STATS

main stat words?

populations, samples, parameters, statistics

Definition of Statistics?

Statistics is the science of collecting, classifying, organizing, summarizing, analyzing, and interpreting data to make informed decisions.

data—> extract useful info

Descriptive Statistics?

organizing data (collecting data)

summarizing data

presenting data in an informative way

Inferential statistics?

Determining something about a population based on a sample.

Or methods for making decisions/predictions and drawing conclusions about populations.

Making inferences

population

sample group

inference?

intelligent guess

Sample group to population

Population?

group you are interested in researching

all individual who matter

sampling?

population to sample group

created through randomenss

will face loss of information

Sample group?

represent population

not enough resources to research total population

created through random draw

z tests

for population means

t tests

for comparing one, two, and paired samples

chi square test

for independece and fitness

f tests

for comparing variances

simple linear regression

for modeling relationships between somehting

infernce

uncertainty

can’t be 100% certain conlusion is right

confidence interval quantifies certiantiy

relationship between uncertainty and sample size

bigger the sample size —→ the less uncertainty

inverse relaitonship

Data

refer to any collection of numbers, characters, images, or other items that provide information about something.

Population

A collection or set of all units (usually people, individuals, objects, or events) that we are interested in studying. Populations can be classified into two types: finite and infinite.

Sample

A representative subset of the population's units.

Census

A data collection from every member of the population.

no loss of data 100% certain

Parameter

A numerical value that summarizes a characteristic of an entire population.

unknown but fixed

population

The proportion of all

can only know the true value if there is a census

acts a guideline, something to be based on

Statistic

A numerical value that summarizes the data from a sample

known but vary

sample

The proportion of in our sample

Unit / Subject

The entity from which data is collected or observed in a statistical study.The term "unit" is often used interchangeably with "individual" or "subject" in statistical contexts. Units can be people, animals, objects, or any other entities that are the focus of study and data collection.

Variable

A characteristic of each individual element of a population or sample.

(yes/no)

blank or blank

binary variable

two choices

yes or no

left or right

data matrix

Variable, Case, and Observation

row=case

column=variabe

types of populations

finite

infinite

your turn

pop: us adults

sample: 1000

Types of Variables (or Data)

Qualitative (Categorical)

Quantitative (Numerical)

Qualitative (Categorical)

A variable that describes attributes, labels, or nonnumerical entries.

simple description

1. Car model

2. Days of the week

3. Type of cell phone

4. Zip code

5. Which club you have joined

Qualitative (Categorical): Nominal

No rank or order

• Gender

• Nationalities

• Colors

• Blood Types

jersey numbers

Qualitative (Categorical): Ordinal

Natural order

rime and reason

• Course letter grades: A, B, C, D, or F

• Educational level

• Socioeconomic status

Quantitative (Numerical)

A variable that consists of numerical measurements or counts.

amount, calculated

1. GPAs

2. Student heights

3. Parents’ income

4. Number of text messages per day

5. Weight of textbooks

Quantitative (Numerical): Discrete

counted items

• Number of students in a class

• Number of books on a shelf

• Number of languages a person speaks

list

whole numbers

Quantitative (Numerical): Continuous

Measured items

• Age of preschool children

• Height college students

• Weights of supermodels

• Temperature (oC or oF)

decimal points

can be changed into ordinal if grouped in order

Measurment scales

nominal

ordinal

interval

ration

Nominal level of measurement

categorizes data into mutually exclusive, non-overlapping groups, with no inherent order or ranking among the categories.

Zip code

Gender (male, female)

Major field (Statistics,

Biology, etc.)

Eye color (blue, brown,

green, hazel)

Ordinal level of measurement

organizes data into categories that can be ranked or ordered, but the precise differences between the ranks are not defined.

Grade letter (A, B, C, etc.)

Rating scale (poor, good, excellent)

Judging (first place, second place, etc.)

Interval level of measurement

orders data and allows for meaningful comparisons of differences between values; however, it lacks a true zero point.

Temperature,

IQ score,

SAT score

GPA

true zero=absence of measurement

can’t have no temperature, no IQ

can’t use ratio to compare, something can’t be 2x more than something

always greater than zero

Ratio level of measurement

includes all the properties of the interval level, while also possessing a true zero point. Moreover, meaningful ratios can be formed when comparing measurements of the same variable across different individuals or objects.

Height

Weight

Time

Salary

Age

Can have zero height, wieght, salary

Can use ratios like something being 2x more than something else

Why Do We Use Samples in Statistics?

Difficult to access the entire population: length of all fish

Limited resources: time and money

Destructive measurements: safety car tests

Sampling can be conducted in two ways:

With replacement:

Without replacement

Sampling can be conducted in two ways: With replacement:

perfect randomness

random

a population member may be selected more than once (e.g., Rolling a die, recording the outcome, and then rolling it again—each number can appear multiple times.)

Sampling can be conducted in two ways: Without replacement

non-random

a population member may be selected only once (e.g., drawing a lottery ticket).

population much be large enough

Methods of Sampling

random sampling methods

non-random sampling method

parameter acts as a original guideline, what its based on

3 or more, not specific

matrix tables count each event as a scene, row

each crash is a scene

frequency table

a descriptive table summarizing the number of occurrences for each outcome within the sample

row=types of occurrences

not specific scenes