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Lecture 4
Data Analysis
Today’s Agenda
 Announcements
 Recap of Markets
 Qualitative Analysis
 Quantitative Analysis
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)
Recap of Markets
Announcements
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
2.
Price starts high and is lowered until a buyer makes a bid
___________________
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 Tools
1.
2.

_______________
_______________
Goals of Summary Data
1.
2.
Allows you to see _________________________ that require
further investigation
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
e.g. “Does treatment X affect outcome Y?”
o

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:
Buyer’s Valuation
Seller’s Cost
Announcements
Recap of Markets
Qualitative Analysis
Quantitative Analysis
What does this market look like?
Experimental Market
12
Price
10
8
Supply
6
Demand
4
2
0
0
1
2
3
4
5
6
7
8
Quantity
 Notice that the equilibrium quantity for this market is 5, while
the equilibrium price is somewhere between ____________
Announcements
Qualitative Analysis
Recap of Markets
Quantitative Analysis
How do we draw this in Excel?
1.
Need to organize the data properly
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
Announcements
Recap of Markets
Qualitative Analysis
Quantitative Analysis
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
Histogram of Total Surplus
5
Frequency
4
3
2
1
0
18
20
Total Surplus
22
Announcements
Recap of Markets
Qualitative Analysis
Quantitative Analysis
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.
2.
3.
4.
A single _____________________
A single _______________________
A ______________________________
A single _________________________
o
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
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.
2.
Recorded values for observations may not be exactly the actual
values
o
Misheard an oral action
o
Made a mistake writing it down
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
2.

Each point in the population has the same probability of being
picked
_____________________
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
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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