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reliability.pdf, Exercises of Statistics

Reordering of the items and/or regrouping of items in the test/scale can result in different reliability estimates using the split-half method.

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HANDOUT ON RELIABILITY
Reliability refers to the consistency and stability in the results of a test or scale. A test is
said to be reliable if it yields similar results in repeated administrations when the attribute being
measured is believed not to have changed in the interval between measurements, even though the
test may be administered by different people and alternative forms of the test are used. For
example, if you weighed yourself twice consecutively and the first time the scale read 130 lbs.
And the second time 140 lbs., we would say that the scale was an unreliable measure of weights.
In addition, to be reliable, an instrument or test must be confined to measuring a single construct
and only one dimension. For example, if a questionnaire designed to measure anxiety
simultaneously measured depression, the instrument would not be a reliable measure of anxiety.
A reliable instrument or test must meet two conditions: it must have a small random error; and it
must measure a single dimension.
Among others, one major source of inconsistency in test results is random measurement
error. A primary concern of test developers and test users is therefore to determine the extent to
which random measurement errors influence test performance. The classical true score model
provides a useful theoretical framework for defining reliability and for the development of
practical reliability investigations. In the classical true score model, an examinee’s or a subject’s
observed score on a particular test is viewed as a random sample of one of the many possible test
scores that a person could have earned under repeated administrations of the same test; and the
observed score (X) is envisioned as the composite of two hypothetical components - a true score
(T) and a random error component (E). T is defined as the expected value of the examinee’s test
scores over many repeated testings with the same test and E is the discrepancy between an
examinee’s observed score and his/her true score. The following equation summarizes the
relationship between X, T and E:
X = T + E
An important question which follows from the above is: How closely related are the
examinees’ true and observed scores on a particular test or instrument? Based on the classical
true score model1, two indices are derived to measure the relationship between true and observed
scores.
1. Reliability coefficient - defined as the correlation between parallel measures2 .
1“X = T + E” is only one of the assumptions of the classical true score theory. Please
consult texts on measurement/test theory for other assumptions in the model as well as how the
reliability coefficient and the reliability index are derived from the model.
2According to classical true score theory, two measures/tests are defined as parallel when
1) each examinee or subject has the same true score on both measures/tests, and 2). The error
variances of the two measures/tests are equal. Based on this definition, it is sensible to assume that
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HANDOUT ON RELIABILITY

Reliability refers to the consistency and stability in the results of a test or scale. A test is

said to be reliable if it yields similar results in repeated administrations when the attribute being

measured is believed not to have changed in the interval between measurements, even though the

test may be administered by different people and alternative forms of the test are used. For

example, if you weighed yourself twice consecutively and the first time the scale read 130 lbs.

And the second time 140 lbs., we would say that the scale was an unreliable measure of weights.

In addition, to be reliable, an instrument or test must be confined to measuring a single construct

and only one dimension. For example, if a questionnaire designed to measure anxiety

simultaneously measured depression, the instrument would not be a reliable measure of anxiety.

A reliable instrument or test must meet two conditions: it must have a small random error; and it

must measure a single dimension.

Among others, one major source of inconsistency in test results is random measurement

error. A primary concern of test developers and test users is therefore to determine the extent to

which random measurement errors influence test performance. The classical true score model

provides a useful theoretical framework for defining reliability and for the development of

practical reliability investigations. In the classical true score model, an examinee’s or a subject’s

observed score on a particular test is viewed as a random sample of one of the many possible test

scores that a person could have earned under repeated administrations of the same test; and the

observed score (X) is envisioned as the composite of two hypothetical components - a true score

(T) and a random error component (E). T is defined as the expected value of the examinee’s test

scores over many repeated testings with the same test and E is the discrepancy between an

examinee’s observed score and his/her true score. The following equation summarizes the

relationship between X, T and E:

X = T + E

An important question which follows from the above is: How closely related are the

examinees’ true and observed scores on a particular test or instrument? Based on the classical

true score model 1 , two indices are derived to measure the relationship between true and observed

scores.

