Stats full review

Statistics

The science of collecting

Descriptive Statistics

Organizing and summarizing data

Inferential Statistics

Making generalizations from a sample to a population

Population

Entire group of individuals or objects

Sample

Subset of a population

Variable

A characteristic that can change

Data

Observations on variables

Categorical (Qualitative)

Describes characteristics

Numerical (Quantitative)

Numerical measurements

Discrete

Countable values

Continuous

Any value in an interval

Univariate

One variable

Bivariate

Two variables

Multivariate

More than two variables

Symmetrical Distribution

Both sides mirror each other

Uniform Distribution

All values occur equally

Skewed Right

Tail extends right

Skewed Left

Tail extends left

Bimodal Distribution

Two peaks

SOCV

Shape

Mean

Average (μ for population

Median

Middle value (50th percentile)

Mode

Most frequent value

Range

Max − Min

IQR

Q3 − Q1

Standard Deviation

Typical distance from mean (σ population

Variance

Standard deviation squared

Resistant

Not affected by outliers

Non-resistant

Affected by outliers

Median & IQR

Resistant

Mean & SD

Non-resistant

Symmetrical

Mean = Median

Skewed Right

Mean > Median

Skewed Left

Mean < Median

Z-Score

Number of standard deviations from the mean

Standard Normal Distribution

μ = 0 and σ = 1

Empirical Rule

68%-95%-99.7%

5-Number Summary

Minimum

Outliers

Points beyond 1.5 IQR

Sample Space

All possible outcomes

Event

Any set of outcomes

Complement

Outcomes not in the event

Union (A ∪ B)

A or B

Intersection (A ∩ B)

A and B

Mutually Exclusive

Cannot happen together

Independent Events

One does not affect the other

Addition Rule

P(A or B) = P(A) + P(B) − P(A and B)

Multiplication Rule

P(A and B) = P(A) · P(B) if independent

Conditional Probability

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

Correlation Coefficient (r)

Strength and direction of a linear relationship

Least Squares Regression Line (LSRL)

Line that minimizes residuals

Residual

Actual value minus predicted value

Coefficient of Determination (r²)

Percent of variation in y explained by x

Extrapolation

Predicting outside the data range (not valid)

Census

Entire population

Simple Random Sample (SRS)

Every sample equally likely

Stratified Sample

SRS taken within groups

Cluster Sample

Sample entire clusters

Systematic Sample

Every nth individual

Voluntary Response Bias

Self-selected participants

Convenience Sampling

Easy-to-reach subjects

Undercoverage

Some groups left out

Nonresponse Bias

People do not respond

Response Bias

False or influenced answers

Observational Study

Observe without imposing treatment

Experiment

Treatment imposed on subjects

Control Group

Baseline comparison group

Placebo

Treatment with no active ingredient

Blinding

Subjects unaware of treatment

Double Blind

Subjects and evaluators unaware

Random Variable

Numerical outcome of a random process

Discrete Random Variable

Counts

Continuous Random Variable

Measurements

Binomial Distribution

Fixed number of trials

Geometric Distribution

Trials until first success

Sampling Distribution

Distribution of a statistic from all possible samples

Central Limit Theorem

Large sample size leads to normal sampling distribution

Confidence Interval

Statistic ± margin of error

Margin of Error

Critical value multiplied by standard deviation

Degrees of Freedom

n − 1

Null Hypothesis (H₀)

No effect

Alternative Hypothesis (Hₐ)

What is suspected to be true

P-Value

Probability of observing results assuming H₀ is true

Significance Level (α)

Threshold to reject H₀

Type I Error

Rejecting a true null hypothesis

Type II Error

Failing to reject a false null hypothesis

Power

1 − β

Goodness of Fit Test

One categorical variable

Test of Independence

Relationship between two categorical variables

Test of Homogeneity

Comparing distributions across multiple groups