sakesan tongkhambanchong, ph.d.(applied behavioral science research)

Statistical Analysis by SEM:From Theoretical Model to Hypothetical Model and

Statistical Analysis

Sakesan Tongkhambanchong, Ph.D.(Applied Behavioral Science Research)Faculty of Education, Burapha University

• Introduction to SEM– Research Process & Designs– Statistical Designs & Models– Variance & Covariance Matrix (CM) &

Correlation Matrix (KM)– LISREL’s Matrix –MRA: Multiple Regression Analysis by LISREL –MMRA: Multivariate Multiple Regression

Analysis by LISREL• Confirmatory Factor Analysis (CFA) – First-order CFA – Second-order CFA

• Structural Equation Modeling (SEM)

Agenda

Conceptualization

What Research is?

Operationalization

Empirical Evidence

ระดับหลักการ แนวคิด

ระดับปฏิบติัการ

รายงานผลการวจิยั

ความรู-้ความเขา้ใจ(Cognitive Process)การประยุกต์ระเบยีบวธิวีจิยัสู่การปฏิบติั, การดำาเนินการอยา่งมีระบบเป็นการแสดงหลักฐาน และสื่อสารไปยงัประชาคมวจิยั

Knowledge Inquiry and Validation

Bouma Gary D. & G.B.J.Atkinson. (1995) A Handbook of Social Science Research. (p.3)

How we know, what we know and

How we know, we know

What Research is?

• Research is…

“…the systematic process of collecting and analyzing information (data) in order to increase our understanding of the phenomenon about which we are concerned or interested.”

Research Process

Interest Idea Theory

? YY ?

X YA B?? A B C D

E F G H I

ConceptualizationSpecify the meaning of

the concepts and variables to be studied.

OperationalizationHow will we actually

measure the variables under study?

Choice of Research MethodExperimental Research

Survey Research Field Research Content Analysis Existing Data Research Comparative Research Evaluation Research Mixed Design

Population & SamplingWhom do we want to be

able to draw conclusions about?Who will be observed for the purpose?

ObservationCollecting data for

analysis and interpretation

Data ProcessingTransforming the data collected into a form

appropriate to manipulation and analysis

AnalysisAnalyzing data and drawing conclusions

ApplicationReporting

results and assessing their implications.

1

2

5

7 9

3

6

4

8

Interest Idea Theory

? YY ?

X YA B?? A B C D

E F G H I

ConceptualizationSpecify the meaning of

the concepts and variables to be studied.

OperationalizationHow will we actually

measure the variables under study?

Choice of Research MethodExperimental Research

Survey Research Field ResearchContent Analysis Existing Data Research Comparative Research Evaluation Research Mixed Design

Population & SamplingWhom do we want to be

able to draw conclusions about?Who will be observed for the purpose?

ObservationCollecting data for

analysis and interpretation

Data ProcessingTransforming the data collected into a form

appropriate to manipulation and analysis

AnalysisAnalyzing data and drawing conclusions

ApplicationReporting

results and assessing their implications.

Measurement Design

Statistical Design

Sampling DesignResearch Design

Data Collection Design

Problem Formulating Design

Research Process <------> Research Design

1

2

5

7 9

3

6

4

8

Validity

&

Reliability

of

Research

Low Validity = Low Accuracy = High BiasLow Reliability = Low Precision = High Variance

Prob

abilit

y De

nsity

High VarianceLow Precision

Reference value

High BiasLow Accuracy

ValueParameter

Statistics

Low Validity and Low Reliability

Low Validity = Low Accuracy = High BiasHigh Reliability = High Precision = Low Variance

Prob

abilit

y De

nsity

High Precision

Low Variance

Reference value

High BiasLow Accuracy

ValueParameter

Statistics

Low Validity and High Reliability

Validity = Accuracy = Low BiasReliability = Precision = Low Variance

Prob

abilit

y De

nsity

Precision

Reference value

Accuracy

Value

Parameter

Statistics

Validity and Reliability of Research Finding

Discrepancy between Conceptual Model & Data Collection

AB

SN

PBC

Intention Behavior

Research Conceptual FrameworkHypothesized Model: Causal Model (if X then Y)Statistical Design: Structural Equation Model (SEM)

Time-1

Time-2

Time-3

Data Collection: Cross-sectional

DesignAll variables were

collected at the same 1-point of time

(1-point of time)