1. Reliability coefficient - defined as the correlation between parallel measures

2

(^1) “X = T + E” is only one of the assumptions of the classical true score theory. Please

consult texts on measurement/test theory for other assumptions in the model as well as how the reliability coefficient and the reliability index are derived from the model.

2 According to classical true score theory, two measures/tests are defined as parallel when

  1. each examinee or subject has the same true score on both measures/tests, and 2). The error variances of the two measures/tests are equal. Based on this definition, it is sensible to assume that

Dr. Robert Gebotys 2003

This coefficient ( Dxx,) can be shown to equal the ratio F

2 T/F

2

X , the proportion of

observed score variance due to true score variance.

2. Reliability index - defined as the correlation between true and observed scores on a single

measure (i.e. DXT) and is equivalent to Fx/FT.

However, in reality, we rarely know about the true scores. Besides, the reliability

coefficient defined above is purely a theoretical concept because it is not possible to verify that

two tests are truly parallel. Therefore reliability of tests have to be estimated using other

methods.

Methods of Estimating Reliability:

The methods of estimating reliability can be roughly categorized into two groups: one

group of methods includes methods that require two separate test administrations; and another

group of methods includes those using one test administration.

1. Methods Requiring Two Separate Test Administrations:

a. Test-Retest Method -

Test-Retest method yields a reliability estimate, m 12 , is based on testing the same

examinees/subjects twice with the same test/scale and then correlating the results. If each

examinee/subject receives exactly the same observed score on the second testing as

he/she did on the first, and if there is some variance in the observed scores among

examinees/subjects, then the correlation is 1.0, indicating perfect reliability. The

correlation coefficient obtained from this test-retest procedure is called the coefficient of

stability, which measures how consistently examinees/subjects respond to this test/scale

at different times.

b. Alternate-Forms Method -

This method involves constructing two similar forms of a test/scale (i.e. both forms have

the same content) and administering both forms to the same group of examinees within a

very short time period. The correlation between observed scores on the alternate

test/scale forms, (i.e. mxy computed using the Pearson product moment formula), is n

estimate of the reliability of either one of the alternate forms. This correlation coefficient

is known as coefficient of equivalence.

a. Test-Retest with Alternate Forms Method

This method is a combination of the test-retest and alternate-forms methods. In

parallel tests are matched in content.

Dr. Robert Gebotys 2003

the two halves of the test/scale are parallel forms of one another, the Spearman Brown

prophecy formula is used to estimate the reliability coefficient of the entire test/scale.

The Spearman Brown prophecy formula is:

Dxx’ = 2 DYY, / 1 + DYY,

where Dxx ’ is the reliability projected for the full-length test/scale, and DYY` is the

correlation between the half-tests. DYY, is also an estimate of the reliability of the

test/scale if it contains the same number of items as that contained in the half-test.

If the two halves of test/scale are not parallel, the reliability of the full-length

test/scale is calculated using the formula for coefficient " for split halves:

" = 2 [ F^2 x - ( F^2 Y1 + F^2 Y2 ) ] 1 / F^2 x

Where F

2

Y1 and^ F

2

Y2 are the variances of scores on the two halves of the test, and^ F

2 x

is the variance of the scores on the whole test, with X = Y l + Y 2.

In the SPSS program, the ‘SPLIT-HALF” model for reliability analysis is

conducted on the assumption that the two halves of the test/scale are parallel forms.

Hence, coefficient " has to be obtained by hand calculations.

Besides, it must be noted that split-half reliability estimate is contingent upon how

the items in the test/scale are arranged. Reordering of the items and/or regrouping of

items in the test/scale can result in different reliability estimates using the split-half

method. Hence, reliability estimate obtained from the even/odd method (a method which

is similar to split-half method and which will be mentioned below) on the same test/scale

will most likely be different from the reliability estimated by using the split-half method.

c. Even/Odd Method -

Even/odd method is similar to split-half method, with the exception that the

estimation of reliability for the entire test/scale is no longer based on correlating the first

half of the test/scale with the second half, but instead it is based on correlating even items

with odd items.

