Lecture 4 Data Analysis. Today’s Agenda Announcements Recap of Markets Qualitative Analysis ...

51
Lecture 4 Data Analysis Data Analysis

Transcript of Lecture 4 Data Analysis. Today’s Agenda Announcements Recap of Markets Qualitative Analysis ...

Lecture 4

Data AnalysisData Analysis

Today’s Agenda

Announcements

Recap of Markets

Qualitative Analysis

Quantitative Analysis

Other Updates Tutorials are on this week!

Assignment #1 to be posted by the end of the week

o Remember, you can work in groups of up to 3

o You do not need to work with students in the same tutorial

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

What did we learn about markets?

Markets are composed of ________________________

Individual buyers and sellers have their own __________ ____________________

A buyers demand is driven by her _________________ ___________ (as well as the other factors discussed last week)

A sellers supply is driven by her ___________________

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

What did we learn about markets?

To get the demand and supply for the entire market, we ___________________________________

Aggregating horizontally implies that we add up ___________________________________

Aggregate demand and supply schedules may have a ________ in them

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

What did we learn about markets?

Our measure of _________________ is concerned with _____________

Total surplus is the ____________________________ __________________________

When total surplus is maximized, we say the market is _______________________

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

What did we miss out in on markets?

Some of the institutions:1. Posted Prices

2. Uniform Prices

3. One-sided Sequential Auctions

4. Double Auctions

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Posted Prices

This market institution is most often found in _________________________

Sellers quote prices on a take-it-or-leave-it basis in many ___________________________

Posted prices became common in the last century in large stores in which the owner/managers had to rely on numerous sales clerks

Government regulation in industries such as alcohol sometimes require that prices be posted with the regulatory agency and that discounts not be granted

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Posted Prices: Experimental Rules

At the beginning of each trading period, sellers decide on a price offer which they write down and submit on cards

Buyers will then be free to make bids to purchase from sellers

Buyers will be ordered randomly, and allowed to make bids one at a time

Once all buyers have had a chance to make a bid, the trading period is over

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Posted Prices: Effect on Market

Consider the simplest possible market with one buyer and one seller of a single unit

Suppose the seller has a cost of $1 and the buyer a valuation of $2

In a market with decentralized negotiations, one would expect traders to reach an agreement somewhere in the middle (i.e. $1.50)

In a posted price market, theory tells us that the seller could sell it for __________

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Uniform Prices

The price discrimination that occurs in posted price institutions can cause a sense of regret among buyers

The sale of all units at a uniform price, in contrast, can create an appearance of fairness

In practice, a ____________ is a form of uniform price auction where both buyers and sellers submit bids

The auctioneer then constructs the corresponding demand and supply schedules in order to determine the uniform price (i.e. the equilibrium price)

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

One-sided Sequential Auction

This institution can be used when we have a single seller of a single good, along with multiple buyers

There are 2 types of such auctions:

1. ___________________

o Price starts high and is lowered until a buyer makes a bid

2. ___________________

o Price starts low and increases until there is only 1 buyer willing to pay at that price

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Double Auction

Both buyers and sellers can actively post and accept prices

_______________ of all the market institutions

Thousands of experiments have been done investigating this institution and have found that neither complete information (i.e. buyers and sellers knowing each others costs and valuations) nor large numbers of traders is a necessary condition for convergence to competitive equilibrium outcomes

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Double Auction: Experimental Rules

During a trading period, any buyer is free at any time to raise his/her hand and make a bid to buy a unit at a specified price

Any seller is free at any time to raise his/her hand to state an asking price for a unit at a specified price

Any bid or asking price will remain on the blackboard until it is either accepted or improved (i.e. replaced by a higher bid or a lower asking price)

When a bid or ask is accepted, all outstanding bids and asks are cancelled and the market is re-set

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Qualitative vs Quantitative Analysis

___________________ gives us an overview of what the data have to say

Basis Tools1. _______________2. _______________

Goals of Summary Data1. Allows you to see _________________________ that require

further investigation2. Guide subsequent __________________________

experimental data usually are ________________, so a descriptive summary is essential

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Qualitative vs Quantitative Analysis

________________ gives specific answers to specific questions

o e.g. “Does treatment X affect outcome Y?”

Basis Tools

1. ______________________

Goals of Inferential Statistics

1. Determine whether there is a statistically significant difference between treatments

2. Determine whether there is a statistically significant difference between experimental outcomes and theoretical outcomes

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Learning Statistics by Example

For the rest of this lecture, we are going to work with some of the experimental data from our tutorials to learn the necessary statistical concepts and tools

In particular, we are going to be working with the following market:

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Buyer’s Valuation

Seller’s Cost

What does this market look like?

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Notice that the equilibrium quantity for this market is 5, while

the equilibrium price is somewhere between ____________

Experimental Market

0

2

4

6

8

10

12

0 1 2 3 4 5 6 7 8

Quantity

Pri

ce Supply

Demand

How do we draw this in Excel?

