Part 4 - Auctions & Statistical Basics Flashcards
What do you need to consider when stating statistical hypotheses?
- Identify the null and alternative hypotheses
- Decide on an appropriate significance level
- One or two-tailed tests?
What is the confidence interval?
Confidence is defined as 1 minus the significance level
– When we construct a 95% confidence interval, we are saying that we are 95% certain that the true population mean is covered by the interval
What is the significance level?
“chance that we are wrong” = higher significance level means higher chance of rejecting H₀, but also greater error chance
with experiments: keep in mind low sample size, therefore greater significance level might make sense
What 5 steps do you go through with hypothesis testing?
- State statistical hypotheses
- Check assumptions
- Calculate test statistic
- Evaluate the statistic
- Interpret your results
What is a two-tailed test?
Non-directional (two-tailed) - the direction of deviation of the alternative case is not specified
What is a one-tailed test?
Directional hypotheses (one-tailed) - the direction of deviation from the null value is clearly specified; a specific predicted outcome is stated
What is a type I error?
- Falsely reject H₀
- Denoted by α = chance of making an error
What is a type II error?
- Fail to reject H₀ when H₁ is true
- Denoted by β = power of statistical test
What do you do when checking the assumptions of a statistical test?
- check assumptions for the particular test to use
- more violations mean less confidence in the final p-value
- Measurement Level = type of variables
- Independence of Observations = we usually assume randomized, independent respondents
What types of variables are there?
- Nominal = categories
- Ordinal = ordered categories -> interval data = with certain ranges
- Numeric
Parametric vs. Nonparametric Test?
- nonparametric: not high statistical power, but more robust to violations
Assumptions for Kolmogorov-Smirnov Test?
– Random sampling is assumed, as with all significance tests
– Continuous interval or ratio data are required for the Kolmogorov-Smirnov goodness-of-fit test for exact results
–Ordinal data or grouped interval data may be (and commonly are) used if approximate results are sufficient
What is the Kolmogorov-Smirnov Test for A Single Sample?
- Tests whether the distribution of a variable obtained using a sample matches a given distribution (e.g. is a variable normally distributed)
- Non parametric and distribution free (makes no assumption about the distribution)
- Observed distribution - the distribution of the variable in the sample
- Hypothetical distribution - the expected distribution of a variable with the same parameters if it conformed to a particular type of distribution
What are metric variables?
with a numerical value, i.e. ratios, numbers, intervals
What is homogeneity of variance?
that two samples have the same distibution
What are nonparametric tests?
Logit, Probit
What kind of independent and dependent variables do you need for ANOVA (analyses of variance)?
- categorical independent variable
- metric dependent variable
What assumptions (except nature of variables) does ANOVA need to match?
- normal distribution in population
- factors (= independent variables) must be independent
- homogeneity of variance
- linear model structure = additivity of independent variables
What types of ANOVAs are there?
- one-/two-/three-factorial ANOVA (1-3 independent variables, 1 dependent variable)
- multi-dimensional ANOVA (more than one dependent variable)
What are the general characteristics of incentive-compatible revelation of reservation prices?
– Reservation prices are an especially precise measure for how attractive certain goods are to individuals since they directly address the sacrifice component
– With incentive compatible mechanisms, it is in the own interest of a decision maker, to reveal her reservation price
– The comparison of different institutions to reveal reservation prices is part of experimental economics research
What is nudging?
positive reinforcement and indirect suggestions as ways to influence the behavior and decision making of groups or individuals.
= subtle steering of behavior through beh. econ. findings
What is the Becker, DeGroot, and Marshak (1964) mechanism?
– Individual must state a bid (=maximum price she is willing to pay for a good)
- bid is compared to a price determined by a random number generator (picked from an interval between a pre-specified minimum and maximum price of a good)
- If the subject’s bid is greater than the price, she pays the price and receives the item being auctioned. If the subject’s bid is lower than the price, she pays nothing and receives nothing.
What are disadvantages to the Becker, DeGroot, and Marshak (1964) mechanism?
- complexitiy + explanation
- providing right interval (capturing all WTP)
- interval is an anchoring point
What is the Vickrey auction?
= second-price-auction
Bidders submit written bids without knowing the bid of the other people in the auction. The highest bidder wins but the price paid is the second-highest bid.