Determining Reliability Using SPSS:

Example 1:

The following illustrative example contains six items extracted from a scale used

to measure adolescents’ attitude towards the use of physical aggressive behaviours in

their daily life. Each item in the scale refers to a situation where physical aggressive

behaviour is or is not used. Adolescents are asked whether they agree or disagree with

each and every item on the scale. Adolescents’ responses to the items are converted to

scores of either 1 or 0, where 0 represents the endorsement of the use of physical

aggressive behaviours and 1 represents disapproval of the use of physical aggressive

behaviours. Below are the contents of the six items as well as the scores of 14

adolescents on these six items:

Item No. Content

1 When there are conflicts, people won’t listen to you unless you get physically

aggressive.

2 It is hard for me not to act aggressively if I am angry with someone.

3 Physical aggression does not help to solve problems, it only makes situations

worse.

4 There is nothing wrong with a husband hitting his wife if she has an affair.

5 Physical aggression is often needed to keep things under control.

6 When someone makes me mad, I don’t have to use physical aggression. I can

think of other ways to express my anger.

The command “statistics all” will instruct the computer to give us the following additional

statistics from reliability analysis: 4

a. Item means and standard deviations;

b. Inter-item covariance matrix;

c. Inter-item correlation matrix;

d. Scale mean, variance and standard deviation;

e. Summary statistics for item means, item variances, inter-item covariances, inter-item

correlations, and item-total statistics (i.e. summary statistics comparing each item to the

scale composed of other items (including alpha (") if that item is deleted));

f. ANOVA;

g. Hotelling’s T-Squared;

h. Other statistics like Friedman’s chi-square, Kendall’s coefficient of concordance and

Cochran’s Q, if applicable.

2. Assessing Split-Half Reliability:

reliability variables=item1 to item6 /

statistics=scale/

summary=means variances covariance correlations/

scale (test score) =item1 to item6/

model=split

The “scale (test score) =item1 to item6" subcommand specifies the number as well as the

order of the items on which subsequent reliability analysis is to be performed. The

subcommand “model=split’ instructs the computer to use the “SPLIT-HALF” model for

reliability analysis on the scale. A split-half reliability analysis will be performed based on

the order in which the items were named on the preceding “scale” subcommand, i.e., the

first half of the items (rounding up if the number of items is odd) form the first part/half,

and the remaining items form the second part/half. In this case, items 1, 2 and 3 will form

the first part and items 4, 5 and 6 will form the second part.

Since the inter-item covariance matrix, inter-item correlation matrix, item means and

standard deviations as well as the item-total statistics produced from this reliability analysis

are the same as those produced in the preceding “ALPHA” model (because the two

analyses were performed on the same set of data), we may not want to look at these again

at this stage. However, we may be interested in knowing the following:

a. the means and standard deviations of each of the two parts of the scale;

b. the summary statistics (i.e. item means, item variances, inter-item

4 Only outputs containing statistics categorized under a to e will be reproduced and discussed in subsequent pages because these are already sufficient in terms of serving the purposes

and needs of our present analyses. Statistics under categories f to h will not be reported.

Dr. Robert Gebotys 2003

covariances and inter-item correlations) of each of the two parts of the scale.

The insertion of the two subcommands, namely, “statistics=scale” and “summary=...

correlations”, into the computer program will enable us to obtain the above-mentioned

statistics which were not provided by the previous analysis based on the “ALPHA” model. 5

3. Estimating Even/Odd Reliability:

reliability variables=item1 to item6/

scale (test score) =item1 item3 item5 item2 item4 item6/

model=split

statistics all

Since “EVEN/ODD” model for reliability analysis is not an available option in SPSS, the

“SPLIT-HALF” model is used for this analysis. However, in order that the “SPLIT-

HALF” model can be successfully employed for estimating even/odd reliability, the order

of the items listed in the preceding “scale” subcommand must have been arranged in such a

way that the odd items form the first part of the scale and that the even items form the

remaining part. Please see the above “scale” subcommand for an illustration.

