Stats 67 Exam 1 (Lec 1-6)

label

variable used to distinguish cases

What are some features of categorical variables?

they have finite possibilites, can either be ordered or unordered

What is the difference between an ordered(ordinal) and unordered(nominal) categorical variable.

In an ordered categorical variable, the categories have a meaningful sequence, while unordered categorical variables do not have any intrinsic ranking between the categories.

What are some features of quantitative variables

These are variables which have qualities that make sense to use mathematical operations on. They can either be continuous or discrete.

What is the difference between a continuous and a discrete quantitative variable.

In a continuous variable, the value can reasonably be any number. In a discrete variable, the values are counted, and have meaningful differences between values.

What is anecdotal data?

Anecdotal data is data that is not meaningfully representative of a whole population.

What is available data?

Available data is data that was collected to answer a different question, that can also be used to answer the current one.

What is an observational study?

a study where you do not influence a response and observe what people do

What is an experiment

a study where you impose conditions and do not influence responses, and observe what happens

what is a confounding variable?

when an explanatory variable is related to one or more variables → influencing a response variable

census

an attempt to collect data for every individual in a population

What are two types of bad samples

convenience sample, voluntary response

What is a convenience sample?

when you sample people easily available to you

What is the problem with a convenience sample?

you may over or under represent one group in the sample

What is a voluntary response sample?

a sample where people voluntarily respond

What is the problem with voluntary response?

people with strong opinions are more likely to respond.

What is a simple random sample?

a sample where you choose n individuals, and each individual has the same random chance to be chosen

what is a systematic sample

randomly select starting point, select every kth individual for some int k

what is a stratified sample

a sample where you divide the population into similar groups called strata, perform a simple random sample in each strata to get the full sample

What is a cluster sample

choose clusters from the popluation randomly, SRS each cluster

what is a multistage sample

a sample where you divide the population into clusters, choose certain clusters, get a random sample from each cluster.

what is a factor

an explanatory variable

What are the principles of experimental design?

Controlling, Randomization, Replication, Blocking

What is controlling in statistics?

The act of controlling variables, isolating experimental conditions.

What is randomization in statistics?

randomize patients into groups to control uncontrollable variables

what is replication in statistics?

repeating treatments to reduce chance variation in the results

what is blocking in statistics?

grouping similar subjects by important characteristics, then randomly assigning treatment within each group

what is completely randomized experiment design

very subject is randomly assigned a treatment without regards for any other characteristic

what is a matched pair experimental design

choose two subjects that are as similar as possible, give treatment one to one person and treatment two to the other.

what is placebo

giving someone a fake treatment to prevent people from biasedly responding to treatment.

what is a block experiment design

block subjects based on a similar characteristic (ex. men or women), then perform the same experiment on the different blocks

what is blinding when performing experiments.

hiding the treatment a subject is receiving from the subjects or experimenters.

what is a single blinded experiment

either the researcher or the subject is blinded, but not both

what is a double blinded experiment?

an experiment where both the researchers and the subject are blinded.

what is the experimenter effect?

when a researcher influences the outcome of an experiment due to the knowledge of the treatment they are being given

what is the difference between a frequency table and a relative frequency table?

a freq table only includes counts, where a relative freq table contains proportions

what kind of plot/graph would you use for categorical data?

pie chart or bar graph

what kind of plot/graph would you use for quantitative data

histogram, box plot, stemplot, dotplot, line plot

what are some other names for a two way table?

contingency tables or cross-classification tables

what is a marginal distribution

row and column totals for each row/col

what is a joint distibution?

a two way table in which the entries are proportions of the whole data set.

what is simpsons paradox

a statistical phenomenon where a trend or relationship appearing in different groups of data completely disappears or reverses direction when those groups are combined into a single dataset

lurking variable

a variable that is not explanatory or response, but may influence interpretation of results

what is a mode?

a value that appears the most in a dataset

what does a unimodal dist look like?

one hump

what does a bimodal dist look like?

two humps.

what does skewed data look like?

