unit 1 stats

data

systematically recorded information

used to calculate, analyze, or predict

something

Statistics

it is the study of how to collect,

organize, analyze, and interpret data (usually

collected from a group)

descriptive statistics

Using tables, graphs (histograms, scatterplots,

etc) and numbers (mean, median, standard

deviation, correlation, etc) to organize and

summarize and describe the data at hand

(usually sample data).

inferential statistics

Analyze a “small” specific set of data (sample)

in order to draw a conclusion about a “large”,

more general group (population)

• 2 Types

– Confidence intervals

– Hypothesis tests

individual

a person or object that you are interested in

finding information about

variable

the measurement of observation recorded for each

individual

population

set of all individuals that are of interest for some

question or study (typically very “large” and often

implied/unstated)

sample

a subset from the population that you actually

collect data for (usually “small” compared to the the

population and always known)

parameter

is a numeric descriptor of / number

calculated from a population

– It is a fixed number, usually unknown, that you want to find

– EX: μ, σ (typically Greek letters)

statisitc

is a numeric descriptor of / number

calculated from a sample

– readily known/found and used to estimate parameter

– EX: ̅ 𝑥, s

what is the difference between a parameter and statistic

Parameters are fixed, but statistics vary from

sample to sample

qualitiative

A word or name that describes a quality of the individual

(does not count or measure anything)

• Non-numeric (typically)

quantitative

Something that can be counted or measured from the individual

• Numeric

types of quantitative data

discrete and continuous

discrete data

finite number of subdivisions (things you count)

continuous

infinite subdivisions (things you measure)

census

Collects data on the entire population

SRS

every individual has same chance and every

sample has the same chance- known as best method

stratified

break into strata (not random) and

then take SRS from each strata

systematic

take every Kth individual for the

sample

cluster

divide into clusters (not random) and

then get info from all individuals in some

randomly selected clusters

convience

sample individuals that are nearby

or conveniently located

data collection bias

– Measurement Device

– Personal Bias (Blind/Double Blind)

– Questioning technique / wording

sampling method bias

– Voluntary Response

– Convenience Sampling

– Nonresponse

– Undercoverage

– Response Bias

distribution

A list of all possible values of a variable and how

often each value occurs

When describing distributions of quantitative

variables, we focus on…

– Shape

– Center

– Spread (variation)

– Outliers

frequency

how often something occurs

frequency distribution

A summary table of a distribution listing variable

values, frequencies, and often other information

relative frequency

Percent of total, listed as percent or decimal; also

called sample proportion

frequency table

organizes collected data in table form using categories

(or classes) and frequencies (counts)

relative frequency table

organizes raw data in table form using categories (or

classes) and proportions (or percentages).

• Relative frequency tables are useful when comparing data sets where the sample sizes are not the same

graphical displays for qualitative data

• pie chart

• bar chart (bars dont touch)

• pareto chart

univariate data

one variable

bivariate data

two variables

multivariate data

3 or more variables

graphical displays for quantitative data

• histogram

• scatterplot

• stem plot

histogram

a graph of the frequencies (or relative

frequencies)

• for quantitative data

• bunched into classes

class width

(max-min)/# of classes

• always round up

symmetrical

does not need to be perfect, also called bell shaped

skewed left

tail to the left (negatively skewed)

skewed right

tail to the right (positively skewed)

uniform

symmetric

stem plots

are used for small (typically 𝑛𝑛 ≤ 40)

quantitative data sets involving a single variable

• can be used to determine shape

scatterplots

display trends in the relationship

between the 2 quantitative variables