做研究做久了，有些陳述似乎變成就是習慣一定要這樣做，裡如抽樣要來做分層抽樣，然後分層的依據都是根據學校規模。這樣的抽法上到台灣最大的大型教育資料庫(TASA)，到最小的碩士論文，都是根據學校規模分層，但我沒看過有人進一步陳述說為什麼。我也是如此，但直到被Reviewer一問，我得自己去找答案，我從自己的專業出發，可能的解釋是我國資源分配受到學校規模影響很深(張良丞、王保進、許添明, 2010; Zhang & Sheu, 2013; 也請看教學實務現場的分享文)，大校擁有的資源不論是老師數還是分配到的款項遠多於小校，而這些資源非常有可能去影響研究者正在調查的某項專案成效(例如考試成績、教師教學效果等)，Smith and Humlum (2015) 甚至發現學校規模對於學生未來的長期產出(如高中畢業率、薪資等)都有顯著影響。如所以分層以學校規模是有道理的(淡化了資源影響)，因為這使得大中小型學校都有被抽到的機會，換句話說，這使得樣本具有代表性來解答研究問題。

當然，我知道應該有比這個更好的說法~有興趣可以一起在這討論
或是我Facebook

文獻

• 張良丞、王保進、許添明（2010）。以學生學業成就評估國民小學教育經費適足性—以台北市為例。教育與心理研究。33(4)，109-136
• Humlum, M. K., & Smith, N. (2015). Long-term effects of school size on students’ outcomes. Economics of Education Review, 45(0), 28-43. doi: http://dx.doi.org/10.1016/j.econedurev.2015.01.003
• Zhang, L. -C., & Sheu, T. -M. (2013). Effective investment strategies on mathematics performance in rural areas. Quality & Quantity, 47(5), 2999-3017.

Endnote is probably the most popular reference management software. Its drag and drop function allow you to directly put the reference into your word file by using your mouse alone. In this article, I would like to provides some tips to save you more time.

• Add a reference without a first name

This usually happens when you want to add a reference with its author having no first name. For example, a report is published by a government or a university, so you can not copy their name and paste it on your endnote. You should use the format:

Last name, first name

and leave the first name blank (since it does not have one) like the following picture (using Harvard University as an example):

• Use Google Scholar to download the citation

Most publishers allow you to export the citation from their website:

However, sometimes, especially for old books, it is hard to find the citation. You can try Google Scholar, and type in the reference title and click the button ,import into Endnote:

Sometimes what we have is the old reference but we some new references to back-up our topic. A follow-up trick of using Google Scholar is to use it to update your references. 

• Overcome software crash

This happens especially when you update your endnote files from different devices. I found it is solved by upgrade to version 7 (Endnote X7). 

• Stop endnote from auto updating the bibliography in word

After updating the bibliography, you might do some minor corrections without the intervention of Endnote. You can stop the instant formatting like the following figure. 

This article will continuously be updated and I welcome anyone of you to post your experience here.

Without no doubts, a researcher should several nice tools to handle their data, and testify their results. EXCEL, SPSS, and R represent different stages for doing a research.

1. EXCEL
Most data retrieved from a database has a excel format like xls or xlsx. We probably spend lots time on cleaning missing values and doing some simple valuable transformations with EXCEL.

2. SPSS
What is great about SPSS is that it provides the most direct interface for storing your raw data. Consider SPSS as a extension of EXCEL. It allows the definition of a variable could be stored directly in SPSS format dataset. This will be extremely useful if you are collecting data from surveys.

3. R
The preceding tools provide you with the basic method for analysing your data. On the other hand, R is a powerful statistical language,also suggested by an article from Nature, for analysing more difficult problems. Once you know how to write a function in R, it will save lots of time through avoiding clicking the buttons in the above tools. Data visualization for your data is also a great advantage of R especially using its package, ggplot2. See the examples from Rstudio.


This article will continuously be updated and I welcome anyone of you to post your experience here.

These concepts will involve the definition of technology, functional form, and other matters especially some important theories in micro-economics. These are the fundamental assumptions when developing the methodology of efficiency measurement. My advice is that read Intermediate Microeconomics_A Modern Approach (8th ed), (Ch. 18, 19, 20, 21) or Microeconomic Analysis (3rd) (Ch. 1~6, 12, 26, 27) and then study very carefully about how to estimate these functional forms especially considering their error sources (these are detailed in the book chapter, A Survey of Functional Forms in the Economic Analysis of Production.) If you want to know how to estimate these in practice, the lecture note, Introduction to Econometric Production Analysis with R, is really worth reading since it combines all R codes and data.

