# Latin square

Latin square is an n × n array filled with n different symbols, each occurring exactly once in each row and exactly once in each column. Here is an example:

 A B C C A B B C A

For the past three decades, Latin Squares techniques have been widely used in many statistical applications. Much effort has been devoted to Latin Square Design. In this paper, I introduce the mathematical properties of Latin squares and the application of Latin squares in experimental design. Some examples and SAS codes are provided that illustrates these methods.

——Lei gao 2005

http://www.mth.msu.edu/~jhall/classes/MTH880-05/Projects/latin.pdf

## The Latin Square design

The Latin square design is used where the researcher desires to control the variation in an experiment that is related to rows and columns in the field.

Field marks:

• Treatments are assigned at random within rows and columns, with each treatment once per row and once per column.
• There are equal numbers of rows, columns, and treatments.
• Useful where the experimenter desires to control variation in two different directions

This is just one of many 4×4 squares that you could create. In fact, you can make any size square you want, for any number of treatments – it just needs to have the following property associated with it – that each treatment occurs only once in each row and once in each column.

Note that a Latin Square is an incomplete design, which means that it does not include observations for all possible combinations of ij and k.  This is why we use notation k = d(i, j).  Once we know the row and column of the design, then the treatment is specified. In other words, if we know i and j, then k is specified by the Latin Square design.

This property has an impact on how we calculate means and sums of squares, and for this reason we can not use the balanced ANOVA command in Minitab even though it looks perfectly balanced. We will see later that although it has the property of orthogonality, you still cannot use the balanced ANOVA command in Minitab because it is not complete.

The randomization procedure for assigning treatments that you would like to use when you actually apply a Latin Square, is somewhat restricted to preserve the structure of the Latin Square. The ideal randomization would be to select a square from the set of all possible Latin squares of the specified size.  However, a more practical randomization scheme would be to select a standardized Latin square at random (these are tabulated) and then:

1. randomly permute the columns,
2. randomly permute the rows, and then
3. assign the treatments to the Latin letters in a random fashion.

via https://onlinecourses.science.psu.edu/stat503/node/21

Posted in research, user study

# The illustrated guide to a Ph.D.

Every fall, I explain to a fresh batch of Ph.D. students what a Ph.D. is.

Imagine a circle that contains all of human knowledge:

By the time you finish elementary school, you know a little:

By the time you finish high school, you know a bit more:

With a bachelor’s degree, you gain a specialty:

A master’s degree deepens that specialty:

Reading research papers takes you to the edge of human knowledge:

Once you’re at the boundary, you focus:

You push at the boundary for a few years:

Until one day, the boundary gives way:

And, that dent you’ve made is called a Ph.D.:

Of course, the world looks different to you now:

So, don’t forget the bigger picture:

Keep pushing.

Research Design: Qualitative, quantitative, and mixed methods approaches (強烈建議買第三版的)，在我寫 proposal  的時候給我不少指引。

1. What do we need to better understand your topic?
2. What do we know little about in terms of your topic?
3. What do you propose to study?
4. What are the setting and the people that you will study?
5. What methods do you plan to use to provide data?
6. How will you analyze the data?
7. How will you validate your findings?
8. What ethical issues will you study present?
9. What do preliminary results show about the practicability and the value of the proposed study?

1. 是否能用一句話表達本文目的為何？
2. 文章傳達了什麼讓人意外的資訊？結果與期望是否相互矛盾？採訪對象曾說過讓人震撼或非常有趣的事情？我們的調查是否揭露了受訪者令人意想不到的態度？
3. 讀者對此話題所持有的假設為何？這些假設對我們所提出的主題有多少幫助？
4. 文章結尾是否有比目前序言表達更好的內容？
5. 讀者是否已經沒有疑惑？或者，我們是否已經確定眼前這個結論就是真正的結論？

Publish,Don’t Perish! Resources
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=857344
Editors’ Association of Canada: for professional editing services
http://www.editors.ca/hire/index.html
SFUStudent Learning Commons: Writing ResourcesforHonours andGraduate Students
THESISWRITING
“Dissertation Success Strategies”: University ofIllinois
http://www.couns.uiuc.edu/brochures/Dissertation.htm
TIMEMANAGEMENT
“Time Management” by theUniversity ofGuelph Learning Commons
http://www.learningcommons.uoguelph.ca/ByTopic/Learning/TimeManagement/index.html
University of MarylandUniversity College: creating a writing plan and projectschedule
http://www.umuc.edu/prog/ugp/ewp_writingcenter/writinggde/appendix_d/appendix_d‐02.shtml
“Writing and Presenting Your Thesis orDissertation” by S.Joseph Levine, Prof. Emeritus, Michigan State
University
http://www.learnerassociates.net/dissthes/
MUTUAL SUPPORT
http://http‐server.carleton.ca/~felgar/dts/
“So long, and thanksforthe PhD”: a computerscience graduate schoolsurvival guide
http://www.cs.unc.edu/~azuma/hitch4.html

Posted in funny, research

# T检验、F检验和统计学意义（P值或sig值）

1.T检验和F检验的由来

F值和t值就是这些统计检定值，与它们相对应的概率分布，就是F分布和t分布。统计显著性（sig）就是出现目前样本这结果的机率。

2. 统计学意义（P值或sig值）

3. T检验和F检验

4. T检验和F检验的关系

t检验过程，是对两样本均数(mean)差别的显著性进行检验。惟t检验须知道两个总体的方差(Variances)是否相等；t检验值的计算会因方差是否相等而有所不同。也就是说，t检验须视乎方差齐性(Equality of Variances)结果。所以，SPSS在进行t-test for Equality of Means的同时，也要做Levene’s Test for Equality of Variances 。

4.1

4.2.

4.3

4.4

t检验有单样本t检验，配对t检验和两样本t检验。

F检验又叫方差齐性检验。在两样本t检验中要用到F检验。

via http://blog.znsun.com/2008/04/653/t-test-and-f-test-and-p-or-sig-value

One-way Anova(單因子變異數分析)是只有一個類別變數當作independent variable，檢驗此類別變數與其它連續變數(continuous variable)和結果的關係。比方說如果你想看性別、IQ對數學成績的影響，性別就是類別變數，IQ是連續變數，數學成績是結果變數(outcome variable)。

Two-way Anova(雙因子變異數分析)是有兩個以上的類別變數作為independent variables。比如說性別、種族與IQ對數學成績的影響，性別和種族就是類別變數。

2009/4/17 補充：

2011/11/18修正：原本寫的是

「另外，常犯的錯就是把前、後測是否有顯著差異用T-test來檢定。即使有兩組，前、後測也不是用T-test來檢定的，更別說有人「假裝」把前測當一組，後測當一組，拿來做T檢定。」

「另外，常犯的錯就是把前、後測是否有顯著差異用two-sample t-test來檢定，不能「假裝」把前測當一組，後測當一組，拿來做two-sample T檢定，而是應該用paired-sample t-test來檢驗是否有差異。」

Posted in research,

Tags: , ,

### TomTom

BlueAsteroid

Just another WordPress.com site

Jing's Blog

Just another WordPress.com site

Start from here......

Just another WordPress.com site

Where On Earth Is Waldo?

A Project By Melanie Coles

the Serious Computer Vision Blog

A blog about computer vision and serious stuff

Cauthy's Blog

paper review...

Cornell Computer Vision Seminar Blog

Blog for CS 7670 - Special Topics in Computer Vision

datarazzi

Life through nerd-colored glasses

Luciana Haill

Brainwaves Augmenting Consciousness

1,2,∞

Dr Paul Tennent

and the university of nottingham