Nature of Model: Longitudinal Design(3-points of time)

EXAMPLES OF CAUSAL MODEL TESTING

Emotional

Capital

psychological well-being

Affect Balanc

e

Resilience

Ultimate Dependent

VariableMediator Variable

Exogenous Variable

Endogenous Variable

Independent Variable

Emotional

Capital


Affect Balance

Resilience

Mindfulness

Ultimate Dependent


Exogenous Variable

Endogenous Variable


Emotional

Capital


Affect Balance

Resilience

Mindfulness

Ultimate Dependent


Exogenous Variable

Endogenous Variable


Moderator Variable

Emotional

Capital


Affect Balance

Resilience

Mindfulness

Ultimate Dependent


Exogenous Variable

Endogenous Variable


Research Conceptual FrameworkTheory of Planned Behavior :TPB (Ajzen, 1991)

Hypothesized Model & Number of Parameter Estimation

Testing Hypothesized Model & Parameter Estimated

Last Trimming Model & Parameter Estimated

Hypothetical

Model

&

Statistical

Models

10

X

1 00 10 0

1 0 00 1 00 0 10 0 0

d1

d2

d1

d2

d3

Observed variable (Nominal Scale)

Observed variable(Interval Scale)

1 Latent

variable

Causal relationshipRelationship

d1

1

Statistical Model: Symbols

Y

Mean

Mode

Median(Y)

Mean

Mode

Median

(X1)

Mean

Mode

Median

(X2)

Mean

Mode

Median

(X3)

Descriptive Statistics: How Importance?Central Tendency: Mean, Mode, MedianDispersion: Variance, Standard Deviation, Average Deviation

2X1 2

X2 2X3 2

Y

Statistical Analysis: Descriptive Statistics

Statistical Analysis: Mean, Mode, Median, AD, SD, SD2

X MeanA 5 5 0 0 0 AB 5 5 0 0 0 BC 5 5 0 0 0 CD 5 5 0 0 0 DE 5 5 0 0 0 EF 5 5 0 0 0 FG 5 5 0 0 0 GH 5 5 0 0 0 HI 5 5 0 0 0 IJ 5 5 0 0 0 J

Sum (S) 50 50 0 0 0 1 2 3 4 5 6 7 8 9Mean 5 5 0 0.00 0.00 SD2

AD 0.00 SD Me Mo Md

(X-M)2Abs[x-M]No. Data 1 Different (X-M)

X MeanA 1 5 -4 4 16B 2 5 -3 3 9C 3 5 -2 2 4D 4 5 -1 1 1E 5 5 0 0 0F 5 5 0 0 0G 6 5 1 1 1H 7 5 2 2 4I 8 5 3 3 9 EJ 9 5 4 4 16 A B C D F G H I J

Sum (S) 50 50 0 20 60 1 2 3 4 5 6 7 8 9Mean 5 5 0 2.00 6.00 SD2

AD 2.45 SD Me Mo Md

(X-M)2Abs[x-M]No. Data 2 Different (X-M)


X MeanA 1 5 -4 4 16B 1 5 -4 4 16C 3 5 -2 2 4D 3 5 -2 2 4E 5 5 0 0 0F 5 5 0 0 0G 7 5 2 2 4H 7 5 2 2 4I 9 5 4 4 16 A C E G IJ 9 5 4 4 16 B D F H J

Sum (S) 50 50 0 24 80 1 2 3 4 5 6 7 8 9Mean 5 5 0 2.40 8.00 SD2

AD 2.83 SD Mo Mo Mo MoMe,Mdn

No. Data 3 Different (X-M) Abs[x-M] (X-M)2

X MeanA 1 5 -4 4 16B 1 5 -4 4 16C 2 5 -3 3 9D 2 5 -3 3 9E 5 5 0 0 0F 5 5 0 0 0G 8 5 3 3 9H 8 5 3 3 9I 9 5 4 4 16 A C E G IJ 9 5 4 4 16 B D F H J

Sum (S) 50 50 0 28 100 1 2 3 4 5 6 7 8 9Mean 5 5 0 2.80 10.00 SD2

AD 3.16 SD Mo Mo Mo Mo

Abs[x-M]

Me,Mdn

No. Data 4 Different (X-M) (X-M)2


X MeanA 1 5 -4 4 16B 2 5 -3 3 9C 3 5 -2 2 4D 2 5 -3 3 9E 1 5 -4 4 16F 7 5 2 2 4G 8 5 3 3 9H 9 5 4 4 16I 9 5 4 4 16 E D J IJ 8 5 3 3 9 A B C F G H

Sum (S) 50 50 0 32 108 1 2 3 4 5 6 7 8 9Mean 5 5 0 3.20 10.80 SD2

AD 3.29 SD Mo Mo Me,Mdn Mo Mo

Data 5 Different (X-M)

(X-M)2Abs[x-M]No.

