Exam 1

  1. Metainformation

    Tag Value
    fileReliability_eur-reliability-114-en_eur-reliability-114-en
    nameeur-reliability-114-en
    sectionReliability/Analysis/Cronbach's alpha
    typenum
    solution0.827
    tolerance0
    TypeCalculate
    ProgramCalculator
    LanguageEnglish
    LevelStatistical Literacy

    Question

    The “Three Minutes Test” (TMT) is a test to assess technical reading level. Children have to accurately read as many words as possible during three minutes. A teacher from grade 5 wants to use the test, which was constructed for children in grade 2, to assess the reading skills of her grade 5 children. Cronbach’s alpha based on the grade 2 population is .88 and the standard deviation of the test scores in grade 2 is 3.

    The standard deviation of the observed scores in grade 5 turned out to be 2.5. Calculate the reliability of the TMT in grade 5 and assume that the error variance is equal for the grade 2 and grade 5 populations. Use the following formula, but note that you might have to alter the formula in some way:

    rxx=SXt2SXo2r_{xx} = \frac{S^2_{X_t}}{S^2_{X_o}}

    And

    SXo2=SXt2+SXe2S^2_{X_o}= S^2_{X_t} + S^2_{X_e}


    Solution

    We can calculate the error variance by using: rxx=SXt2SXo2=SX02−SXt2SXo2r_{xx} = \frac{S^2_{X_t}}{S^2_{X_o}} = \frac{S^2_{X_0}-S^2_{X_t}}{S^2_{X_o}}.We can fill in the reliability (.88) and the variance (3^2) of the scores of grade 2: .88=9−SXt29.88 = \frac{9-S^2_{X_t}}{9}. Then, the variance of the error is: .88×9−9=−sxe2.88 \times 9 - 9 = - s^2_{x_e}, thus sxe2=1.08s^2_{x_e} = 1.08 and sxe=1.04s_{x_e} = 1.04. We can use this error variance to calculate the reliability in grade 5:rxx=SXt2SXo2=2.52−1.082.52=5.176.25r_{xx} = \frac{S^2_{X_t}}{S^2_{X_o}} = \frac{2.5^2-1.08}{2.5^2} = \frac{5.17}{6.25} = .827.