Author: Zongwei Zhou | 周縱葦
Weibo: @MrGiovanni
Email: zongweiz@asu.edu
選錯課系列筆記...
Textbook: Design and Analysis of Experiments, edited by Dean, Morris, Stufken and Bingham, CRC Press, 2015
Lecture #1：2018.08.20
Basic Terminology
Treatment：試驗的變量
Response Variable
Experimental Unit：試驗的對象
Observational Unit
Basic Concept
Replication：多次重復試驗，統(tǒng)計上的差異
Randomization: Not full randomization but restricted randomization.
Blocking [?] (隨機區(qū)組設計): can increase the precision of inferences. To group some experiments together. blocking is the grouping of similar experimental units.
Lecture #2: 2018.08.22
``8'' estimate freedom [?]
CRD: Completely Randomized Designs
unrestricted randomization.
Goal: assess the effect of increasing acidity of the soil on scab disease among potatoes (scab disease does not thrive in acid soil)
The acidity is to be increased by adding sulphur to the soil at some time prior to the potatoes being planted
Does it matter when the sulphur is added? Does it matter how much sulphur is added?
Two times of application are considered: Fall or Spring
Four amounts: 0, 3, 6, 12
| 0 | F3 | S3 | F6 | S6 | F12 | S12 |
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
統(tǒng)計學根據(jù)顯著性檢驗方法所得到的P 值，一般以P < 0.05 為顯著蘸劈， P <0.01 為非常顯著，其含義是樣本間的差異由抽樣誤差所致的概率小于0.05 或0.01肴盏。
degree of freedom 自由度
在統(tǒng)計學中，自由度(degree of freedom, df)指的是計算某一統(tǒng)計量時帽衙，取值不受限制的變量個數(shù)菜皂。通常df=n-k。其中n為樣本數(shù)量厉萝，k為被限制的條件數(shù)或變量個數(shù)恍飘，或計算某一統(tǒng)計量時用到其它獨立統(tǒng)計量的個數(shù)。自由度通常用于抽樣分布中谴垫。
Treatment Contrasts
When treatments have a factorial treatment structure, we may be interested in contracts for main-effects, two-factor interactions, and so on.
In general, a treatment contrast is any function with
[?]
A point estimator is , which can also be used to construct a confidence interval.
One contrast of possible interest is control vs the average of the active treatments, i.e.,
Each contrast corresponds to 1 df (degree freedom) and its SS (sum of square):
To partition a Treatment SS we use orthogonal treatment contrasts. Two treatments contrasts and
are orthogonal if
For a CRD, the treatment contrasts and
are orthogonal if
We can always find pairwise orthogonal treatment contrasts, but want to use treatment contrasts that are meaningful.
In this example, one could for example use:
- control vs ave of others (1 df)
- fall vs spring (1 df)
- differences between amounts (2 df)
- interaction between time and amount of application (2 df)
Think about contrasts that you will use, orthogonal or not, prior to the experiment.
