semester 1 final

statistics

the science of collecting, analyzing, and drawing conclusions from data

statistic

a specific calculation from a data set

data

information with context

sample

group we gather data from

population

overall group of interest

variable

attribute that can take different values for different individuals

categorical variable

assigns labels that place each individual into a particular group

quantitative variable

numerical values that count or measure some characteristic of each individual

frequency table

lists category names and counts for each category

relative freaquency table

lists category names and percent for each category

bar graph

shows each category as a bar, heights of bars show category frequencies or relative frequencies

pie chart

shows each category as a slice of the pie, areas of slices are proportional to the category frequencies

two-way frequency table

table of counts that summarizes data on the relationship between two categorical variables for some groups of individuals

marginal relative frequency

gives percent or proportion of individuals that have a specific value for one categorical variable

conditional relative frequency

table of counts that summarizes data on the relationship between two categorical variables for some groups of individuals

side-by-side bar graph

displays distribution of a categorical variable for each value of another categorical variable, bars are grouped together based on the condition and placed side by side

segmented bar graph

displays distribution of a categorical variable as segments of a rectangle, area of each segment is proportional to percent of individuals in the corresponding category

mosaic plot

modified segmented bar graph in which the width of each rectangle is proportional to the number of individuals in the corresponding category, vertical axis is percent, don’t need spaces

mean

average value

median

middle number of a data set

mode

value that occurs the most

range

difference between the max and min

dotplot

shows each data value as a dot above its location on a number line

stemplots

shows each data value separated into two pars: a stem, which consists of all but the final digit, and a leaf, the final digit

histogram

shows each interval of values as a bar, heights of the bars show the frequencies or relative frequencies of values in each interval

boxplots

visual representation of the five-number summary

Q1

median of numbers below median

Q3

median of numbers above the median

IQR

Q3 - Q1

skewed to the right

right side of graph is much longer than left side

skewed to the left

left side of graph is much longer than right side

scatterplot

shows the relationship between two quantitative variable measured on the same individuals

correlation

measures the direction and strength of a linear association between two quantitative variables

regression line

line that describes how a response variable changes as an explanatory variable changes

least-squares regression line

line that makes the sum of the squared residuals as small as possible

residual plot

a scatterplot that displays the residuals on the vertical axis and the explanatory variable on the horizontal axis

coefficient of determination (r²)

measures the percent of variability in the response variable

high leverage point

data point whose x-value is far from the mean of x

influential point

any point that, if removed, substantially changes the slope, y-intercept, or correlation of the regression model

population

entire group of individuals we want information about

convenience sampling

selects individuals from the population who are easy to reach

voluntary response sampling

individuals choose to be in the sample by responding to a general invitation

bias

the design of a statistical study shows bias if it is very likely to underestimate or overestimate the value you want to know

random sampling

involves using a chance process to determine which members of a population are included in the sample

simple random sample

each combination of people has an equal chance of being chosen

stratified random sampling

divide population into groups of individuals based on common traits and choose a simple random sample from each group

cluster sampling

divide population into smaller groups and use a simple random sample to randomly choose entire clusters for the sample

systematic random sample

divide population into equal size groups, randomly decide a starting point in the first group, then take every nth term from there

undercoverage

when some members of the population are less likely to e chosen or cannot be chosen in a sample

nonresponse bias

when an individual chosen for the sample can’t be contacted or refuses to participate

response bias

anything in the survey design that influences the responses

sampling variability

different random samples of the same size from the same population produce different estimates

parameter

number that describes some characteristic of a populaton

observational study

researchers don’t assign choices or treatments, they just observe them

retrospective

examines existing data

prospective

tracks individuals into the future

experiment

deliberately imposes some treatment on individuals to measure their responses

experimental unit

the object to which a treatment is randomly assigned

factor

an explanatory variable that is manipulated and may cause a change in the response variable

levels

the amounts of each experimental factor administered

treatments

levels of the explanatory variable applied to the individuals in an experiment

confounding variable

a variable that is related to the expanatory variable and influences the response variable and may create a false perception of association between the two

statistically significant

when the observed results of a study are too unusual to be explained by chance alone

random process

generates outcomes determined purely by chance

trial

each occasion upon which we observe a random phenomenon

outcome

result ofa trial

event

collection of outcomes

sample space

a list of all possible outcomes

theoretical probability

the likelihood of an event occurring based on expected outcomes

law of large numbers

as we repeat a random process over and over, the proportion of times that an event occurs settles down to one number

conditional probability

probability an event will occur given another event has already occurred

random variable

takes on values based on the outcomes of a random event

discrete random variable

a variable that can only take a countable number of values

continuous randome variable

a variable that can take on any numeric value within an interval

probability distribution

gives all possible values of a random variable and their probabilities

binomial probability

the probability of getting a certain number of successes within a SET number of trials

geometric probability

the probability of getting the FIRST success on the xth trial