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ECO221 midterm 1
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Economics
Undergraduate 2
02/21/2008

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Term
statistics
Definition
the collection, display, analysis, and interpretation of numerical information.
Term
descriptive statistics
Definition
methods of collecting, organizing, summarizing, and presenting data in an informative way.
Term
inferential statistics
Definition
methods used to interpret a sample and to draw conclusions about a population on the basis of that sample.
Term
variable
Definition
characteristic or attribute that can assume different values
Term
data
Definition
calues that variables can assume
Term
data set
Definition
collection of data values
Term
random variables
Definition
variables whose values are determined by chance
Term
population
Definition
the entire group of items that interests us
Term
sample
Definition
part of the population we actually observe
Term
statistical inference
Definition
using the sample to draw conclusions about the characteristics of the population from which the sample came.  Also invovles making future predictions about certain populations on the basis of the study of past and present.  use probability theory to trust sample is a good rep.
Term
probability theory
Definition
used to look at the relation between the sample and population.  used because there is an element of chance in selecting a sample.  can tell how likely it is that the sample proportions will be close to the population proportion. allows us to decide how confident we can be when claiming a relationship between 2 variables.
Term
Qualitative Variable
Definition

gender

brand of car

employment status

eye color

etc. 

Term
Quantitative Variable
Definition

Discrete

assumes values that can be counted.

children in a family

successful pitches

 

Continuous

assumes infinite # of values in an interval between 2 boundaries, obtained by measuring. rounded to the nearest unit.

weight, height, time, temperature 

Term

measurement scales:

nominal

Definition

e.g. zip code, gender, eye color, nationality

 

no ranking or order 

Term

measurement scales:

ordinal

Definition

e.g. judging, grade, rating scale, preference

 

no precise differences but ranking 

Term

measurement scales:

interval

Definition

e.g. temperature, year/date on calendar

 

precise differences, ranking, but no "true" zero

zero is arbitrary 

Term

measurement scales:

ratio-level

Definition

i.e. height, weight, time, salary, age

 

there is a "true" zero 

Term
experiments
Definition
aim to isolate one factor (independent variable) and to see if it has any effects on the dependent variable.  Must conduct experiments under controlled conditions (control group/treatment group)
Term
Hawthorne Effect
Definition
people's behavior and performance change following any new or increased attention
Term
placebo effect
Definition
e effect on patient outcomes (improved or worsened) that may occur due to the expectation by a patient (or provider) that a particular intervention will have an effect
Term

sampling techniques:

random sampling

Definition
subjects are selected by random numbers (computer generated or from random tables)
Term

sampling techniques:

systematic sampling

Definition
subjects are selected by using every kth number after the first subject is randomly selected from 1-k
Term

sampling techniques:

stratified sampling

Definition
subjects are selected by dividing up the population into groups (strata) and subjects w/n those groups are randomly selected
Term

sampling techniques:

cluster sampling

Definition
subjects are selected by using an intact group that is representative of the population.
Term
Misuses of Statistics
Definition

unrepresentative samples (small, convenience samples)

misleading representations of data (1% of pop. vs. 2,000,000 ppl)

detached statistics (y brand has twice as much x)

implied connections (studies suggest that using this will....)

framing questions

Term
frequency distributions
Definition
interested in how data is distributed
Term
class
Definition
data divided into classes to measure frequency. can be used for qualitative or quantitative data
Term
frequency
Definition
....of a class is the # of data values that fall into that specific class.
Term
categorical frequency distribution
Definition
used for data that can be placed in specific categories, such as nominal or ordinal-level data.
Term
quantitative frequency distributions
Definition
used for quantitative variables.For qfd each class has a lower and upper limit. when the range of the data is large we group data into classes that are more than 1 unit--grouped frequency distribution.
Term
class midpoint
Definition
add lower and upper boundaries and divide by 2
Term
Rules for Classes
Definition

should be 5-20 classes

class width preferably odd #

classes must be mutually exclusive (non overlapping class limits)

must be continuous 

must accommodate all data

must be equal in width 

Term
histogram
Definition
[image]displayes the frequencies of classes in the form of contagious vertical bars of various heights (for continuous variables)
Term
Frequency Polygon
Definition
displays data by using lines that connect points plotted for the frequencies at the midpoints of the classes.
Term
ogive
Definition
represents the cumulative frequencies for the classes in a frequency distribution
Term
relative frequency histogram
Definition
represents the relative frequencies for the classes w/ vertical bars
Term
relative frequency
Definition
uses proportions instead of raw data as frequencies.  divide frequency of each class by the total number of frequencies.
Term
pie chart
Definition
a circle that is divided into sections according to the percentage of the frequencies in each category of the distribution.
Term
time series
Definition
represents data that occur over a specific period of time
Term
pareto chart
Definition
represents a frequency distribution for a categorical variable. the frequencies are displayed by the heights of vertical bars, which are arranged in order from highest to lowest.
Term
graphical integrity requires that...
Definition
  • design does not change inappropriately--shows data variation (not design)
  • irregular use of scale is not used to misrepresent
  • must not quote data out of context
  • clear, detailed, and thorough labeling
  • w/ money in a time series, deflated or standardized units of measurement better
Term
a statistic
Definition
a characteristic or measure obtained by using all the data values from a sample
Term
a parameter
Definition
a characteristic or measure obtained by using all the data values from a population
Term
mean
Definition
the mean is the balance point of the data in that the cumulative distance from the mean of those observations above the mean is equal to those below the mean
Term
median
Definition
the half-way point or the middle value when the data is arranged in numerical order from the smallest to largest value.
Term
mode
Definition

most commonplace value/occurs the most in the data set

 