X MeanA 1 5 -4 4 16B 1 5 -4 4 16C 1 5 -4 4 16D 1 5 -4 4 16E 1 5 -4 4 16F 9 5 4 4 16 E JG 9 5 4 4 16 D IH 9 5 4 4 16 C HI 9 5 4 4 16 B GJ 9 5 4 4 16 A F

Sum (S) 50 50 0 40 160 1 2 3 4 5 6 7 8 9Mean 5 5 0 4.00 16.00 SD2

AD 4.00 SD Mo Me,Mdn Mo

Abs[x-M]No. Data 6 Different (X-M) (X-M)2

Bivariate relationship

(Correlation)

2X1 2

X2 2X3 2

Y

Cov (X1,Y)

Cov (X1,X2

)

Cov (X1,X3

) Cov (X2,X3

)

Cov (X2,Y)

Cov (X3,Y)

Bivariate: Variables, Variance & Covariance

Bivariate Correlation Analysis (rxy)

YX

rx

yYX

?

Z

? ?

r*xy = (rxy)/sqrt(rxx*ryy)

Measurement error = 0, reliability = 1

r*xy = (0.90)/(1.0*1.0)

= (0.90)/(1.0) = 0.90

0.90

r*xy =

(0.90)/(0.60*0.70) = (0.90)/(0.648) = 1.389

If rxx or ryy 1.00 , Measurement error 0

Bivariate Correlation (r > 1)

Statistical Model: The Meaning of r = 0The Misconception: If Pearson’s product–moment correlation, rxy, turns out equal to 0.00, this indicates that there is no relationship between the X and Y scores used to compute that correlation coefficient.Pearson’s r works well only if the relationship between X and Y is linear. If the relationship between the two variables is curvilinear, the value for r will underestimate the strength of the existing relationship

Statistical Model: The Strange of r

Statistical Model: The Meaning of r = 0

Statistical Model: Relationship Strength and r

The Misconception: If the data on two variables having similar distributional shapes are correlated using Pearson’s r, the resulting correlation coefficient can land anywhere on a continuum that extends from 0.00 to ±1.00; therefore,an r of +.50 (or –.50) indicates that the measured relationship is half as strong as it possibly could be.Pearson’s r: 1.0 = Perfect correlation

0.8 = Strong correlation 0.5 = Moderate correlation 0.2 = Weak correlation

0.00 = No correlation

Statistical Model: The Meaning of r & r2 The coefficient of determination, r2 , is a better measureof relationship strength than the correlation coefficient, r. This is because the square of r indicates the proportion of variability in one of the two variables that is explained by variability in the other variable

Statistical Model: The Meaning of r (why r> 0.30)30 40 50 60 70 80 90 100 110 120 130

t-table 1.700 1.680 1.680 1.670 1.670 1.660 1.660 1.660 1.650 1.640 1.640df 30 40 50 60 70 80 90 100 110 120 130

