Reliability & Reliability & NormalityNormality

Tests ofTests of

Prepared by:Prepared by:Assoc. Prof. Dr Bahaman Abu SamahAssoc. Prof. Dr Bahaman Abu Samah

Department of Professional Development and Continuing EducationDepartment of Professional Development and Continuing EducationFaculty of Educational StudiesFaculty of Educational Studies

Universiti Putra MalaysiaUniversiti Putra Malaysia43400 Serdang, Selangor43400 Serdang, Selangor

A reliability analysis is used to A reliability analysis is used to measure: measure:

►► The extent to which a scale or instrument will The extent to which a scale or instrument will yield the same score when administered in yield the same score when administered in different times, locations, or populationsdifferent times, locations, or populations

►► Internal consistency of instrumentInternal consistency of instrument

►► Refers to the degree of consistency among Refers to the degree of consistency among the items that make up the instrument/scalethe items that make up the instrument/scale

►► Two estimates of internal consistency:Two estimates of internal consistency:1.1. Split-half coefficientSplit-half coefficient2.2. Cronbach alpha coefficientCronbach alpha coefficient

►► These two estimates can be used for These two estimates can be used for instrument that has multiple items and these instrument that has multiple items and these items are summed to obtain a total scoreitems are summed to obtain a total score

►► Cronbach alpha coefficient is one of the Cronbach alpha coefficient is one of the most commonly used measure of internal most commonly used measure of internal consistencyconsistency

►► For dichotomous data, this is equivalent to For dichotomous data, this is equivalent to the Kuder-Richardson 20 (KR20) coefficient the Kuder-Richardson 20 (KR20) coefficient

►► By convention, alpha should be .70 or higherBy convention, alpha should be .70 or higher

►► Cronbach alpha is quite sensitive to the Cronbach alpha is quite sensitive to the number of items in the scale; less items number of items in the scale; less items tends to produce a lower alphatends to produce a lower alpha

AlphaAlpha IndicatorIndicator

> .9> .9 Very goodVery good

> .8> .8 GoodGood

> .7> .7 AcceptableAcceptable

> .6> .6 QuestionableQuestionable

> .5> .5 WeakWeak

> .4> .4 UnacceptableUnacceptable

(George and Mallery, 2001)(George and Mallery, 2001)

procedurprocedureses

Item Statistics

3.4500 .82558 20

3.1000 1.37267 20

3.5500 1.23438 20

3.7000 1.30182 20

2.8500 1.18210 20

3.6000 1.35336 20

3.4000 1.35336 20

attitude item 1

attitude item 2

attitude item 3

attitude item 4

attitude item 5

attitude item 6

attitude item 7

Mean Std. Deviation N

Item Statistics

3.4500 .82558 20

3.1000 1.37267 20

3.5500 1.23438 20

3.7000 1.30182 20

2.8500 1.18210 20

3.6000 1.35336 20

3.4000 1.35336 20

attitude item 1

attitude item 2

attitude item 3

attitude item 4

attitude item 5

attitude item 6

attitude item 7

Mean Std. Deviation N

Check for anomalies in the data thru mean and varianceAre the means within the range of possible values?Are there any unusually largevariances?

Inter-Item Correlation Matrix

1.000 .655 .416 .622 .342 .499 .678

.655 1.000 .711 .872 .626 .759 .827

.416 .711 1.000 .468 .528 .548 .649

.622 .872 .468 1.000 .516 .765 .819

.342 .626 .528 .516 1.000 .849 .632

.499 .759 .548 .765 .849 1.000 .839

.678 .827 .649 .819 .632 .839 1.000

att1

att2

att3

att4

att5

att6

att7

att1 att2 att3 att4 att5 att6 att7

The covariance matrix is calculated and used in the analysis.

Inter-Item Correlation Matrix

1.000 .655 .416 .622 .342 .499 .678

.655 1.000 .711 .872 .626 .759 .827

.416 .711 1.000 .468 .528 .548 .649

.622 .872 .468 1.000 .516 .765 .819

.342 .626 .528 .516 1.000 .849 .632

.499 .759 .548 .765 .849 1.000 .839

.678 .827 .649 .819 .632 .839 1.000

att1

att2

att3

att4

att5

att6

att7

att1 att2 att3 att4 att5 att6 att7

The covariance matrix is calculated and used in the analysis.

In general, are the correlations among the variables positive?If not, should you reverse the scales for items with negativecorrelation?