usually for categorical data 

Term
range
Definition
highest value - lowest value
Term
coefficient of variation
Definition
standard deviation divided by the mean. allows us to compare the standard deviations of 2 different variables.
Term
empirical normal rule
Definition

for normal distributions

  • 68% of data values will fall w/n 1 s.d. of the mean
  • 95% of data values will fall w/n 2 s.d. of the mean
  • 99.7% of data values will fall w/n 3 s.d. of the mean
Term
z score/standard score
Definition
represents the number of standard deviations that a data value falls above or below the mean. used to compare position of different raw data.
Term
percentiles
Definition
divides the data into 100 equal groups and indicates the position of an individual in a group. NOT THE SAME AS PERCENTAGES! gives position w/ respect to rest of data. 
Term
quartiles
Definition

divide the distribution into 4 groups separated by Q1 (corresponding to 25th percentile), Q2 (50th percentile--the median), Q3 (75th percentile)

 

  • interquartile range- difference between Q1 and Q3 and is the range of the middle 50% of the data 
Term
Quantiles
Definition
divide the distribution into groups 5 groups
Term
deciles
Definition
divide distribution into 10 groups
Term
probability
Definition

the chance of an event occurring.

 

can be expressed as fractions, decimals, or percentages. 

Term
probability experiment
Definition
a chance process that leads to well-defined results called outcomes.
Term
outcome
Definition
the result of a single trial of a probability experiment.
Term
sample space
Definition
set of all possible outcomes of a probability experiment.
Term
event
Definition

consists of a set of outcomes of a probability experiment.

 

  • simple event-event w/ 1 outcome
  • compound event- an event that consists of more than one outcome
Term
Classical/Theoretical Probability
Definition

uses sample spaces to determine the numerical probability that an event will happen and it assumes that all outcomes in the sample space are equally likely to occur (have the same prob of ocurring)

  • 0<p(E)<1
  • if event can't occur, P(E)=0
  • if event is certain, P(E)=1
  • sum of all probabilities of the outcomes = 1 
Term
complement of an event
Definition

the set of outcomes in the sample space that are not included in the outcomes of the event E.

 

1- P(E) 

Term
empirical probability
Definition
relies on actual experience to determine the likelihood of outcomes. based on observation.
Term
Law of Large Numbers
Definition
if the empirical prob. of getting tails is computed by using a small number of trials, it is usually not exactly 1/2. However, as the number of trials increases, the empirical probability of etting a tail will approach hte theoretical probability of 1/2.
Term
subjective probability
Definition

personal or subjective definitions of probability assert probabilities on the basis of personal beliefs concerning the particular situation.

 

if logically consistent, it provides a functional basis for prob. theory

Term
mutually exclusive
Definition
two events are mutually exclusive if they cannot occur at the same time (no outcomes in common)
Term
mulitiplication rules
Definition
used to find the probability of two or more events that occur in sequence.
Term
independent events
Definition
if event A occurs and does not affect the probability of B occurring.
Term
dependent events
Definition
when the outcome or occurrence of the first event affects the outcome or the occurrence of the second event in such a way that the probability of the second event is changed.
Term
conditional probability
Definition

of an event B in relationship to an event A is the probability of that event B occurs after event A has already occurred.

 

P(B/A) 

Term
counting rules
Definition
used to determine when we want to know the number of all possible outcomes for a sequence of event.
Term
fundamental counting rule
Definition

in a sequence of n events in which the first one has k1 possibilities of outcomes, and the second event has k2 possibilities, and the third has k3 possibilities, and so forth, the total number of possibilities of the sequence will be

 

k1 . k2 . k3.....kn 

Term
factorial notation
Definition

for any counting n

 

n!= n(n-1)(n-2)....1

0!=1 

Term
permutation
Definition

an arrangement of n objects in a specific order. the arrangement of n objects in a specific order using r objects at a time is written nPr

 

nPr=(n!)/(n-r)! 

Term
combination
Definition

a selection of distinct objects from n objects without regard to order. the number of combinations of r objects selected from n objects is denoted by nCr

 

nCr=(n!)/(n-r)!r! 

Term
discrete probability distribution
Definition
consists of values a random variable can assume and the corresponding probabilities of the values. probabilites determined theoretically or by observation.
Term
expected value
Definition
the expected value of a discrete random variable of a prob. distribution is the theoretical average (Mean) of the variable.
Term
binomial model
Definition

a probability experiment whose outcomes are two or could be reduced to two. used to analyze categorical (ordinal or nominal) data. appropriate w/ sampling w/ replacement and w/o

4 requirements:

  • must be an n number of (bernoulli) trials
  • each trial has 2 categories of outcomes, not necessarily equally likely; success or failure
  • prob of success p is same for each trial
  • trials are independent. 
Term
binomial distribution
Definition

in n binomial trials with the probability of p of success in each trial , the prob of exactly x successes is

 

P(x successes) = (n!/x!(n-x)!) . p^x . q^n-x

Term
probability histogram/population histogram/probability distribution
Definition
graph of complete set of probabilities. data and probability histograms are related by the fact that in the long run, the observed frequencies will be very close to the theoretical probabilities.  describes what our data would look like if the experiment were repeated innumerable times.
Term
major characteristics of normal probability distribution
Definition
  • bell-shaped; mean, median, and mode are all equal and located at center of distribution
  • symmetrical about the mean
  • curve is continuous w/ no gaps or holes, for each x there is a y
  • falls smoothly from mean in either direction. it is asymptotic (curve gets closer and closer to x-axis but never touches it)
  • location of normal distribution is determined by the mean. the dispersion is determined by the standard deviation.
  • empirical normal rule applies
  • the prob that the value of x will be in a specified interval is shown by the corresponding aread under a probability density curve (total area=1)
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