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.
What is the secret-price-mechanism (Schade and Kunreuther 2002)?
- A secret selling price p is pre-selected by the seller
- The buyer gets no information with respect to how the price is determined or from which interval it is taken
- The buyers bid a maximum buying price b for the good (product, lottery etc.)
- The buyer gets the good (product, lottery etc.) for the secret price if her bid is equal to or higher
- With a lower bid, she pays nothing, but the good will not be allocated to her
What are disadvantages to the Vickrey auction?
– Actually rather poor; pseudo-strategic behavior and virtual competition may occur
– A strong bias in maximum buying prices may result
– Kagel (1995) concludes, on the basis of a number of studies, that participants tend to overbidding
What is the connection between dynamic environments and experiments?
Experiments take variables of interest “out of the chaos” - so they extract the subset of variables which the researcher is interested in, which is more reliable than a “field snapshot”
How would you interpret y𝓰ₖ for one-factorial analysis of variance?
y𝓰ₖ = individual observation g = labels for factor steps k = labels of observation values within factor steps
What is the total deviation?
Sum of the squared total deviations
What is the explained deviation?
Sum of the squared deviations between the factor stages
What is the non-explained deviation?
Sum of the squared deviations within the factor stages
What is Person’s coefficient of correlation?
- Most common measure of “correlation” or “predictability“
* Can have a value anywhere between -1 and 1
What is R²?
- squared correlation coefficient
- measure of how much
of the variability in one variable can be “explained by” variation in the other
What is Binary Logistic Regression?
- Investigate the interrelation between a dependent dichotomous variable and an independent variable of any type (discrete/categorical, continuous, dichotomous)
- Dichotomous variable – can assume only two values (male/female, correct/incorrect)
- Calculates the probability of belonging to any group or the probability that some event occurs