Other suggestions are also listed as follows. Carefully read these references in the following order (words in the parentheses indicate the suggested sections).

Production, cost, profit function
Intermediate Microeconomics_A Modern Approach (8th ed), (Ch. 18, 19, 20, 21)
Microeconomic Analysis (3rd) (Ch. 1~6, 12, 26, 27)
Microeconomic Theory (Ch. 5)
Applied production analysis: a dual approach (All)

Distance function
Multi-Output Production and Duality: Theory and Applications

This article will continuously be updated and I welcome anyone of you to post your experience here.

As a economist or a decision maker, we cannot avoid decision making, from whether expand the scale of a company to judge which firm is the most efficient one. The question is "is there any useful information for making these tough decisions?"

• Efficiency

See my previous post here.

• Scale

Whether a firm should expand its size or not usually depends on the possible cost induced by the further expansion. Consider a firm producing only one type of product. If the its single-product cost function could be depicted as follows, it is encouraged to expand its size since the unit cost is decreasing with the level of output due the spreading  the fixed cost over a large number of units of a type of product.       

• Scope

When a firm consider to produce one more type of output, economies of scope could be present if the total cost of joint production is less than the separate production.

this webpage perfectly explain the differences between economies of scale and scope.

• Cost-effectiveness ratio

This index is wildly used in the filed of health economics to help decide whether certain treatment is effective and cheaper. See O'Hagan's work for the framework.

This article will continuously be updated and I welcome anyone of you to post your experience here.

If you agree on the statement that science is based on the previous evidence and that evidence could affect the researchers' thoughts toward the next researches, it is not surprising that every study will involve some subjective judgement while conducting the researches. This is not the terrible part. The worse part of the judgement is that this could affect the estimation implicitly. In other words, we did not consider this judgement during building the model. Bayes theorem is what we need to include all the possible information including researcher's judgement into the model and then use the data we collected to update the model. This theorem is powerful but not valued as a essential tool for researches especially in the field of social science. The massive usage of probability and mathematics could be the causes. In this post, I would like to introduce some references that are extremely useful for the stepping stone of learning Bayes theorem. You don't have to read every book in the section. Instead, I encourage you to find every book in each section and try to find one  that best fits you.  For a reading list for programming in Bayesian estimation, read my another post here.

• Mathematics

1. Calculus and its applications
2. Fundamental Methods of Mathematical Economics

• Probability theory

1. Introduction to probability (by Blitzstein) 
2. Introduction to probability

• Bayes' Theory 

Bayes' theory would be a game changer for statistical estimations. It is not just a method for estimations but also a philosophy which fits our common sense toward the estimation.  Sooner or latter, most statistics textbook could be revised because of statistical concepts from Bayes' theory. Other estimation could be just a special case of Bayes' theory and this makes Bayes' Theory demand more backgrounds of math and probability. Therefore, before I provide the book list of Bayes' theory. I have to warn you that you would not even survive the chapter one if you do not have any concepts of calculus and probability. Thus, you should read the references I mentioned above, and then you can have fun and feel the power of Bayes' Theory through the following books I suggest.

1. Bayesian Analysis for the Social Sciences: (PPT of this book could be found in author's website) This book provides many useful plots to give you the most direct learning of Bayes' theory.  The author also offers clear proofs in the appendix. For readers who only want to realize the basics, you should at least read introduction and chapter one of this book. 
2. Bayesian Ideas and Data Analysis: This book has the goodness of explanation of the reasons for using different priors. Best of all, it provides detailed Winbugs and R codes in their website. 
3. Bayesian Econometrics: This book is very popular in the field of economics. I especially like that the author introduces the Bayes' theory by closely relating it to linear models which we are familiar with most. Since the author is one of the leading researcher in Bayesian efficiency estimation (see my another post), you will also benefit a lot from reading this book before you jump in that field. This author's another book,Bayesian Econometric Methods, is also worth reading. It also focus on the linear model but provides more detailed proofs and clearer math notation. Other short introduction of Bayesian methods in econometrics could be found in chapter 13, Microeconometrics Methods and Applications.    
4. Bayesian Data Analysis: Very well-known and wildly used for an Bayesian analysis. The first two edition uses Winbugs for demonstrating their Bayesian results while the latest edition use Stan instead. This book is not appropriate for beginners but it provides wide topics. Therefore, you should consider it as a very good model source. The best of it, the math notation is very close to the first book I recommended, so you save lots time when you finish reading the first one.   
5. Bayesian Inference: with ecological applications

This article will continuously be updated and I welcome anyone of you to post your experience here.