Stat 200 Exam 1

a dataset

has many cases or units

cases or units

the subjects or objects that we obtain information about

variable

any characteristic/feature that is recorded for each case (columns)

case

rows, ex: students, countries, people

variable types

categorical and quantitative

categorical

divides cases into categories, often words/symbols

nominal categorical

ex: political party, eye color

ordinal categorical

natural order (year in school, quality of service, letter grade scale)

quantitative

measures a numerical quantity for each case

discrete and continuous

discrete quantitative

can only take a countable set of values (classes missed, puppies in a litter)

continuous quantitative

can take any value within some range (height, distance biked per day, G/dl)

population

includes ALL individuals or objects of interest

sample

all of the cases we have collected data on, a SUBSET of the population

statistical inference

the process of using data from the SAMPLE to gain information about the POPULATION

inference is only valid if…

the sample is REPRESENTATIVE of the population

sampling

drawing from population

drawing from a sample is a process called…

statistical inference

how to avoid bias

take a RANDOM sample from the population

“lottery machine” & never trust people to pick at “random”

simple random sample

each unit of the population has the same chance of being selected, regardless of the other units chosen for the sample

non-ideal methods of sampling

sampling cases based on something obviously related to the variables you are studying

sampling realities

random sampling is ideal, but not always feasible

sometimes it’s OK to reimagine the population of interest

sampling bias or selection bias

participants included are not representative of the entire population

nonresponsive data

some participants included in the sample do not participate in the survey or study

response bias

some participants respond based on leading questions

association

if values of one variable tend to be related to values of another

causation

changing the value of one variable influences the value of another

confounding variable

a THIRD variable that is ASSOCIATED with both the explanatory and response variable

in observational studys/experiments

observational study is

association and has confounders

randomized experiment

causation

control group

when determining whether a treatment is effective, it is important to have a comparison group

treated exactly the same but does not receive treatment

placebo

placebo only works if

blinded/masked

two types of randomized experiments

randomized comparative and matched pairs

randomized comparative

randomly assign cases to different treatment groups and then compare results on the response variables

matched pairs

each case gets both treatments in random order, and then we study the difference in the response variable between the two treatments for each pair

parameter

a summary measure for the entire population

statistic

a summary measure for a sample

sample proportion

p-hat = x/n

n = sample size and x = successes

side-by-side bar chart

height of each bar is the count from the corresponding cell in the two-way table

height could also be expressed as percentages

segmented bar chart

stacked instead of side-by-side

risk

common way to refer to a proportion

number in category/total number in group

risk formula

relative risk

captures a relationship between two two-level CATEGORICAL variables

idea: relate the risk to the explanatory variable

if possible ask for control group at bottom, denominator = baseline risk

relative risk example

5 times the risk

two groups have same risk

= 1

numerator has bigger risk

>1

denominator has bigger risk

<1

odds

a related quantity

compares chance an event happens to the chance it does not

odds example

3 to 2, 1 to 2, 60 to 40 —→ 3 to 2

histogram

the height of each bar corresponds to the number of cases within that range of the variable

x-axis is numeric

histogram

cannot change order of bars

histogram

no numerical x-axis

bar chart

could change order of bars without changing the meaning

bar chart

sample size, number of cases is denoted by

n

xn

n values of the variable x

for symmetric distributions

the mean and median will be about the same

for skewed distributions

the mean will be “pulled” in the direction of the skewness

a distribution is left skewed so the

median is higher

resistant statistics

a stat is resistant if relatively unaffected by extreme values

is the median a resistant statistic?

yes

is the mean a resistant statistic?

no

standard deviation

measures the spread of a distribution

standard deviation is roughly…

the average distance from data points to the mean

the larger the standard deviation…

the more variability there is in the data and the more spread out the data is

the 95% rule

if distributions of data is approximately bell-shaped, about 95% of the data should fall within 2 standard deviations of the mean

2 standard deviations of the mean

x-bar - 2s and x-bar + 2s

x = mean

s = standard deviation

z-score

tells us how many standard deviations a particular value is from the mean

z = observed value - mean / sd

is range a sensitive statistic?

yes, not resistant

is IQR resistant?

yes, quite resistant because it is in the middle 50% of data

positive association

same direction

negative association

different direction

no association

if knowing that value of one variable does not give you any information about the value of another

correlation

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

sample correlation

r (statistic)

population correlation

p (rho) (parameter)

strongest/perfect correlation

-1 < x < 1

the sign in a correlation indicates…

the direction

the magnitude in a correlation indicates…

strength

r = 0

has NO linear correlation

can you still have association and be zero/no linear association

yes

(non-zero) correlation does not imply…

causation

is correlation resistant?

no it is very sensitive, not resistant at all

residual

the vertical distance from the line to the point

residual equation

y - yhat

actual - predicted

do not use the regression equation or line…

to predict outside the range of x values observed in your data

if none of the x values are anywhere near 0…

than the intercept is not directly interpretable

in simple linear regression we assume the relation between x and y is…

linear (makes sense to draw the line)

influential point

an outlier with usually large impact

only used if LINEAR

an influential point

graph(s) to use for ONE CATEGORICAL variable

bar chart and pie chart

graph(s) to use for ONE QUANTITATIVE variable

histogram, box plot, and dot plot

graph(s) to use for one CATEGORICAL & QUANTITATIVE variable

box plot and bar chart

graph(s) to use for TWO QUANTITATIVE variables

scatter plot

graph(s) to use for TWO CATEGORICAL variables

segmented bar chart