向度數、題數及樣本數分別與六種信度估計法估計誤差交互作用效果之探討

The Interacting Comparison of Effect Sizes by Using Six Estimating Reliability Errors on Dimensions, Items and Sample Sizes

本研究以不同向度數、題數及樣本數產生符合平行、τ等值及同因素三種假定的測量模式模擬資料，採二因子混合設計ANOVA分析向度數、題數及樣本數三個自變項分別與ρ_(glb)、λ_2、λ_3、λ_4、λ_6、ω_t六種不同信度估計法估計誤差之交互作用效果。研究結果顯示：（1）λ_4及ω_t之估計誤差最不受向度數之影響，其餘依序為ρ_(glb)、λ_6、λ_2、λ_3。（2）λ_4及ω_t之估計誤差最不受題數影響，其餘依序為ρ_(glb)、λ_2、λ_3、λ_6。（3）ω_t之估計誤差最不受樣本數影響，其餘依序為λ_2、λ_3、λ_4、λ_6、ρ_(glb)。建議研究人員優先採用R軟體的omega及guttman兩個函數來得到最不受向度數、題數及樣本數影響的ω_t及λ_4兩種信度估計值，如要使用SPSS進行信度分析，那在Models選項部份得選擇Guttman，就可以得到λ_1至λ_6，由於SPSS的λ_4並不是最大折半信度，建議使用λ_2及λ_6作為單、多向度測驗之信度。

The purpose of this study is to investigate the interactions between the estimation error given by six reliability estimates (ρ_(glb), λ_2, λ_3, λ_4, λ_6 & ω_t) and dimensionality, numbers of item, and sample sizes by using a two-factor mixed ANOVA design, based on data simulated from three different measurement model, namely, classical, tau-equivalent and congeneric measurements. The main findings of this study are as following: (a) the estimation error given by λ_4 and ω_t show least influenced by the number of the factors (or dimensions), followed by ρ_(glb), λ_6, λ_2, λ_3 in order; (b) the estimation error given by λ_4 and ω_t are least affected by the number of items, followed by ρ_(glb), λ_2, λ_3, λ_6; and (c) ω_t gives the smallest estimation error under each sample sizes, and followed by λ_2, λ_3, λ_4, λ_6, ρ_(glb). The researchers are recommended use the omega and guttman packages of R to calculate ω_t and λ_4, which are least influenced by the dimensionality, number of items, and sample sizes. If the reliability coefficients need to be obtained by using SPSS instead, then the Guttman option had to be checked, so that λ_1~λ_6 could be presented in the output. The λ_4 provided by the SPSS is not the maximum split-half reliability as discussed in this article; thus, λ_2 and λ_6 could be used as the reliability for the unidimensional and multidimensional tests, respectively.