As already mentioned, the command “statistics all” instructs the computer to produce the

eight categories of additional statistics from reliability analysis

6

In a later section, it will be

shown that the item-total summary statistics, items means and standard deviations, inter-

item covariance matrix, and the inter-item correlation matrix produced in this analysis are

virtually the same as those produced from the “ALPHA” model of reliability analysis, with

the exception that the statistics are displayed slightly differently as a result of reordering

the six items. Alternatively, additional statistics which are specific to this model of

reliability analysis and which are of interest to us can be obtained by using the same

“statistics=scale” and “summary=... correlations” subcommands as those shown in the

computer program for “SPLIT-HALF” model of reliability analysis.

Conducting All the Above-mentioned 3 Models of Reliability Analyses on the Set of Scores

Obtained from 14 Adolescents for the 6 Items Using SPSS

1. SPSS Computer Program

5 If you want the full set of additional statistics from split-half reliability analysis, you have to write into the program the command “statistics all” in the same manner as that shown in the computer program for conducting the “ALPHA” model of reliability test.

(^6) Again, only statistics under categories a to e will be reported and discussed in

subsequent pages.

Dr. Robert Gebotys 2003

R E L I A B I L I T Y A N A L Y S I S - S C A L E (T E S T S C O R)

Correlation Matrix

ITEM1 ITEM2 ITEM3 ITEM4 ITEM

ITEM1 1.

ITEM2 .6889 1.

ITEM3 .6455 .3443 1.

ITEM4 .3443 .3443 .4167 1.

ITEM5 .6455 .3443 .7083 .4167 1.

ITEM6 .3778 .6889 .3443 .3443.

ITEM

ITEM6 1.

It is shown in the above inter-item correlation matrix that the largest correlation coefficient

occurs between items 3 and 5 (i.e. r = .7083). Item 2 is also fairly highly correlated with

both item 1 and item 6 (i.e. r in both cases are .6889). The lowest correlation coefficient is

.3443, which occurs between a number of pairs of items (e.g. between item 1 and item 4,

etc.)

R E L I A B I L I T Y A N A L Y S I S - S C A L E (T E S T S C O R)

R E L I A B I L I T Y A N A L Y S I S - S C A L E (A L P H A)

R E L I A B I L I T Y A N A L Y S I S - S C A L E (A L P H A)

N of Cases = 14.

N of Statistics for Mean Variance Std Dev Variables Scale 2.7857 5.1044 2.2593 6

Item Means Mean Minimum Maximum Range Max/Min Variance .4643 .3571 .5714 .2143 1.6000.

Item Variances Mean Minimum Maximum Range Max/Min Variance .2555 .2473 .2637 .0165 1.0667.

Inter-item Covariances Mean Minimum Maximum Range Max/Min Variance .1190 .0879 .1868 .0989 2.1250.

Inter-item Correlations Mean Minimum Maximum Range Max/Min Variance .4665 .3443 .7083 .3641 2.0575.

The section of output reproduced above gives us descriptive statistics for the scale 9 and

summary statistics for the items.

From the above section, it can be seen that the average score for the scale is 2.7857 and the

standard deviation is 2.2593. The average score on an item is 0.4643, with a range of 0.

(i.e. maximum minus minimum). The average of the item variances is 0.2555, with a minimum

of 0.2473 and a maximum of 0.2637. These show that the items in the scale have fairly

comparable variances. The average covariance between the items is .119. The correlations

between the items range from .3443 to .7083. The ratio between the largest and the smallest

correlations is .7083/.3443, or 2.0575. The average correlation between the items is .4665.

The item-total summary statistics forms the next section of the output and is reproduced below:

Item-total Statistics

Scale Scale Corrected Mean Variance Item- Squared Alpha if Item if Item Total Multiple if Item Deleted Deleted Correlation Correlation Deleted

ITEM1 2.4286 3.4945 .7330 .7511. ITEM2 2.4286 3.6484 .6364 .7469. ITEM3 2.2143 3.5659 .6572 .6000. ITEM4 2.2143 3.8736 .4784 .2533. ITEM5 2.2143 3.5659 .6572 .6000. ITEM6 2.4286 3.8022 .5440 .5733.

