AP Stats Flashcards

Terms Definitions
Mean
The average
expected value
mathematical expectation.
resistant
Relatively unaffected by extreme values.
retrospective study
data was already gathered
Observation study
observes individuals and measures variable of interest but does not attempt to influence the responses
Variance
The square of the standard deviation
Control Group
Our baseline in an experiment
Variable
Any characteristic of an individual that can take different values for different individuals.
distribution
describes how a quantitative variable behaves. Generally include shape, center, spread, & unusual features.
Independent
Two events are considered independent if the occurrence of one event does not affect the likelihood (probability) of the occurrence of the other.
Ex: Event #1: Subject is a Male
Event #2: Subject is Pregnant
(these two events are not independent)
General probability rule for "and" probabilities...
SEE FORMULAs:
Anecdotal Evidence
Evidence that is haphazardly collected and is usually based on a few striking individual cases and as such is not representative of the population as a whole and is not reliable.
Skewed
not symmetrical--could be to the left or right
Single-Blind
When one (subject or evaluators) is blinded
Symmetric
A distribution where two sides are mirror images of each other
control
the effects of lurking variables on the response, most simply by comparing two or more treatments
sample surverys
estimates populations parameter so the sample needs to be representative as possible
range
the maximum data value minus the minimum data value
Center
use either the median or mean depending on the skewness of the data.
addition rule
method for finding the probability that either or both of two events occurs
Variable of Interest
The characteristic or trait being measured/observed
mathematical model
An equation used to imitate a relationship--usually used for prediction
Response Bias
Anything in a survey design that influences responses
scatterplot
a graphed cluster of dots, each of which represents the values of two variables. The slope of the points suggests the direction of the relationship between the two variables. The amount of scatter suggests the strength of the correlation (little scatter indicates high correlation). (Also called a scattergram or scatter diagram.) (Myers Psychology 8e p. 031)
Experiment
A study which imposes a treatment or intervention on individuals in order to observe their responses.
Discrete variables
a variable that assumes values that can be counted
simple random sample
abbreviated SRS, this requires that every item in the population has an equal chance to be chosen and that every possible combination of items has an equal chance to exist. No grouping can be involved.
modified boxplot
a display for quantitative data that graphs the five-number summary on an axis and shows outliers of they exist
random error
error that has a random distribution and can be attributed to chance
Observational Study
A study in which no treatment is imposed. Such studies include research of available data or sample surveying.
discrete numerical data
possible values are isolated points on the number line
Central Limit Theorem
The sampling distribution model of the sample mean and proportion from a random sample is approximately normal for large n regardless of the distribuion of the population as long as observations are independent
probability
a number between 0 and 1 that reports the likelihood of the event's occurence
Linear Transformations
when all data is multiplied by a constant, or a constant is added or subtracted, or a combination of the two operations.
FORMULA:
**multiplying by a constant changes the center and spread by that same constant.
**adding a constant changes the center but not the spread by that constant.
right skewed
A distribution with a long tail on the right side.
Mode
Hump or local high point in shape of a distribution
Variences s²
This of a set of observations is the average of the square of the deviations of the observations from their mean.
Direction, Form, and Strength
the three things you look for when examining a scatterplot
least squares regression line
also know as the regression line or line of best fit it is the line that minimizes the sums of the squares of the vertical distances from the actual points to the line
Simple Random Sample (of size = n)
A sample in which a) Every individual in a given population is given an equal probability of making it into the sample b) Every sample of a given size = n has an equal probability of actually being the sample chosen
RA
random assignment
categorical
individual observations are categorical responses
Factor
Explanatory variables in an experiment
categorical (quantitative) data
trait, quality, category
Minimum
The smallest number in a distribution
blocking
using extraneous factors to create experimental groups that are similar with respect to those factors, thereby filtering out their effect
srs
population is divided into several subpops and then srs is drawn from each one
sample
a representative subset of a population, examined in hope of learning about the population
Parameter
A numerical summary that describes a variable's distribution in a given population such as mu = pop mean, and sigma = pop standard deviation.
Interquartile Range
The difference between the 3rd quartile and the 1st quartile
Independence
When the probability of one even occurring has no affect on the probability of a second event occurring
nonresponse
occurs when an individual chosen for the sample can't be contacted or does not cooperate
5 W's
who, what, when, where, why, how
population
the entire group of individuals or instances about whom we hope to learn
Undercoverage/Non-Response Bias
a situation when certain individuals are left out of the sample or individuals are not included in the data set that were originally part of the sample.
standard error
standard deviation of a distribution of a sample statistic
left skewed, right skewed, or approximately symmetric
Descriptions of shape.
lurking variables
a variable that has an important effect on the relationship among the variables in a study but is not included among the variables studied
placebo treatment
a treatment that resembles the other treatments in an experiment in all apparent ways but that has no active ingredients
Statistically Significant
When an observed difference is too large for us to believe that it is likely to have occurred naturally
block design
a random assignment of units to treatments is carried out separately within each block
Individuals
the objects described by a set of data. They may be people, animals or things.