hump(s) is/are not in the center of the plot

what does left skewed data look like

tail left

what does right skewed data look like

tail right

is the mean sensitive to outliers

yes

are the mean and median similar in symmetric data?

yes

what is a quantile

a cut point that divides a sorted list of data into equally sized groups. ex quartiles. divides into 4 groups.

what is a resistant measure?

a measurement that is resistant to outliers

what does the 1.5X IQR rule do

helps find outliers. val > Q3 + 1.5*IQR or val < Q1 - 1.5IQR are outliers.

what does variation measure?

averages of the squared distance each point is from the mean

what does std dev measure?

measures variance abt mean

what does it mean if std dev =0?

each item in the sample is the same

is std dev a resistant measure?

no

what values are in the 5 num summary?

min, q1, median, q3, max

what is usually paired with the mean to describe a distribution(think center and how it varies)

std dev

what is usually paired with the median when describing a distribution (think center and how it varies)

IQR

if you have a symmetric distribution, what values would you use to describe its center and variation?

mean and std dev

If you have a skewed distribution, what values would you use to describe its center and variation?

median and IQR

what are the two parts of a probability model?

sample space and a way of assigning probabilities to events

define an event

outcome or set of outcomes of random phenomenon, subset of sample space

what two conditions make 2 events A and B disjoint?

if they have no outcomes in common and they can never ocurr together.

P(A or B) = ?

P(A) + P(B)

are individual outcomes of random phenomenon always disjoint?

yes. you cant have two outcomes at once

what is the multiplication rule for independent events?

P(A and B) = P(A)*P(B)

what is P(A or B) if A and B are not disjoint?

P(A) + P(B) - P(A and B)

how do you find P(B|A) ?

= P(A and B) / P(A)

how can you find the probability that two events A and B happen together?

= P(A) * P(B|A)

how do you find P(A and B and C)?

P(A)* P(B|A) * P(C| A and B )

how do you find P(A or B or C)?

P(A) + P(B) + P(C) -[P(A or B) + P(B or C) +P(A or C) + P(A and B and C)]

A and B are independent if?

P(B|A) = P(B), or if P(A and B) =P(A)*P(B)

what is Bayes Rule?

P(A|B) = (P(B|A) *P(A)) / P(B)

what are some properties of a density curve?

they are always at or above the horizontal axis, and its integral evaluates to one.

what is the probability of any event using a density curve?

area under the curve and values above X that make up the event *note: this is a somewhat unintuitive definition, just think of integrating the model with specific little x’s for the bounds.

what is the difference between X and x (notation)?

X is a random variable, and x is an outcome of the random variable

what is a probability distribution

model that describes the likelihood of different possible outcomes for a random variable

what does the mean of a probability distribution represent?

the expected outcome. think averaging a graph.

how is the mean of a probability distribution denoted

mu or E(X)

how is E(X) calculated for discrete random variables

SUMMATION xi * Pi for all outcomes, where x is an outcome

how is E(X) (mean) calculated for continuous random variables that are skewed?

integral x*F(x) dx, where f(x) is the probability density function

The probability distribution of a continuous random variable is described

by?

a density curve

where does the mean lie in a symmetric density curve?

center

what is the law of large numbers

as you keep adding more observations, your observed mean will get closer and closer to the theoretical value

(Rules for means) E(a + bx) =

a + bE(X)

(Rules for means) E(X+Y) =

E(X) + E(Y)

(Rules for means) E(x-y) =

E(X) - E(Y)

Var(X) = ? (related to expected value/mean)

E(X²) - E(X)²

var(X) (sigma notation)?

summation(x i - mu x)²*p i

std dev =? (related to variance)

sqrt(var) or sqrt(sigma²) or sigma

how do you find the variance of a continous random variable

integral (x-mu x)² *f(x) dx, where f(x) is the probability density function

does adding a constant to the variability change it?

no

what effect does multiplying the var by a constant a do?

it multiplies the variance by b²

Var(X+Y) = (independent)

Var(X) + Var(Y)

Var(X-Y) =(independent)

Var(X) - Var(Y)

Var(X+Y) = (random)

Var(X) + Var(Y) +2Cov(X,Y)