1. Need to organize the data properly

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Demand Supply Quantity

10 2 0

10 2 1

9 3 1

9 3 2

8 4 2

8 4 3

7 5 3

7 5 4

7 5 4

7 5 5

5 7 5

5 7 6

5 7 6

5 7 7

How do we draw this in Excel?

1. Need to organize the data properly

2. Highlight all the data and select the Chart Wizard

i. Choose “XY scatter” as the Chart Type

ii. Choose “scatter with data points connected by lines without markers” as the Chart Sub-type

3. If at this point the graph does not look right, click on the “series” tab and adjust what data represents the x and y coordinates

4. Add a title and label the axes, then click “finish”

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

What is the maximum surplus of this market?

Remember, surplus is maximized at the ___________ ______________________

In this market, we know the __________________, but the ___________________ could exist anywhere from $5 to $7

In such a case, we will ALWAYS assume the theoretical equilibrium price is at the ____________ of this range which is ____

CS = _______________________________________

PS = _______________________________________

TS = _______________________

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Graphic Presentation of Data

In our example, there are 6 trading rounds

Suppose we want to see how often the total surplus reaches certain levels

To do this, we first have to calculate each __________ ______________________ (i.e. surplus) and then add them all up for each trading period

We can represent this information graphically with something called a ______________, also known as a ____________________

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Graphic Presentation of Data

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Histogram of Total Surplus

0

1

2

3

4

5

18 20 22

Total Surplus

Fre

qu

ency

Graphic Presentation of Data

A histogram is a ______________ that shows the amount of data that belongs to each “category”

o In this example, the “categories” are the different levels of total surplus, namely ________________

In other words, a histogram shows us the ______________ of our outcome of interest

What we notice from this histogram is that most often, a total surplus of _______ is achieved

This tells us that most often, our market is ______________ total surplus, however we ___________________ with any statistical significance

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Numerical Descriptive Statistics

A histogram gives us a nice visual of the distribution of our outcome of interest

Another way to get an understanding of the distribution of outcomes is to calculate some numerical statistics:

1. __________________

2. __________________

3. __________________

4. __________________

5. __________________

6. __________________

Some of these statistics will become very useful when we want to start inferring the results of our experiment

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Numerical Descriptive Statistics

Mean

The mean is also known as the _______________

The mean is calculated by ____________________________ _________________ and dividing this sum by the _________ ______________

Mathematically, we represent the mean as follows:

o ______________________________

In our example, the mean is:

o ______________________________

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Numerical Descriptive Statistics

Median The median is the value of the data that occupies the middle

position when the data are ____________________

Notice that the _______________________ is important when calculating the median

o If there are an ______ number of observations, there is a unique ______________, and the median is just the value of the number occupying that position

o However, if there are an ________ number of observations, the median is the _______________________________

In our example, we have 6 observations:

o 18,20,20,20,20,22

o Thus the median is _________________________

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Numerical Descriptive Statistics

Mode The mode is the value of y that occurs the

________________

The histogram provides an easy way to pick out the mode, as the mode will be the “category” that occurs _______________

In our example, ____ is obviously the mode

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Numerical Descriptive Statistics

Range

The range is simply the difference between the ____________ __________________

In our example, the range is _____________

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Numerical Descriptive Statistics

Variance

The variance is a measure of __________________________

Mathematically, we calculate variance as follows:

o ___________________________

In our example, the variance is:

o s2 = _________________________________________________

o s2 = ______________________________

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Numerical Descriptive Statistics

Variance

Notice how the variance would ____________ if each of our outcome values (i.e. 18,20,22) each occurred twice

o ӯ = ______________________________

o s2 = _________________________________________________

o s2 = ______________________________

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Numerical Descriptive Statistics

Standard Deviation

The standard deviation is also a measure of the ___________ ______________

The standard deviation is directly related to the ___________:

o _____________

The standard deviation shows how much ________________ ______________________

In our example, the standard deviation is:

o s =______________

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Why do we need quantitative analysis?

Suppose our graphs and descriptive statistics do not give crystal clear answers to some of our questions even though our experimental design and descriptive statistics are well chosen

At this point we need to turn to the second phase of the data analysis: ______________________________________

Formal tests are meant to provide specific answers to questions:

o ____________________________________________________

o ____________________________________________________

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Why do we need quantitative analysis?

