Two Level Factorial Design Analysis

Two level factorial design analysis estimates main effects and interactions of factors each run at a low and a high level, judging them by F tests when runs are replicated or by Lenth's method otherwise.

2수준 요인설계 분석은 각 요인을 낮은 수준과 높은 수준 두 가지로 바꾼 실험에서 주효과와 교호작용을 추정하고, 반복이 있으면 F 검정으로, 없으면 Lenth 방법으로 판정합니다.

Which of my four process settings, each tested at two levels, actually change the yield, and do any of them interact?

네 가지 공정 조건을 각각 두 수준으로 바꿔 실험했는데, 어떤 조건이 수율에 실제로 영향을 주고 서로 교호작용이 있나요?

Code each factor as -1 and +1, estimate every effect as the difference between the mean response at the high and low level, and test main effects and two-factor interactions. Without replicated runs, compare effects with Lenth's pseudo standard error and inspect a half-normal plot.

When to use Two Level Factorial Design Analysis

• Every factor was set at exactly two levels in a full or resolution V fractional factorial
• You are screening several factors to find the few that matter
• You want interaction effects as well as main effects from a small number of runs

When to use something else

• Factors have three or more levels or are continuous and curvature matters; use response surface methodology
• Runs are grouped in blocks or plots that restrict randomization; use a split-plot or blocked ANOVA

Assumptions and requirements

• Runs are independent and performed in random order
• Residuals are approximately normal with constant variance
• Without replication, higher-order interactions are negligible (effect sparsity)

What the analysis reports

• Effect estimate and regression coefficient for each term
• ANOVA F tests when error degrees of freedom exist
• Lenth's PSE, margin of error and simultaneous margin of error
• Half-normal plot coordinates of the effects
• Lack-of-fit test when replicates are available

How to report it

A 2^[k] factorial experiment (N = [value] runs) showed significant effects of [factor] (effect = [value], F(1, [df]) = [value], p = [value]) and the [factor × factor] interaction (effect = [value], p = [value]).

Related methods

• Response Surface Methodology
• Two way ANOVA
• Latin Square Design Analysis

Run Two Level Factorial Design Analysis on Quorant