rxy 1-r2 root(1-r2) t-value t-value t-value t-value t-value t-value t-value t-value t-value t-value t-value0.100 0.990 0.995 0.532 0.620 0.696 0.765 0.829 0.888 0.943 0.995 1.044 1.092 1.1370.150 0.978 0.989 0.803 0.935 1.051 1.155 1.251 1.340 1.423 1.502 1.577 1.648 1.7160.200 0.960 0.980 1.080 1.258 1.414 1.555 1.683 1.803 1.915 2.021 2.121 2.217 2.3090.250 0.938 0.968 1.366 1.592 1.789 1.966 2.129 2.280 2.422 2.556 2.683 2.805 2.9210.300 0.910 0.954 1.664 1.939 2.179 2.395 2.593 2.777 2.950 3.113 3.268 3.416 3.5580.350 0.878 0.937 1.977 2.303 2.589 2.845 3.081 3.300 3.505 3.699 3.883 4.059 4.2270.400 0.840 0.917 2.309 2.690 3.024 3.324 3.599 3.854 4.094 4.320 4.536 4.741 4.9380.450 0.798 0.893 2.666 3.106 3.491 3.838 4.155 4.450 4.727 4.988 5.237 5.474 5.7010.500 0.750 0.866 3.055 3.559 4.000 4.397 4.761 5.099 5.416 5.715 6.000 6.272 6.5320.550 0.698 0.835 3.485 4.060 4.563 5.015 5.431 5.816 6.178 6.519 6.844 7.154 7.4510.600 0.640 0.800 3.969 4.623 5.196 5.712 6.185 6.624 7.036 7.425 7.794 8.147 8.4850.650 0.578 0.760 4.526 5.273 5.926 6.514 7.053 7.554 8.024 8.467 8.889 9.291 9.6770.700 0.510 0.714 5.187 6.042 6.791 7.465 8.083 8.657 9.195 9.703 10.186 10.648 11.0900.750 0.438 0.661 6.000 6.990 7.856 8.635 9.350 10.014 10.637 11.225 11.784 12.317 12.8290.800 0.360 0.600 7.055 8.219 9.238 10.154 10.995 11.776 12.508 13.199 13.856 14.484 15.0850.850 0.278 0.527 8.538 9.947 11.179 12.289 13.306 14.251 15.137 15.974 16.769 17.528 18.2550.900 0.190 0.436 10.926 12.728 14.305 15.725 17.026 18.235 19.369 20.440 21.457 22.429 23.3600.950 0.098 0.312 16.099 18.755 21.079 23.170 25.089 26.870 28.541 30.119 31.618 33.049 34.421

sample size(n)

Criteria

The Misconception: A single outlier cannot greatly influence the value of Pearson’s r, especially if N is large.Pearson’s r:

Statistical Model: The Effect of a Single Outlier on r

Statistical Model: The Effect of a Single Outlier on r

STATISTICAL MODEL

ANALYSIS USINGDEPENDENT TECHNIQUES

Sakesan Tongkhambanchong, Ph.D (Applied Behavioral Science Research)

10X

1Y

One-way ANOVA (Independent sample t-test)

Ypo

stYpre

One-way ANOVA with repeated measured (Dependent sample t-test)

One Factor Within-subjects Design

?

?

Different

DifferentChange, Gain, Development

One Factor Between-subjects DesignDirect effects

Direct effects

X1

Y

1 00 10 0

One-way ANOVA (F-test)

YT2YT1

One-way ANOVA with repeated measured

Within-subjects Design

YT2

?

? ??

Between-subjects DesignDirect effects

10X

1 Y

Two-way ANOVA (non-additive model) -- > Interaction effects

X2

1 00 10 0

?Main effect

?Main effect

Interaction effect

?Between-subjects Design

Y

10

10

1 00 10 0

Multi-way ANOVA (Non-additive model) (the interactive structure)X1

X2

X3

Between-subjects Design

Y

One-way Analysis of Covariance (ANCOVA) additive model

X1

1 00 10 0

(Covariate)

X1

? Between-subjects Design

Bivariate Correlation Analysis (rxy)

YX

rx

y YX Z

Cov(x,y)

rx

y

ry

z

rx

z

Cov(x,z)

Cov(y,z)

Cov(x,y)

Standardized Score

Raw Score

X1

X2

X3

Y

Simple Regression Analysis (SRA)Multiple Regression Analysis (MRA) (Convergent Causal structure)

No Correlatio

n(r = 0)

Direct effects

y.x1

y.x2

y.x3X Yy.x

YX

rx

y

X1

X2

X3

Multivariate Multiple Regression Analysis (MMR)(Convergent Causal structure two or several times)

Y1

Y2

Direct effects

No Correlatio

n(r = 0)

10

X1

X2

X3

Two-groups Discriminant Analysis (Discriminant structure)Binary Logistic Regression Analysis

(Y)

W

W

W

Direct effects

No Correlatio

n(r = 0)

X1

X2

X3

Multiple Discriminant Analysis(Discriminant Structure with more than two population groups)

1 00 10 0

(Y)

W

W

W

Direct effects

No Correlatio

n(r = 0)

Y1

10

10

1 00 10 0

Multivariate Analysis of Variance -- MANOVA(Interactive Structure two or several times)

