單因子變異數分析與多重比較法

One-Factor Analysis of Variance and Multiple Compariosons

筒茂發(Maw-Fa Chien)

《測驗統計年刊》 1期 (1993/12) Pp. 63-83

https://doi.org/10.6773/JRMS.199312.0063

並列摘要

The analysis of variance is a method by which the sources of variation observed in experimental data may be segregated and analyzed. In all problems where the samples are randomly drawn from normal populations having the same variance, the analysis of variance provides an effective and powerful technique. The simplest type of analysis of variance model is the one in which observations are classified into groups on the basis of a single property. The kn subjects are randomly assigned into each of k treatments in such a way that for each treatment there is n subjects. In this article the analysis of variance for a simple randomized, or completely randomized, design is illustrated. The following steps are involved:1. Partition the total sum of squares into two components, a withingroups and a between-groups sum of squares, using the appropriate computation formulas.2. Divide these sums of squares by the associated number of degrees of freedom to obtain MSw abd NSb, the within-and between-group variance estimates.3. Calculate the F ratio, MSb/MSw and refer this to the table F(Table A of the Appendix).4. If the probability of obtaining the observed F value is small, say, less than .05 or .01, under the null hypothesis, reject that hypothesis.There are a variety of statistical procedures available for multiple comparison between specific means following analysis of variance if the null hhypothesis is rejected. Methods in common use, using a t statistic, the F test, and studentized range, have been developed by Dunnet (1955), Scheffe (1953), Tukey (1949), Newman (1939), Keuls (1952), and Duncan (1955,1957), In terms of percomparison Type Ⅰ error, multiple-comparison procedures may be ordered from low to hign as follows: Scheffe, Tukey, Newman-Keuls, and Duncan. In terms of Type Ⅱ error, the order of the procedure is the reverse: Duncan, Newman-Keuls, Tukey, and Scheff'e.