statistics 121 test 1

the entire group of individuals that is the target of our interest; generally too big to actually measure or observe

subgroup of the population which we can examine or observe, measure and collect data from

single entity that is being observed

characteristic measured on each individual

variable whose possible values are meaningful numbers

variable whose possible responses are non-quantitative categories (words/labels/attributes)

value of a variable for an individual

measurements for a set of individuals (Goal of Statistics: convert this to useful information)

data identified with contextual information (who was observed, what was measured, why is study done) often given in a table

• organize and summarize data

• discover features, patterns and striking deviations

• interpret patterns in context

• include visual displays and numerical values

distribution of a variable: summary of data one variable at a time (all the possible values and how often they occur)

1. Collect data

2. Summarize data

3. Interpret data

numerical fact about the variable in the population

numerical fact about the variable in the sample

select individuals in the easiest possible way

individuals select themselves

force the sample to meet specified quotas

every possible set of a specified size has an equal chance of being selected

a random sample of clusters is taken and all individuals in selected clusters are included in sample

select a random sample (SRS) from each stratum and combine these SRSs together

take a sample at each hierarchical level of the population

the condition applied to a subject in an experiment (one of the subcategories/values of the explanatory variable)

variables that affect both the explanatory and response variables but are not measured or included as a planned factor in the study

an effort to reduce the effects of lurking variables

situation in which effects of lurking variables cannot be distinguished from effects of factors

study involving only one treatment, where treated subjects are compared to untreated subjects from some external source

assigns one subject only to each treatment

treatment groups are handled differently in some way OTHER than the treatment

some individuals have no possibility of being selected

some selected individuals choose not to be in the sample because they refuse to provide information or cannot be contacted

people lie or give inaccurate answers (often about sensitive issues)

person asking questions influences responses (for in-person/phone surveys)

the order that questions are asked promotes certain responses

the way a question asked leads, misleads or confuses

allow for almost unlimited possible responses (short answer), less restrictive but more difficult to analyze

limit response options (multiple choice), easier to analyze but may be biased by the options provided. should include "other/unsure" option

individuals are not assigned to treatments, are self selected, cannot conclude causation

study where individuals are assigned to treatments, causation okay if valid

individual to which treatment is applied

characteristic measure on each subject; outcome of interest

characteristic/measurement that is use to predict or explain changes in the response variable; variable we think could help us know about the response (measured earlier or more easily); independent variable

planned explanatory variable

two or more groups; controls lurking variables by including comparison treatments

randomly assign subjects to groups; neutralizes effects of lurking variables by assigning subjects to treatments using a random device

two or more subjects in each group; assign more that one subject to each treatment to detect important effects

neither subjects nor the researchers in direct contact with the subjects know which treatment is received

favorable response of a human subject to a placebo because of trust in the medical provider or belief that the treatment will work

diagnosis of subjects is biased by preconceived notions about the effectiveness of the treatment (person administering treatments expects certain responses)

realism is compromised by the conditions of the study

people in experiment behave differently than they would normal behave, not like real life

subjects fail to submit to the assigned treatment or refuse to follow the protocol of the experiment

• safety and well-being of the subjects must be protected • all individuals must give their informed consent before data are collected • individual data must be kept confidential

randomly assign subjects to treatments, grouped by treatment

randomly assign to treatments within blocks, grouped by treatment or by block

• removes confounding of lurking variables

• reduces chance variation by removing variation associated with the blocking variable

• yields more precise estimates of chance variation

two treatments; matched individuals or two measurements per subject

• randomly assign two treatments to two individuals or randomize the order of treatment application to each individual

• replication = number of pairs

• compare the two treatments

• always plot data first

• look for an overall pattern and for striking deviations

• look at shape, center, spread of distribution

• add numerical summaries to supplement graph

• if pattern is regular, use mathematical model to describe data

blood pressure, IQ, biological factors

mean, median, and mode are the same

concentration of data on left, tail extends to the right; mean > median

salary, home price, children, economic variables

concentration of data on right and the tail on the left; median > mean

test scores, olympic high jump

a distribution with two modes

speed limits, restaurant patrons

relatively equal across graph

rolling a die, day of the month born

typical, middle value; half of data to each side

consistency/inconsistency of data; look for maximum and minimum

values that are far outside most of data

• is data point miscoded?

• unusual conditions?

• should data point be excluded?

most frequently occurring score, corresponds to a peak

the middle score in a distribution; half the scores are above it and half are below it

center of gravity; the arithmetic average of a distribution, obtained by adding the scores and then dividing by the number of scores

• construct graph to evaluate skewness and outliers

• use median if distribution is markedly skewed or outliers are present

• use mean if distribution is roughly symmetric

maximum - minimum

the difference between the first and third quartiles

average distance of values from the mean

a number for which 25% of the data is less than that number; same as the median of the data which are less than the overall median

median

a number for which 75% of the data is less than that number; same as the median of the part of the data which is greater than the median

use 5 number for skewed, and 2 number for symmetric

minimum, Q1, median, Q3, maximum

individual outcome unpredictable, but outcomes from large number of repetitions follow regular pattern

the set of all possible outcomes

a collection of possible outcomes

The proportion of times that an outcome occurs in many, many repetitions of the random phenomenon

• 0<P(A)<1

• summation of all probabilities is 1

• if two events cannot occur simultaneously, the probability of one or the other equals the sum of separate probabilities

• probability of event not occurring equals one minus the probability of event occurring

number of favorable outcomes divided by total number of possible outcomes

number of outcomes divided by total of repetitions

As the number of repetitions of a probability experiment increases, the proportion with which a certain outcome is observed gets closer to the theoretical probability of the outcome

the long-run relative frequency with which an event will occur

all possible events and their associated probabilities

a variable whose value is a numerical outcome of a random phenomenon

a variable that can take on any possible value, all values cannot be listed

variable whose possible values are a list of distinct values

mean of a population

mean of a sample

standard deviation of a sample

standard deviation of a population