Slide 1

ReliabilityThere are four methods in estimating the reliability of good measuring instrument. These methods are as follows;test-retest method parallel-form method, split-half method, and internal-consistency method.

Test-Retest MethodThe same measuring instrument is administered to the same group of subjects. The scores of the first and second administrations of the test are determined by correlation coefficient.

Limitations of Test-Retest Method(1)when the time interval is short, memory effects may operate. The subjects may recall of his previous responses and tends to make the correlation of the test high;

Limitations of Test-Retest Method(2) when the time interval is long, such factors as unlearning, forgetting, among others, may occur and may result to low correlation of the test; and

Limitations of Test-Retest Method(3)regardless of the time interval separating the two administrations , other varying environmental conditions such as noise, temperature, lighting, and other factors may effect the correlation of the test

Spearman Rank Correlation Coefficientrs = 1 (n3 n) 6d2Spearman Rho Formula () or (rs )

where: d2 = sum of the squared difference between ranks n = the total number of cases

Spearman Rank Correlation -is a nonparametricmeasure of statistical dependence between two variables. -it assesses how well the relationship between two variables can be described using a monotonicfunction. -if there are no repeated data values, a perfect Spearman correlation of +1 or 1 occurs when each of the variables is a perfect monotone function of the other.

Scale of Correlation0.81 to 1.0 (very strong relationship)0.61 to 0.8 (strong relationship)0.41 to 0.6 (moderate relationship)0.21 to 0.4 (weak relationship) 0 to 0.2 (weak or no relationship)

A positive Spearman correlation coefficient corresponds to an increasing monotonic trend betweenXandY.

A negative Spearman correlation coefficient corresponds to a decreasing monotonic trend betweenXandY.

Spearman Rank CorrelationEx: Twelve students in third year high school are used as pilot sample to test the reliability of an achievement test in Mathematics.

Table 1 Shows student scores and reliability in two administrations and computations of spearman rho STUDENTSSCORESS1 S2 RANKSR1 R2DIFFERENCESD D2123456789101112n = 1255 6671 7972 7043 5035 3164 7257 5770 6769 6948 50 43 4175 758 73 12 410.5 9.512 126 37 84 65 59 9.5 10.5 11.01 2 1 1.0 2 4.0 2 4.0 1 1.0 0 0 3 9.0 1 1.0 2 4.0 0 00.5 0.250.5 0.25 1 1.0 d2 = 25.50

rs = 1 (n3 n) 6d2(6)rs = 1 n= 12 d2 = 25.50(25.50) [(12)3 12]rs = 0.91 rs = 1 1531716very high relationshipAchievement test in mathematics is reliable

Test the reliability of the summative test of Grade 4 pupils in mathematics given the set of scores of twenty pupils. StudentScore 1Score 2 88 93 72 64 45 56 63 58 69 80 77 71 90 84 40 34 65 59 81 76

StudentScore 1Score 2 11 80 86 12 58 64 13 51 54 14 66 7015 69 6516 74 8017 81 8518 46 5219 71 7120 83 81

Parallel Forms MethodParallel or equivalent forms of a test may be administered to the group subjects, and the paired observations correlated. In estimating reliability by the administrations of parallel or equivalent forms of a test, criteria or parallelism are required. The two forms of the test must be constructed that the content, type of item difficulty, instructions for administrations, and many others should be similar but not identical. Moreover these two forms should have approximately the same average and variability of scores.

Parallel Forms MethodEx. Form A Convert 100 C to F Form BConvert 212F to C

Split -Half MethodThe test in this method may be administered once, but the items are divided into two halves. The common procedure is to divide a test into odd and even items. The two halves of the test must be similar but not identical in content, number of times, difficulty, means and standard deviations.

Split -Half MethodSpearman-Brown Formula: rwt = 1+ rht 2rhtwhere rwt = reliability of the whole test rht = reliability of a half test.

Split -Half Methodrwt = 1+ rht 2rhtEx: rht = 0.76 2(0.76)rwt = 1 + 0.76rwt = 1.521.76rwt = 0.86 -the whole test is reliable high relationship

Internal Consistency MethodThis method is used with psychological test which are constructed of dichotomously scored items. the testee either passes or fails in an item. A one (1) is assigned for a pass and a zero (0) for a failure. The method of obtaining reliability coefficients in this method is determined by Kuder-Richardson formula 20. This formula is a measure of internal consistency or homogeneity of the measuring instrument. The formula is

Kuder RichardsonThe KR 20 formula:

where: n = the number of items sd2 = the variance of scores on test piqi = the product of proportion of passes and fails for item 1.

n

n 1

x

Rxx = sd2 pi qi

sd2 sd2 = (x x )2 n 1

TABLE 2RESPONSES OF TWELVE STUDENT S FOR A TEST OF FIFTEEN ITEMSitemSTUDENTFpiqipiqi1234567891011121314151 2 3 4 5 6 7 8 9 10 11 121 1 1 1 1 1 1 1 1 1 1 01 1 1 1 1 1 1 1 1 1 0 01 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 01 1 1 1 1 1 1 1 0 0 0 01 1 1 1 1 1 1 0 0 0 0 01 1 1 1 1 1 1 0 0 0 0 01 1 1 1 1 1 1 0 0 0 0 01 1 1 1 1 1 1 0 0 0 0 01 1 1 1 1 0 0 0 0 0 0 01 1 1 1 1 0 0 0 0 0 0 01 1 1 1 0 0 0 0 0 0 0 01 1 1 0 0 0 0 0 0 0 0 01 1 1 0 0 0 0 0 0 0 0 01 1 0 0 0 0 0 0 0 0 0 0111088877775543320.920.830.670.670.670.580.580.580.580.420.420.330.250.250.170.080.170.330.330.330.420.420.420.420.580.580.670.750.750.830.07360.14110.22110.22110.22110.24360.24360.24360.24360.24360.24360.22110.18750.18750.1411T151514 12 11 9 9 5 2 2 1 0piqi=3.0768

STUDENTx(x - X)(x - X)2123456789101112151514121199522107.087.086.084.083.081.081.08-2.92-5.92-5.92-6.92-7.9250.126450.126436.996416.64649.48641.16641.16648.526435.046435.046447.886462.7264n= 12x = 95X = 7.92(x X)2 = 354.9168 sd2 = (x x )2 n 1354.9212 1 sd2= sd2= 32.265

Kuder Richardson n

n 1

x

Rxx = sd2 pi qi

sd2sd2 = 32.265 pi qi = 3.0768n = 1515Rxx = 15 1 x32.265 3.076832.265 Rxx = 1.07x0.9046 Rxx =0.96796