Item-total Statistics

For each item, the first column of the above set of statistics shows what the average score for

the scale would be if the item were excluded from the scale. For example, if item 1 were

deleted from the scale, the mean score of the scale would be 2.4286. The next column in this

set of statistics is the scale variance if the item were eliminated. The column labeled

“Corrected Item-Total Correlation” is the Pearson correlation coefficient between the score

on the individual item and the sum of the scores on the remaining items. For example, the

smallest correlation reported is .4784, which occurs between the score on item 4 and the sum

of the scores of items 1, 2, 3, 5 and 6. We can say that the relationship between item 4 and the

other items is not very strong. Comparatively speaking, the relationship between item 1 and

the other items is much stronger, with r = .7330.

Another way of looking at the relationship between an individual item and the rest of the scale

is to try to predict a person’s score on the item based on the scores obtained on the other

(^9) The scale in this case is formed by items 1 to 6. For each individual adolescent (or case), a

score on the scale is computed by adding his/her scores on the six items.

R E L I A B I L I T Y A N A L Y S I S - S C A L E (S P L I T)

N of Cases = 14.

N of Statistics for Mean Variance Std Dev Variables Part 1 1.2857 1.6044 1.2666 3 Part 2 1.5000 1.3462 1.1602 3 Scale 2.7857 5.1044 2.2593 6

Item Means Mean Minimum Maximum Range Max/Min Variance Part 1 .4286 .3571 .5714 .2143 1.6000. Part 2 .5000 .3571 .5714 .2143 1.6000. Scale .4643 .3571 .5714 .2143 1.6000.

Item Variances Mean Minimum Maximum Range Max/Min Variance Part 1 .2527 .2473 .2637 .0165 1.0667. Part 2 .2582 .2473 .2637 .0165 1.0667. Scale .2555 .2473 .2637 .0165 1.0667.

Inter-item Covariances Mean Minimum Maximum Range Max/Min Variance Part 1 .1410 .0879 .1703 .0824 1.9375. Part 2 .0952 .0879 .1099 .0220 1.2500. Scale .1190 .0879 .1868 .0989 2.1250.

Inter-item Correlations Mean Minimum Maximum Range Max/Min Variance Part 1 .5596 .3443 .6889 .3446 2.0010. Part 2 .3684 .3443 .4167 .0724 1.2103. Scale .4665 .3443 .7083 .3641 2.0575.

Please note that the descriptive statistics for the entire scale and the summary statistics over

all items in the entire scale given in these sections of the computer output are identical to those

produced in the corresponding sections of the output based on the “ALPHA” model of

reliability analyses (check statistics on the “scale” row of corresponding sets of statistics).

The significant feature of these sections of the output is that descriptive and summary statistics

are given for each of the two parts of the scale, namely, Part 1 which is formed by items 1, 2

and 3, and Part 2 which is composed of items 4, 5 and 6. It is clearly evident that the two

Parts have different means and standard deviations, as well as different item means, item

variances, inter-item covariances and inter-item correlations.

Reliability Coefficients 6 items

Correlation between forms = .7328 Equal-length Spearman-Brown =.

Guttman Split-half = .8439 Unequal-length Spearman-Brown =.

Alpha for part 1 = .7911 Alpha for part 2 =.

3 items in part 1 3 items in part 2

Dr. Robert Gebotys 2003

The above section of the output contains the results of reliability analysis based on the

“SPLIT-HALF” model. The correlation between the two halves (or parts), labeled on the

output as “Correlation between forms”, is .7328. This is an estimate of the reliability of the

scale if it has three items. The equal length Spearman-Brown coefficient, which has a value of

.8458 in this case, tells us what the reliability of the entire scale would be if it was made up of

two equal (or parallel) parts that have a three-item reliability of .7328. If the number of items

on each of the two parts is not equal, the unequal length Spearman-Brown coefficient can be

used to estimate the reliability of the overall scale. In the present example, since the two parts

of the scale are of equal length, the two Spearman-Brown coefficients are identical. The