In the context of our example, we could ask if the amount of experience subjects have affects the efficiency of the market

The most obvious way to answer this question would be to compare the mean market efficiency in say period 1 with the mean market efficiency in some later period

If we see a difference in the mean market efficiency across periods, we might be tempted to conclude that there is some sort of learning taking place

But our conclusions might be incorrect because of ____________ ____________________

In the next few slides we will build some of the conceptual tools for understanding the sources and consequences of experimental error

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Basic Concepts

Observation Statistical procedures begin with a collection of observations The _______________ for an observation is not always clear For example, in market experiments, is it:

1. A single _____________________

2. A single _______________________

3. A ______________________________

4. A single _________________________o If we want to see if people learn over time, then the market efficiency

from one period in a single tutorial group would comprise a single observation

o However, if we wanted to see whether one tutorial group performed better than another, then the average market efficiency across all periods for a given tutorial group would be our unit of observation

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Basic Concepts

Suppose we have picked an appropriate definition of trial and now have a set of observations to analyze

The fundamental problem we now have to deal with is imperfections in our set of observations

To the extent that we get different results on replication, our analysis must deal with ____________ ___________________

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Basic Concepts

Experimental Error

Sources:

1. _________________

2. _________________

___________ error is conceptually straightforward to deal with

___________ error will require a much more extensive discussion

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Basic Concepts

Measurement Error

Types:

1. Recorded values for observations may not be exactly the actual values

o Misheard an oral action

o Made a mistake writing it down

2. Experimenter loses experimental control

o Inadvertently give player 1 private information about player 2

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Basic Concepts

Measurement Error

Solutions:

1. Careful choice of lab procedures, automating data capture and transmission, and building in redundancy should minimize the amount of erroneous data

2. Using our data summaries, check the raw data for large outliers and other anomalies, and check whether the anomalies are actually measurement error…when you detect erroneous data, you should throw them out before you run statistical tests

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Basic Concepts

Sampling Error

The main idea with sampling error are concerns with when our “sample” is not representative of the underlying “population”

The collection of all possible outcomes given our treatments can be thought of as ___________________________

There is always some variability in the population because of uncontrolled nuisances

This variability induces a ______________________

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Basic Concepts

Sampling Error

If we knew the _____________________, our inferential task would be trivial

o For example, if the population mean for double auction market efficiency is higher than the mean for posted offer markets, then we would correctly conclude that the double auction institution is, on average, more efficient

The problem is, the population distribution can ____________ _________ since we will only be able to run a _____________ _________ and not necessarily be able to observe all possible outcomes

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Basic Concepts

Sampling Error

Nevertheless, we do have some useful information about the population distribution because we have actually run a subset of all possible trials and have recorded the outcomes

Thus our actual data constitute a ________________ from the population distribution

________________ arises to the extent that our sample is not representative of the underlying population

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Basic Concepts

Sampling Error

You cannot expect to get a perfect sample, whose distribution exactly reproduces the population distribution, but with some care you can minimize sampling error within the bounds of your finite resources

That is, we can take steps to ____________ samples and to ____________ samples

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Good Samples and Bad Samples

Ways to get good samples

1. _____________________

o Each point in the population has the same probability of being picked

2. _____________________

o Subdivide the population into several segments and draw observations from each segment with a frequency proportional to the weight of the segment in the population distribution

o For example, we could segment the population by age, sex, education, location of residence, income, etc.

balanced sampling tends to produce ___________ sample errors than a random sample

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Good Samples and Bad Samples

Folk wisdom among experimental economists:

o An empirical regularity becomes ______________ when it is replicated with ____ different groups of subjects, preferably from different pools and in different labs

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Inferential Testing

Hypothesis test Hypothesis tests are how we will formally answer our

questions of interest

In hypothesis testing, we cannot prove something is ____, only that something is _______

This is inline with the deductive view of the world commonly attributed to the great philosopher Popper

Popper said that we never no what is true, only what is not true

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Inferential Testing

Hypothesis test Formally, when we want to write down our hypothesis, there

will be two components:

o ______________________

o ______________________

The __________________ will always be what we want to prove or disprove

The __________________ will often express what we think might be going on

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Inferential Testing

Hypothesis test Suppose what we are interested in investigating is the

efficiency of the decentralized bargaining institution

Furthermore, suppose we think this market institution will not result in the efficient competitive equilibrium outcome

Instead of setting up our hypothesis test to try to prove the decentralized bargaining institution is not efficient, what we will do is try to show that it is efficient

Remember, with hypothesis testing, we cannot show what is true, but we can show what is false

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Inferential Testing

Hypothesis test In this example, we will write our hypothesis test as follows:

o ______________

o ______________

Here μ represents the _______________ in our experimental periods, or in other words, the _______________________ in each trading period

In our example, the mean efficiency is ____, but this does not necessarily mean that we will reject the null hypothesis in favour of the alternative

In order to answer our hypothesis test, we will need to construct a special test statistic

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Inferential Testing

Reference Distribution Assess the probability that differences in observed outcome

across treatments are due to sampling error rather than due to differences in the underlying population distributions

Such an assessment requires a _________________ to proxy for the population distribution

In this class, our reference distribution of choice is known as the _________________

Note, to properly describe a distribution, we need to know both the mean and variance

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis

Inferential Testing

t-distribution The t-distribution is very similar to a ____________________,

meaning that most of its density is found near the mean and decreases quickly as we move away from the mean

Most courses at university have a normal distribution of grades, meaning that most people are around the average, and only a few get really high/low marks

o In many economics courses, the class average is a B-

o Usually 80% of the grades are between C- and B+

o Thus, those that fail or ace the course make up a small number of students

Announcements Recap of Markets Qualitative Analysis Quantitative Analysis