Y2

X1X2

X3

ANALYSIS USINGINTERDEPENDENT

TECHNIQUES


U1 V1

Canonical variates

(Independent)

Canonical variates

(Dependent)

U2 V2

RC1, 1

X1

X2

X3

X4

Y1

Y2

Set of Independe

nt variables

Set of Dependent variables

Canonical Function-1

RC2, 2

Canonical Loading2

Canonical Loading2

Simple Correlatio

n

Simple Correlatio

n

Canonical Correlation Analysis (CCA)

Canonical weight

Canonical Weight

Canonical Function-2

FACTOR ANALYSIS:PCA & EFA & CFA


(Conceptualization)

High

Low(Operationalizatio

n)

Leve

l of A

bstra

ctio

n

Concept &

Construct

Variables

Indicator Indicator Indicator

Item Item Item Item Item Item Item Item Item

Conceptual Definition

Theoretical Definition

Real Definition

Operational Definition(How to

measured?)

Generalized idea

Communication

Real world Hypothesis testing

TimeSpace

Context

Test-1 Test-2 Test-n

From Conceptualization to Operationalization & Measurement

Y

X

y1y2

x1x2x3

y3

Formative Indicator Model

Reflective Indicator Model

1

1

2

3

1

Formative & Reflective Indicator Model

Principle Component Analysis (PCA)

2

3

1

X1 X2 X3 X4 X5 X6 X7 X8 X9

The Component Loading or the Structure/Pattern Coefficient

Factor structure / Component / Dimensions / Unmeasured variables

Measured variables (Observed) / Indicators / Items

Measured variables

(Observed) / Indicators /

Items

Factor structure /

Component / Dimensions / Unmeasured

variables

2

3

1

X1 X2 X3 X4 X5 X6 X7 X8

The Factor Loading or the Structure/Pattern Coefficient

Exploratory Factor Analysis (EFA) with Orthogonal Rotation

Measured variables


Items

Factor structure /


variables

Errors or Uniqueness

Measured variables


Items

2

3

1

X1 X2 X3 X4 X5 X6 X7 X8 X9


Factor structure /


variables

Exploratory Factor Analysis (EFA) with Oblique Rotation


2,1

3,1 3,

2

2

3

1

X1 X2 X3 X4 X5 X6 X7 X8 X9


Confirmatory Factor Analysis (CFA)

2,1

3,1 3,

2

Some Errors are correlated

Some Factors are correlated/ Some Factors are not correlated

2,11,1 3,1 4,2 5,2 6,2 7,3 8,3 9,3 Measured variables


Items

Factor structure /


variables


12345678

91011121314151617

18192021222324252627

282930313233

x1x2x3x4x5x6x7x8

x9x10x11x12x13x14x15x16x17

x18x19x20x21x22x23x24x25x26x27

x28x29x30x31x32x33

F-1

F-2

F-3

F-4

First-order Confirmatory Factor Analytic Model

2,1

3,2

4,3

3,1

4,2

4,1

First-order Confirmatory Factor Analysis (CFA)

12345678

91011121314151617

18192021222324252627

282930313233

x1x2x3x4x5x6x7x8

x9x10x11x12x13x14x15x16x17

x18x19x20x21x22x23x24x25x26x27

x28x29x30x31x32x33

F-1

F-2

F-3

F-4

F-A

F-B

Second-order Confirmatory Factor Analytic Model

Second-order Confirmatory Factor Analysis (CFA)

First

, Sec

ond-

orde

r Fac

tor

Anal

ysis

First-order CFA and Second-order CFA

M-1

x1x2x3x4x5x6x7x8

x9x10x11x12x13x14x15x16x17

x18x19x20x21x22x23x24x25x26x27

x28x29x30x31x32x33

LV-1

LV-2

LV-3

LV-4

M-2

Stat

istica

l Des

ign:

Mul

titra

its-

Mul

timet

hods

Mat

rix

First-order CFA and Multitrait-Multimethod Matrix (MTMM)

ANALYSIS USINGDEPENDENT & INTERDEPENDENT

TECHNIQUES


Y

X1

X2

X3

Causal Modeling I: Path Analysis with Observed Variables

Y

X1

X2

X5X4

Total Effect = Direct + Indirect Effects


X3

2

1,1

2,1

3,1

2 Y6,

2

Y4,

2Y5,

2

1X3,

1

X1,

1X2,

1

2X6,

2

X4,

2X5,

2

1Y3,

1

Y1,

1Y2,

1

Causal Modeling II: Path Analysis with Latent Variables Linear Structural Equation Modeling (SEM)

