Statistics

values that fall into separate, non-overlapping categories such as marital status or hair color

values that have measurement units such as dollars, degrees, inches, etc

minimum value, Q1, the median, Q3, and maximum value

• x-bar=(sum of values/number of values)
• not resistant to extreme values

• middle of data set when the data have been ordered
• resistant to outliers
• a more appropriate measure of center when outliers are present or distribution is skewed

• measure of spread (variation)
• not resistant to outliers

• IQR=Q3-Q1
• gives the spread of the middle 50% of the data
• resistant to outliers

• maximum-minimum
• single number
• extremely sensitive to outlying values

z=(data value-mean)/SD

68 - 95 - 99.7%

• 1. identify the variables and state the problem in terms of the observed variables
• 2. standardize the values by converting to z-scores

• with z-score: 2nd Distr --> normalcdf (lower bound, upper bound)
• without z-score: 2nd Distr --> normalcdf (lower bound, upper bound, mean, standard deviation)

defines the groups to be compared with respect to values of the response variables

the variable you hope to predict or explain. the outcome

• no units
• requires quantitative variables
• -1<r<1
• r=0 represents no correlation
• r only measures the strength of a linear relationship
• not resistant to outliers

• y=bo+b1x
• y=a+bx
• bo(a) is the y-intercept
• b1(b) is the slope in "y-units per x-unit"

• observed value - predicted value (y-ycap)
• the sum of the residuals is always equal to 0

• 1. identify the trial to be repeated
• 2. state how you will model the random occurrence of an outcome
• 3. explain how you will simulate the trial
• define the response variable
• 4. run several trials
• 5. summarize the results across all trials
• 6. describe what your simulation shows and draw your conclusions about the real world

entire group of individuals that we hope to learn about

a smaller group of individuals selected from the population

• a number that characterizes some aspect of the population such as the mean or standard deviation of some variable of the population
• Greek letters

• values calculated for sample data
• used to estimate values in the population (parameters)
• standard letters

each possible sample of n individuals has an equal chance of selection

• population is first broken up into homogeneous groups called strata
• strata have something in common that effects the response variable

divides the population into heterogeneous groups called clusters and then takes an SRS of some of the clusters

• undercoverage
• voluntary response bias
• convenience sample
• nonresponse
• response bias

researchers observe individuals and record variables of interest but do not impose a treatment

• researcher deliberately imposes a treatment
• must identify at least one response and explanatory variable
• used to determine a cause-and-effect relationship

groups based on a certain characteristic that they share that may affect the results of the experiment

• a form of block design
• one subject: receives both treatments

no treatment/traditional treatment/placebo

variables that we did not think to measure but which can affect the response variable

reduces bias by equalizing the effects of lurking variables

• should include many subject in a comparative experiment
• experiment should be designed so that other researchers can replicate our results

subjects do not know which treatment group they have been assigned OR those who evaluate the results of the experiment do not know how subjects have been allocated to treatment groups

NEITHER the subject nor the evaluators know how the subjects have been allocated to treatment groups

cannot separate the effect of a treatment (explanatory variable) from the effects of other influences (confounding variables) on the response variable

single attempt or realization of a random phenomenon (rolling a pair of dice)

the value measured, observed, or reported for each trial (the faces shown on the dice)

the set of all possible outcomes

• collection of outcomes
• usually designated by capital letters
• ie: A=the probability of rolling a sum of seven when two dice are rolled

the long-run relative frequency of repeated independent events gets closer and closer to the true relative frequency as the number of trials increases

if the occurrence of one event does not alter the probability that the other event occurs

the set of all possible outcomes that are NOT in the event A

cannot occur together