Analysis Table
분산분석표
일원분산분석표
| 제곱합 (sum of squared) |
자유도 (degrees of freedom) |
제곱평균 (mean of squared) |
검정통계량 (test statistic) |
|
| 처리 (Between) |
$SS_{Reg}$ | $k$ | ${MS}_{Reg}=\dfrac{SS_{Reg}}{k-1}$ | $F=\dfrac{MS_{Reg}}{MS_{Res}}$ |
| 오차 (Within) |
$SS_{Res}$ | $n-k-1$ | $MS_{Res}=\dfrac{SS_{Res}}{n-k}$ | |
| 총 (Total) |
$SS_T$ | $n-1$ | $MS_T=\dfrac{SS_T}{n-1}$ |
이원분산분석표
| 제곱합 (squared sum) |
자유도 (degrees of freedom) |
제곱평균 (mean squared) |
검정통계량 (test statistic) |
|
| 요인$A$ (factor A) |
$SS_A$ | $a-1$ | ${MS_A}=\dfrac{SS_A}{a-1}$ | $F_{1}=\dfrac{MS_A}{MS_E}$ |
| 요인$B$ (factor B) |
$SS_B$ | $b-1$ | ${MS_B}=\dfrac{SS_B}{b-1}$ | $F_{2}=\dfrac{MS_B}{MS_E}$ |
| 요인$A$와 요인$B$의 상호작용 (interaction effect of A, B) |
$SS_{AB}$ | $(a-1)(b-1)$ | ${MS_{AB}}=\dfrac{SS_{AB}}{(a-1)(b-1)}$ | $F_{3}=\dfrac{MS_{AB}}{MS_E}$ |
| 오차 (error) |
$SS_E$ | $n-ab$ | ${MS_E}=\dfrac{SS_E}{n-ab}$ | |
| 전체 (total) |
$SS_T$ | $n-1$ |
단순선형회귀분석표
| 제곱합 (sum of squared) |
자유도 (degrees of freedom) |
제곱평균 (mean of squared) |
검정통계량 (test statistic) |
|
| 회귀 (Regression) |
$SS_{Reg}$ | $1$ | ${MS}_{Reg}=\dfrac{SS_{Reg}}{1}$ | $F_0=\dfrac{MS_{Reg}}{MS_{Res}}$ |
| 잔차 (Residual) |
$SS_{Res}$ | $n-2$ | $MS_E=\dfrac{SS_{Res}}{n-2}$ | |
| 총 (Total) |
$SS_T$ | $n-1$ | $MS_T=\dfrac{SS_T}{n-1}$ |
중선형회귀분석표
| 제곱합 (sum of squared) |
자유도 (degrees of freedom) |
제곱평균 (mean of squared) |
검정통계량 (test statistic) |
|
| 회귀 (Regression) |
$SS_{Reg}$ | $p$ | ${MS}_{Reg}=\dfrac{SS_{Reg}}{p}$ | $F=\dfrac{MS_{Reg}}{MS_{Res}}$ |
| 잔차 (Residual) |
$SS_{Res}$ | $n-p-1$ | $MS_{Res}=\dfrac{SS_{Res}}{n-p-1}$ | |
| 총 (Total) |
$SS_T$ | $n-1$ | $MS_T=\dfrac{SS_T}{n-1}$ |
확률화구획 실험설계 분산분석표
| 제곱합 (squared sum) |
자유도 (degrees of freedom) |
제곱평균 (mean squared) |
검정통계량 (test statistic) |
|
|
처리 (Treatment) |
$SS_{Tr}$ | $k-1$ | $MS_{Tr}=\dfrac{SS_{Tr}}{a-1}$ | $F_1=\dfrac{MS_{Tr}}{MS_E}$ |
|
구획 (Block) |
$SS_B$ | $b-1$ | $MS_B=\dfrac{SS_B}{b-1}$ | $F_2=\dfrac{MS_B}{MS_E}$ |
| 오차 (Error) |
$SS_E$ | $(b-1)(k-1)$ | $MS_E=\dfrac{SS_E}{(b-1)(k-1)}$ | |
| 전체 (Total) |
$SS_T$ | $bk-1$ |