4,2

1,1

5,2

6,3

2,1

3,1

4,2

5,2

6,2

1


SEM = [Path Analysis + Confirmatory Factor Analysis]

Multiple Regression Analysis: MRMultivariate Multiple Regression

Analysis: MMRPath Analysis: PA

LISREL Programs

Multiple Regression Analysis: MR

Y

X1

X2

X3

Independent variables

Dependent variables

No

Correlation

(r = 0)

Direct effects

y.x1

y.x2

y.x3

TI Regression Model

DA NO=250 NI=4 MA=CM

LAY X1 X2 X3

KM1.0000.470 1.0000.516 0.652 1.0000.485 0.506 0.479 1.000

ME6.638 6.338 6.420 6.634

SD1.928 1.945 1.800 1.921

MO NY=1 NX=3 GA=FU PH=SY PS=SY

PA GA1 1 1

PA PH10 10 0 1

PDOU SE TV RS MR EF SS SC MI ND=3 AD=OFF

Multivariate Multiple Regression Analysis: MMR

Y1A

B

C

Independent variables

Dependent variables

No

Correlation

(r = 0)

Direct effects

y1.x

1

y.x2

y1.x

3

TI Testing MMRDA NI=6 NO=320 MA=CMLA Y1 Y2 A B C D KM SY1.0000.269 1.0000.440 0.227 1.000 0.313 0.298 0.175 1.0000.490 0.319 0.501 0.436 1.0000.276 0.262 0.240 0.352 0.424 1.000

ME93.94 87.57 24.47 86.12 110.45 96.27 SD6.347 6.422 3.524 5.416 9.145 6.046 MO NX=4 NY=2 GA=FU PH=SY PS=SY

PA GA1 1 1 11 1 1 1

PA PH10 10 0 10 0 0 1

PA PS10 1

PDOU SE TV RS MR MI ND=3 AD=OFF

D y.1x4 Y2

y2.x

1

y2.x2

y.2x3

y2.x4

Path Analysis with Observed Variable: PA

M1

X1

X2

X3

Independent

variables

Dependent variables

No Correlation(r = 0)

Total effect = Direct effects + Indirect effect

M2

Y

X4

X5

TI Path analysisDA NI=8 NO=320 MA=KM

LAM1 M2 Y X1 X2 X3 X4 X5

KM SY1.000.40 1.000.70 0.60 1.000.40 0.10 0.20 1.000.60 0.10 0.20 0.20 1.00-.40 0.10 0.20 -.20 0.20 1.000.10 0.50 0.20 0.10 0.10 0.10 1.000.10 0.50 0.20 0.10 0.10 0.10 0.20 1.00

MO NX=5 NY=3 GA=FU BE=SD PH=SY PS=SY

PA GA1 1 1 0 00 0 0 1 10 0 0 0 0

PA BE0 0 01 0 01 1 0

PA PH10 10 0 10 0 0 10 0 0 0 1

PA PS10 10 0 1

PDOU SE TV RS MR EF SC MI=OFF ND=2

Research as a Causal ChainFor want of a nail, the shoe was lost.For want of the shoe, the horse was lost.For want of the horse, the rider was lost.For want of the rider, the battle was lost.For want of the battle, the kingdom was lost.And all for the want of a nail.

หากขาดตะปูแค่ตัวเดียว เกือกมา้อาจจะหลดุได้หากไมม่เีกือกมา้ มา้ก็ไมอ่าจใชง้าน

และหากขาดซึง่มา้ ก็ไมอ่าจสง่เอกสารท่ีสำาคัญและเมื่อหากขาดซึง่เอกสารท่ีสำาคัญ การศึกก็อาจจะ

ปราชยัและเมื่อการศึกปราชยั ก็จะสิน้สญูอาณาจกัร

และทกุสิง่น้ีเป็นเหตมุาจากการขาดซึง่ตะปูแค่ตัวเดียว

Thank youPhoenix.sake@gm

ail.com

sakesan tongkhambanchong, ph.d.(applied behavioral science research)

Documents

knowwhat research

analysisanalysisanalyzing

observationcollecting

information data

low reliabilitylow validity

low biasreliability

high biaslow reliability

high reliabilityvalidity