Stratified sample
a sample obtained by dividing the population into subgroups, called strata, according to various homogeneous characteristics and then selecting members from each stratum
y-intercept
the value of the resonse variable when the explanatory variable is zero
Convenience sampling
choosing those who are easiest to reach as your sample.
median
value for which half the numbers are larger and half are smaller
regression line
A straight line that describes how a response variable y changes as an explanatory variable x changes
Response Variable
Variabvles that you hope to predict or explain (Y)
Double Blind
a test procedure in which the identity of those receiving the intervention is concealed from both the administrators and the subjects until after the test is completed
segmented bar charts
divide up area of rectangle according to categories
single blind
when the subjects in an experiment do not know if they are in the treatment or control group
Simple Randomized Comparative Design:
treatment groups are selected randomly and comparisons are drawn across groups.
confounding
the effect (if any) of x on y is confounded with the effect of a lurking variable z
Binomial Probability Model
Counts the number of successes in n trials
Interval level of measurement
a measurement level that ranks data and in which the precise differences between units of measure exist
frequency distribution for categorical data
a table that displays the possible categories along with the associated frequencies or relative frequencies
Power Regression
a line of fit for data that shows a power relationship. To determine this, you would have to determine that the shape of the distribution is not exponential.
A log - log transformation on the explanatory and response variable will straighten out our data and allow us to use linear regression.
Third Quartile
75th percentile
Se
Standard Deviation of residuals
randomization
random assignment of experimental units to treatments or of treatments to trials
correlation measures the strength of only this type of relationship
linear
Matched Pairs
an observational technique that involves matching each participant in the experimental group with a specific participant in the control group in order to eliminate the possibility that a third variable (and not the independent variable) caused changes in the dependent variable
stemplot
Shows the overall shape of a distribution while retaining each numerical value of the data.
Percentile
The percent of the distribution that is at or to the left of the observation
Undercoverage
When part of a population is represented less than another
Experimental Design
A design in which researchers manipulate an independent variable and measure a dependent variable to determine a cause-and-effect relationship
Dependent variable
a variable in correlation and regression analysis that cannot be controlled or manipulated
principles of experimental design
control, randomize, replicate, block
Replacement
placing cards/names etc. back into the sample space to ensure probability is preserved.
multiplication rule
method for finding the probability that both of two events occur
experimental units
Individuals on which teh experiment is done
Categorical Variable
records which of several groups or categories an individual belongs to
double-blind experiment
an experiment in which neither the subjects nor the individuals who measure the response know which treatment was received
Confidence Interval
An inverval used for estimating a parameter
design
refers to the method used to choose the sample from the population
population parameter
a numerically valued attribute for a poppulation ex: mean income of all employed people
Confounding variable
a variable that influences the outcome variable but cannot be separated from the other variables that influence the outcome variable
bar chart
a display for categorical data that uses bar height to represent counts or percentages for each category
Simulation
the imitation of chance behavior on a model that accurately reflects an experiment under consideration
**Make sure your probability model mimics that of the true experiment...
Positively Associated
High values of one variable tend to occur together
Standard Deviation
Measure of spread - tells the average distance each value is away from the mean
population of interest
all of the individuals from which subjects for an experiment may be drawn
Data value or datum
a value in a data set
Continuous Random Variable
a random variable with an infinite number of possible outcomes. The probability distributions of a continuous random variable are shown as density curves. Probabilities are found by finding the area under the curve.
P (X = A) = 0 *Recall that the probability for any given event of a continuous random variable is zero!
Remember that P(X>x) = P(X>x) for a CONTINUOUS random variable (fix formula)
cumulative relative frequency plot
a graph of a cumulative relative frequency distribution
Pilot
Small trial run of a survey to see if questions are clear
advantage of histogram
easy to see shape of distribution & good for large data sets
1 in k systematic sampling
a sample selected from an ordered arrangement of a population by choosing a starting point at random from the first k individuals on the list and then selecting every kth individual thereafter
Simple Random Sample (SRS)
The best way to sample by size n consist of n individuals from the population chosen in such a way that every set of n individuals has an equal chance to be the sample actually selected.
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