86 87 87 88 89 90 90 92 94 96Arithmetic mean = 79.1

相加平均Median = 79.5

中央値Range = 34

レンジMode = 80-81

最頻値

Modal Class = 80-84

最頻値的なクラス

Central Tendency 中心傾向

Statistical Dispersion 統計的ばらつき




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Standard Deviation(SD) 標準偏差

In statistics and probability theory, standard deviation (represented by the symbol sigma, σ) shows how much variation or "dispersion" exists from the average (mean, or expected value). 標準偏差とは、統計値や確率変数の散らばり具合（ばらつき）を表す数値のひとつで σ で表す。

σN

∑(X-X)=√ 2


Arithmetic mean = 79.1 相加平均




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Pulse-rate (beats per minute) of 50 students [ 50人学生の心拍数 ]

0

3

6

9

12

15

55 60 65 70 75 80 85 90 95 100

Pulse-rate (beats per minute) of 75 students [75人学生の心拍数]

0

3

6

9

12

15

55 60 65 70 75 80 85 90 95 100


0

3

6

9

12

15

55 60 65 70 75 80 85 90 95 100


0

3

6

9

12

15

55 60 65 70 75 80 85 90 95 100



�64


0

3

6

9

12

15

55 60 65 70 75 80 85 90 95 100



�65


Arithmetic mean

相加平均

Median

中央値

Mode

最頻値




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The Shape of the normal distribution is such that we can state the PROPORTION of the population that will lie between any two values of the variable. 正規分布の形は、変数の任意の2つの値の間にある口数の比率が計算できる。

Pulse-rate (beats per minute) of 50 students [ 50人学生の心拍数 ]

0

3

6

8

11

14

62 67 72 77 82 87 92 97

Standard Deviation(SD) 標準偏差 !Arithmetic mean 相加平均

⨍(x) σ√2π1

=1"2e

- x-u!σ )(



Arithmetic mean = 79.1

相加平均

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62 64 65 66 68 70 71 71 72 72

73 74 74 75 75 76 77 77 77 78

78 78 79 79 79 80 80 80 80 81

81 81 81 82 82 82 83 83 85 85

86 87 87 88 89 90 90 92 94 96




-2 SD-1 SD

-1/2 SD +1 SD

+1 1/2 SD+3 SD


Z-Values 偏差値



�68

M

68% of all observations

(34%) (34%)

-1SD +1SD

M ± 1SD

Point of Inflection 編曲点

Point of Inflection 編曲点



�69

+3SD0.15%

M-1SD +1SD-2SD (1.96)

+2SD (1.96)

95%

-3SD

99.7%

68%

34%13.5%2.35%0.15% 34% 13.5% 2.35%



�70

M-1SD +1SD50 55 60 Km/H

50Km/H



1000 cars



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34% 50%

84%50

Km/H



M-1SD +1SD50 55 60 Km/H

1000 cars



�72

Asuka LangleyAyanami Rei

80 points 点

Eva Units combat tactics 汎用人型決戦兵器の技術

History of the Second Impact セカンドインパクトの歴史



90 points 点





90

�73

65 70 75 80605550

60 75 105453015

+3SD0.15%

M-1SD +1SD-2SD (1.96)

+2SD (1.96)

95%

-3SD

99.7%

68%

34%13.5%2.35%0.15% 34% 13.5% 2.35%

Eva Units combat tactics 汎用人型決戦兵器の技術History of the Second Impact セカンドインパクトの歴史



�74

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研究方法の概論(research basics)

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