Guttman split-half coefficient is another estimate of the reliability of the overall scale. It does

not assume that the two parts are equally reliable or have the same variance, hence the

reliability coefficient produced is smaller. Finally, separate values of Cronbach’s " are also

shown for each of the two parts of the scale in the output.

c. Reliability Analysis - “EVEN/ODD” Model

R E L I A B I L I T Y A N A L Y S I S - S C A L E (T E S T S C O R)

****** Method 2 (covariance matrix) will be used for this analysis ******

R E L I A B I L I T Y A N A L Y S I S - S C A L E (S P L I T)

Mean Std Dev Cases

  1. ITEM1 .3571 .4972 14.
  2. ITEM3 .5714 .5136 14.
  3. ITEM5 .5714 .5136 14.
  4. ITEM2 .3571 .4972 14.
  5. ITEM4 .5714 .5136 14.
  6. ITEM6 .3571 .4972 14.

Covariance Matrix

Correlation Matrix

ITEM1 ITEM3 ITEM5 ITEM2 ITEM

ITEM1 1.

ITEM3 .6455 1.

ITEM5 .6455 .7083 1.

ITEM2 .6889 .3443 .3443 1.

ITEM4 .3443 .4167 .4167 .3443 1.

ITEM6 .3778 .3443 .3443 .6889.

ITEM

ITEM6 1.

Dr. Robert Gebotys 2003

Item-total Statistics

Item-total Statistics

Scale Scale Corrected Mean Variance Item- Squared Alpha if Item if Item Total Multiple if Item Deleted Deleted Correlation Correlation Deleted

ITEM1 2.4286 3.4945 .7330 .7511.

ITEM3 2.2143 3.5659 .6572 .6000.

ITEM5 2.2143 3.5659 .6572 .6000.

ITEM2 2.4286 3.6484 .6364 .7469.

ITEM4 2.2143 3.8736 .4784 .2533.

ITEM6 2.4286 3.8022 .5440 .5733.

The item-total statistics reported in the present analysis are exactly the same as those reported under

the “ALPHA” model, with the only exception that the statistics are arranged differently. Again this is

a direct result of reordering the items in the scale.

Reliability Coefficients 6 items

Correlation between forms = .5700 Equal-length Spearman-Brown =.

Guttman Split-half = .7234 Unequal-length Spearman-Brown =.

Alpha for part 1 = .8571 Alpha for part 2 =.

3 items in part 1 3 items in part 2

The above are the results of the reliability analysis based on the “EVEN/ODD” model. Please note

that the correlation coefficient between the parts formed respectively by even and odd items is

smaller than the correlation reported in the “SPLIT-HALF” model (i.e. .5700 compared with.

in the “SPLIT-HALF” model). As a result, the Spearman-Brown coefficients reported in this analysis

are comparatively smaller (i.e. .7262 against .8458). This illustrative example shows that “split-

half” reliability analyses are capable of producing different reliability estimates on the same scale,

depending on the methods researchers used in splitting items in the scale.

Determining Reliability Using SPSS:

Example 2:

The following questionnaire was developed by a researcher as part of an effort to collect participants’

feedback on a five-week community-based program designed to teach individuals disease prevention

and to encourage healthier lifestyles. The questionnaire contained six items. Respondents were

asked to respond to each item according to the following scale:

Strongly Agree No Opinion Disagree Strongly Agree Disagree

The 6 items in the questionnaire were:

1. The goals of the program are clear.

2. I feel comfortable in discussing my plans, concerns and experiences with the group.

3. The materials covered in the program are helpful.

4. The health contract is useful in assisting me to make healthy lifestyle changes.

5. Overall speaking, the group is supportive.

6. Overall, the program is useful in assisting me develop positive changes towards healthy lifestyles.

The following is the data obtained from 10 participants:

Items

Person 1 2 3 4 5 6

Conducting Cronbach’s Alpha; Split-Half Reliability & Even-Odd Reliability Analyses on the Set of

Scores Obtained from 10 Respondents for the 6 Items Using SPSS

1. SPSS Computer Program

Covariances Mean Minimum Maximum Range Max/Min Variance .6170 -.1333 1.2667 1.4000 -9.5000.

