.

.

Variable comes from Vary + Able So variable is anything that its values can be varied. Variables are the phenomena or the topics that

researchers want to investigate.

Variable

.

Variable

Describe

?

?

?

.

VariableCorrelational Relationship

Variable

? ? ?

?

?

.

Difference Testing or Measure of Association

Descriptive Statistics or Inferential Statistics

Univariate, Bivariate, Multivariate

.

?

.

, ..

(Attribute)

(Object)

(Number)

(Measure)

.

(Attribute)

(Object)

(Number)

(Measure)

,

(Test, Measure) (Construct Variable) (Subject) (Variable Values)

.

TOEFLS

JDI

(Job Description Index)

(Job Satisfaction)

.

Nominal Scale Ordinal Scale Interval Scale Ratio Scale

.

Nominal , = 1, = 2Ordinal ,

= 1 = 2 = 3

Interval , 0

0

1 = 2.84 2 = 3.65 3 = 4.12

Ratio , 0

0

1 = 0 2 = 7,650 3 = 9,000

.

(Categorical or Discrete Variable) Nominal Scale Ordinal Scale

(Numerical or Continuous Variable) Interval Scale Ratio

.

(Descriptive Statistics) (Inferential Statistics)

.

2

.

(Descriptive Statistics)

Population Parameter , ,m s r

.

(Descriptive Statistics) (Inferential Statistics)

Population

Sample

Parameter

Statistic Mean, SD., r.

, ,m s r

Hypothesis Testing

.

Parameter Statistic

Parameter and Statistic

.

(Central Tendency) (Variation) (Distribution)

.

CentralTendency

VariationDistribution

.

.

Ordinal Scale Interquartile Range

Interval and Ratio Scale Range (Max. - Min.) Variance Standard Deviation

.

(Skewness) (Kurtosis)

.

(Normal Distribution)

MeanMedian

Mode

Symmetric Bell Shaped Mean = Median = Mode

.

(Negatively Skewed)

Mode

Median

Mean

.

(Positively Skewed)

Mode

Median

Mean

.

(Kurtosis)

Platykurtic Leptokurtic Mesokurtic

.

What is random variable?

(Random Variable)

Random Variable = Random Sample + Variable

.

(Probability) 100 20 80

1 100 ?

1

Probability

.

= 20/100 = .20 = 80/100 = .80 1

Probability

.

2 1 20 80 2 80 20

10 3 7 ?

2

Probability

.

10 2

Probability

.

0 1 2

1 1 2

::

HH

m mm mm m

=

1 20 80

2 80 20

7 3 (p=.03)

H1 2

= 10

(p=.03)

.

E K 4 7

.

H0 : = H1 :

E K 4 7

.

Verification Karl Poppers Falsification

Logic of Disconfirming Null Hypothesis Null hypothesis can never be proved to be true, only

falsifying or disconfirming

.

Type I and Type II Error

Type I Error H0 H0 Type II Error H0 H0

.

Type I and Type II Error

Type I Error False Alarm (Alpha)

Type II Error Failed Alarm (Beta)

.

Type I and Type II Error

Effect Size

.

Null Hypothesis

(Effect Size)

Power

.

Type I and Type II Error

H0 : H1 : Type I Error =

Type II Error =

.

Type I and Type II Error

H0 : A 1 .. H1 : A 1 .. Type I Error = A

1 .. Type II Error = A

1 ..

.

Type I and Type II Error

H0 : HIV H1 : HIV Type I Error =

HIV

Type II Error = HIV

.

Type I and Type II Error

H0 : H1 : Type I Error =

Type II Error =

.

Type I and Type II Error

Type I Type II Error

Type I Type II Type II

.

Significance Testing

Confidence Interval

.

Point Estimate Interval Estimate

Confidence Interval

Confidence Interval = Statistics + Sampling Error (Margin Error)

Confidence Interval

X Zn

s

.

(Precision)

H0

Confidence Interval

.

Confidence Interval

X Zn

s

200010,200 1.96400

10,200 196 10,004 10,396 = -

.

Statistical Significance Practical Significance

Significance

.

Types of Statistics

Difference Testing Statistics (Descriptive Statistics) t-test, ANOVA, ANCOVA, Chi-Square

Measures of Association Statistics Pearsons r, Regression, Canonical Correlation

Interdependence Statistics Factor Analysis, Cluster Analysis, Multidimensional

Scaling

.

Types of Statistics

Parametric Statistics t-test, ANOVA, Pearsons r, Regression

Nonparametric Statistics Mann-Whitney U, Wilcoxon, Kruskal Wallis

Robust Statistics Trimmed Mean, Winsorized Mean, Winsorized Variance,

Resampling Statistics

.

(Bivariate Statistics)

t-test Y = X Y X

2 Independent Sample

Assumptions Mann-Whitney U Dependent Sample

Assumptions Wilcoxon Signed Rank

.

(Bivariate Statistics)

ANOVA Y = X Y X

2 ANOVA

Assumptions Kruskal Wallis ANOVA for Repeated Measures

Assumptions Friedman Test

.

(Bivariate Statistics)

Pearsons r Y = X Y X

Chi-square Y = X Y X

.

(Multivariate Statistics)

Multiple Regression Manova (Multivariate Analysis of Variance) Discriminant Analysis Canonical Correlation Factor Analysis

.

(Multivariate Statistics)

Multiple Regression Y = X1+X2+X3+...+Xn Y X

( Dummy) Manova (Multivariate Analysis of Variance)

Y1+Y2+Y3+...Yn = X1+X2+X3+...+Xn Y X

.

(Multivariate Statistics)

Discriminant Analysis Y = X1+X2+X3+...+Xn Y X

( Dummy) Canonical Correlation

Y1+Y2+Y3+...Yn = X1+X2+X3+...+Xn Y X

.

(Multivariate Statistics)

Factor Analysis X1+X2+X3+...+Xn X

Multilevel Analysis Y = X1+X2+X3+...+Xn Y X

( Dummy) X

.

Multilevel Analysis

(OCB)

1. (JS) 2. (ORCOM) 3.

(POS) 4. (MOTIV)

1. (LEADER)

2. (CULTURE)

.

Structural Equation Modeling

EDU

DURA

EXP

TF

CH INS INT IND

QUAL

Q4

Q3

Q2

Q1

Q5

Q6

.