ExampleCalculationOfSEMandReliabilityForSmallNforWebsite
4
Example calculation of Cronbach's alpha and Standard Error of Measurement, using the rearranged formula, as well as an approximation to SEM (SEM*) that does not Items I.1 I.2 I.3 I.4 I.5 I.6 I.7 I.8 Persons S.1 0 1 0 1 1 1 0 0 S.2 1 0 0 0 0 0 0 1 S.3 1 0 0 1 1 1 0 1 S.4 1 0 1 0 0 1 0 1 S.5 1 1 1 1 1 1 0 1 Item variances 0.20 0.30 0.30 0.30 0.30 0.20 0.00 0.20 Sum of item variances = 2.300 =SUM(C12:L12) Number of items = 10 =COUNT(C12:L12) Cronbach's alpha = 0.619658 =G14/(G14-1)*(1-(G13/(O8^2))) = k/(k SEM = 1.40633 =O8*SQRT(1-C17) = (SD persons) * sqr SEM (alternative formula) = 1.40633 = SQRT((G14*G13)/(G14-1) -O8^2/(G1 SEM* = 1.51658 =SQRT(G13) = sqrt (Sum of Item varia Click on the other tab to see the calculation for an example in which SD persons (i..e. all candidates get the same total). Item 7 has zero variance. That means that SPSS will remove it from any calculati that require calculation of covariances, and a different version of alpha (and t The basic reliability command, with no additional statistics, calculates alpha a Note on processing these data in SPSS.
description
ExampleCalculationOfSEMandReliabilityForSmallNforWebsite
Transcript of ExampleCalculationOfSEMandReliabilityForSmallNforWebsite
SD not equal to zeroExample calculation of Cronbach's alpha and Standard Error of Measurement, using conventional formula,the rearranged formula, as well as an approximation to SEM (SEM*) that does not require calculation of alpha.ItemsI.1I.2I.3I.4I.5I.6I.7I.8I.9I.10TotalPersons S.101011100105Statistics for personsS.210000001103Mean persons5.800=AVERAGE(M6:M10)S.310011101117SD persons2.280=STDEV(M6:M10)S.410100101015Variance persons5.200=O8^2S.511111101119Item variances0.200.300.300.300.300.200.000.200.200.30= (e.g.) VAR(L6:L10)Sum of item variances =2.300=SUM(C12:L12)Number of items =10=COUNT(C12:L12)Cronbach's alpha =0.619658=G14/(G14-1)*(1-(G13/(O8^2))) = k/(k-1)* (1- (Sum of Item Variances/( (SD persons)^2))))SEM =1.40633=O8*SQRT(1-C17) = (SD persons) * sqrt (1- alpha)SEM (alternative formula) =1.40633= SQRT((G14*G13)/(G14-1) -O8^2/(G14-1) ) = sqrt (k*(Sum of Item variances)/(k-1) - (SD persons)^2/(k-1)SEM* =1.51658=SQRT(G13) = sqrt (Sum of Item variances)Click on the other tab to see the calculation for an example in which SD persons = 0(i..e. all candidates get the same total).Note on processing these data in SPSS.Item 7 has zero variance. That means that SPSS will remove it from any calculations of reliabilitythat require calculation of covariances, and a different version of alpha (and the number of items) will be obtained.The basic reliability command, with no additional statistics, calculates alpha as here, based on 10 items.
SD equal to zeroExample calculation of Cronbach's alpha and Standard Error of Measurement, using conventional formula,the rearranged formula, as well as an approximation to SEM (SEM*) that does not require calculation of alpha.ItemsI.1I.2I.3I.4I.5I.6I.7I.8I.9I.10TotalPersons S.101011100105Statistics for personsS.210100001115Mean persons5.000=AVERAGE(M6:M10)S.310010101015SD persons0.000=STDEV(M6:M10)S.410100101015Variance persons0.000=O8^2S.501101001105Item variances0.300.300.300.300.300.300.000.200.300.30= (e.g.) VAR(L6:L10)Sum of item variances =2.600=SUM(C12:L12)Number of items =10=COUNT(C12:L12)Example calculation when SD (persons) is zero and hence alpha cannot be calculated but SEM and SEM* still can be.Cronbach's alpha =0.000=G14/(G14-1)*(1-(G13/(O8^2))) = k/(k-1)* (1- (Sum of Item Variances/( (SD persons)^2))))Division by zeroSEM =0.000=O8*SQRT(1-C17) = (SD persons) * sqrt (1- alpha)Division by zeroSEM (alternative formula) =1.700= SQRT((G14*G13)/(G14-1) -O8^2/(G14-1) ) = sqrt (k*(Sum of Item variances)/(k-1) - (SD persons)^2/(k-1)SEM* =1.612=SQRT(G13) = sqrt (Sum of Item variances)Click on the other tab to see the calculation for an example in which SD persons is not equal to zeroNote on processing these data in SPSS.SPSS is unable to process these data in the reliability program because SD = 0, and an error occurs.