Inter-item Correlations Mean Minimum Maximum Range Max/Min Variance .5189 -.1341 .8914 1.0255 -6.6457.

Item-total Statistics

Scale Scale Corrected Mean Variance Item- Squared Alpha if Item if Item Total Multiple if Item Deleted Deleted Correlation Correlation Deleted

ITEM1 12.1000 16.9889 .7281 .7344. ITEM2 12.2000 16.8444 .7267 .9060. ITEM3 13.0000 22.0000 .3788 .8634. ITEM4 11.9000 15.4333 .8273 .7752. ITEM5 12.1000 18.9889 .5660 .9363. ITEM6 13.2000 20.6222 .7830 .8531.

Reliability Coefficients 6 items

Alpha = .8584 Standardized item alpha =.

The Cronbach’s Alpha reported in the above analysis is .8584. This indicates that the 6-item

questionnaire is quite reliable. The last column in the Item-total Statistics indicates that removing

item 4 from the questionnaire will lead to a drop of Cronbach’s " from .8584 to .7973; while

removing item 3 from the questionnaire will lead to an increase of Cronbach’s " from .8584 to

b. Reliability Analysis - “SPLIT-HALF” Model

R E L I A B I L I T Y A N A L Y S I S - S C A L E (T E S T S C O R)

R E L I A B I L I T Y A N A L Y S I S - S C A L E (S P L I T)

N of Cases = 10. N of Statistics for Mean Variance Std Dev Variables Part 1 7.4000 6.9333 2.6331 3 Part 2 7.5000 7.1667 2.6771 3 Scale 14.9000 25.8778 5.0870 6

Item Means Mean Minimum Maximum Range Max/Min Variance Part 1 2.4667 1.9000 2.8000 .9000 1.4737. Part 2 2.5000 1.7000 3.0000 1.3000 1.7647. Scale 2.4833 1.7000 3.0000 1.3000 1.7647.

Dr. Robert Gebotys 2003

Item Variances Mean Minimum Maximum Range Max/Min Variance Part 1 1.2815 .7667 1.5667 .8000 2.0435. Part 2 1.1741 .4556 1.7778 1.3222 3.9024. Scale 1.2278 .4556 1.7778 1.3222 3.9024.

Inter-item Covariances Mean Minimum Maximum Range Max/Min Variance Part 1 .5148 .0778 .9333 .8556 12.0000. Part 2 .6074 .3778 .7778 .4000 2.0588. Scale .6170 -.1333 1.2667 1.4000 -9.5000.

Inter-item Correlations Mean Minimum Maximum Range Max/Min Variance Part 1 .3910 .0710 .6066 .5356 8.5474. Part 2 .5825 .4930 .7408 .2478 1.5026. Scale .5189 -.1341 .8914 1.0255 -6.6457.

Reliability Coefficients 6 items

Correlation between forms = .8354 Equal-length Spearman-Brown =.

Guttman Split-half = .9103 Unequal-length Spearman-Brown =.

Alpha for part 1 = .6683 Alpha for part 2 =.

3 items in part 1 3 items in part 2

RELIABILITY COEFFICIENTS 6 ITEMS

The Spearman-Brown results reported in the output of reliability analysis based on the “SPLIT-

HALF “ model indicate that the reliability of the entire scale/questionnaire is .9103 if it is made up

of two equal (or parallel) parts that have a three-item reliability of .8354 each. Separate values of

Cronbach’s " s are shown for each of the two parts of the scale/questionnaire, i.e. Cronbach’s "

for the first half is .6683 and that for the second half is .7628.

c. Reliability Analysis - “EVEN/ODD” Model

R E L I A B I L I T Y A N A L Y S I S - S C A L E (T E S T S C O R)

N of Cases = 10.

N of Statistics for Mean Variance Std Dev Variables Part 1 7.5000 5.3889 2.3214 3 Part 2 7.4000 8.0444 2.8363 3 Scale 14.9000 25.8778 5.0870 6