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