Reliability Statistics

.929 .928 7

Cronbach'sAlpha

Cronbach'sAlpha Based

onStandardized

Items N of Items

Reliability Statistics

.929 .928 7

Cronbach'sAlpha

Cronbach'sAlpha Based

onStandardized

Items N of Items

Item-Total Statistics

20.2000 45.642 .625 .533 .933

20.5500 36.471 .901 .895 .905

20.1000 41.463 .648 .666 .930

19.9500 38.471 .813 .874 .915

20.8000 41.326 .695 .800 .926

20.0500 37.208 .863 .901 .909

20.2500 36.724 .898 .855 .905

att1

att2

att3

att4

att5

att6

att7

Scale Mean ifItem Deleted

ScaleVariance if

Item Deleted

CorrectedItem-TotalCorrelation

SquaredMultiple

Correlation

Cronbach'sAlpha if Item

Deleted

Item-Total Statistics

20.2000 45.642 .625 .533 .933

20.5500 36.471 .901 .895 .905

20.1000 41.463 .648 .666 .930

19.9500 38.471 .813 .874 .915

20.8000 41.326 .695 .800 .926

20.0500 37.208 .863 .901 .909

20.2500 36.724 .898 .855 .905

att1

att2

att3

att4

att5

att6

att7

Scale Mean ifItem Deleted

ScaleVariance if

Item Deleted

CorrectedItem-TotalCorrelation

SquaredMultiple

Correlation

Cronbach'sAlpha if Item

Deleted

… Cont.

►► One of the major assumption for parametric One of the major assumption for parametric statistics is data in the population must be statistics is data in the population must be normally distributednormally distributed

►► How to check whether your data meet the How to check whether your data meet the above assumption?above assumption?

►► Use Exploratory Data Analysis (EDA) in SPSSUse Exploratory Data Analysis (EDA) in SPSS

►► SPSS provides two statistics:SPSS provides two statistics:1.1. Kolmogorov-SmirnovKolmogorov-Smirnov2.2. Shapiro-WilkShapiro-Wilk

►► You data meet the assumption of normalityYou data meet the assumption of normality−− If the sig-value > alpha (.05)If the sig-value > alpha (.05)

►► In addition, SPSS also produces Normality In addition, SPSS also produces Normality Plots:Plots:−− Normal Q-Q PlotNormal Q-Q Plot−− Detrended Normal Q-Q PlotDetrended Normal Q-Q Plot

►► You data can be considered to be normally You data can be considered to be normally distributeddistributed−− If majority of the points in the Detrended If majority of the points in the Detrended

Normal Q-Q plot are within -.3 and +.3Normal Q-Q plot are within -.3 and +.3

►► Data can be considered normal Data can be considered normal if skewness is if skewness is between -1 and +1. However values between between -1 and +1. However values between ±2 is in many cases acceptable (George, D ±2 is in many cases acceptable (George, D and Mallery, P, 2005)and Mallery, P, 2005)

… Cont.

Descriptives

15.0500 .54035

13.9190

16.1810

15.0556

15.5000

5.839

2.41650

11.00

19.00

8.00

3.50

-.139 .512

-.726 .992

Mean

Lower Bound

Upper Bound

95% ConfidenceInterval for Mean

5% Trimmed Mean

Median

Variance

Std. Deviation

Minimum

Maximum

Range

Interquartile Range

Skewness

Kurtosis

yStatistic Std. Error

Descriptives

15.0500 .54035

13.9190

16.1810

15.0556

15.5000

5.839

2.41650

11.00

19.00

8.00

3.50

-.139 .512

-.726 .992

Mean

Lower Bound

Upper Bound

95% ConfidenceInterval for Mean

5% Trimmed Mean

Median

Variance

Std. Deviation

Minimum

Maximum

Range

Interquartile Range

Skewness

Kurtosis

yStatistic Std. Error

Tests of Normality

.153 20 .200* .952 20 .406yStatistic df Sig. Statistic df Sig.

Kolmogorov-Smirnova

Shapiro-Wilk

This is a lower bound of the true significance.*.

Lilliefors Significance Correctiona.

Tests of Normality

.153 20 .200* .952 20 .406yStatistic df Sig. Statistic df Sig.

Kolmogorov-Smirnova

Shapiro-Wilk

This is a lower bound of the true significance.*.

Lilliefors Significance Correctiona.

Data Set Data Set 3:3:The above data set comprises the following The above data set comprises the following variables:variables:

Support from PeersSupport from Peers S1 − S9S1 − S9Work environmentWork environment W1 − W11W1 − W11MotivationMotivation M1 − M12M1 − M12Job Performance (Y)Job Performance (Y) J1 − J13J1 − J13

VariablesVariables ItemItem

1.1. Test the reliability of the four variables:Test the reliability of the four variables:

Support from PeersSupport from PeersWork environmentWork environmentMotivationMotivationJob Performance (Y)Job Performance (Y)

State your conclusion and justify your State your conclusion and justify your answer.answer.

… Cont.

InstrumentInstrument No. of No. of ConbachConbach Items Items AlphaAlpha

Support from PeersSupport from Peers

Work environmentWork environment

MotivationMotivation

Job PerformanceJob Performance

Table 1: Table 1: Reliability Coeffients of Study Reliability Coeffients of Study InstrumentsInstruments

2.2. Test the normality assumption of the Test the normality assumption of the following variables:following variables:

−− SupportSupport−− WorkWork−− MotiveMotive−− PerformPerform

State your conclusion and justify your State your conclusion and justify your answeranswer

InstrumentInstrument Kolmogorov Kolmogorov pp

Support from PeersSupport from Peers

Work environmentWork environment

MotivationMotivation

Job PerformanceJob Performance

Table 2: Table 2: Normality Test of Study InstrumentsNormality Test of Study Instruments