AP Statistics - Full

Normal Distribution

Normal Distribution

Data near the mean are more common than data far from the mean

Positive Skew distribution

Tail is longer on the right

Negative Skew Distribution

Tail is longer on the left

SOCS

Shape, Outlier/unusual, Center, Spread

z-score

Flashcard: "Z-score formula calculates how many standard deviations a data point is from the mean in a normal distribution. Formula: z = (X - μ) / σ."

Can also be found using invNorm on calculator

Interquartile Range

Q3 - Q1

Outlier

Data point if it is less than [Q1 - 1.5IQR] or more than [Q3 + 1.5IQR]

Standard Deviation

Average distance between an individual data value and the mean

Least-Squares Regression Line

Associations that are approximately linear on a scatter plot

Formula: ŷ = a + bx

Residuals

The difference between the actual value on the scatter plot and the value on the line of the scatter plot

Formula: e= y - ŷ

Line of Best Fit

Residuals on the LSRL being in a random pattern

Lurking Variable

One variable causing two another variables to change together

Confound Variable

The effect of multiple explanatory variables on a response variables cannot be changed

Simple Random Sample (SRS)

Each set of individuals having an equal chance of being randomly selected

Stratified Random Sample

Population divided into groups or strata and use SRS to select individuals from groups

Cluster Sample

Population is divided into non-homogenous groups (ex: geographic location) and use SRS to select individuals in groups

Systematic Sample

Selecting individuals in a certain interval order (ex: every 5th person)

Convenience Sample

Biased sample that selects individuals in a ‘convenient’ manner.

Voluntary Response Bias

Asking for volunteers instead of selecting participants

Non-response Bias

Researchers choose the participants, but refuse to participants

Response Bias

Anything in the survey design that might induce a SPECIFIC answer

Undercoverage Bias

Some portion in population not being included in right proportion

Single-Blind

One party (researchers or participants) are blinded

Double-Blinded

Both parties are blinded

Placebo

Fake treatment

Conditional Probability

The likelihood of an event happening given that another event has already occurred. It is calculated by dividing the probability of both events occurring by the probability of the given event.

P(A|B)

Compound Events (AND)

Compound Events (AND): Events that occur simultaneously or in conjunction. The outcome is dependent on the occurrence of both events. Independent

P(A ∩ B)=P(A)⋅P(B)

Compound Events (OR)

In probability, this refers to events that can occur separately or together, resulting in at least one of the events happening.

P(A U B) = P(A) +P(B) - P (A ∩ B)

Independent Events

One event does not affect the probability of another event

If P(A and B)=P(A)⋅P(B)

If P(A|B) = P(A)

Mutually-Exclusive Events

Both events cannot occur at the same time

If P(A ∩ B) = 0

Uses the (OR) formula

Binomial Probability

A probability distribution that describes the number of successes in a fixed number of independent trials with the same probability of success.

binomPdf(n,p,x)

n = number of trials

p = probability of success

x = number of successes

Geometric Distribution

A probability distribution that models the number of trials needed to achieve the first success in a series of Bernoulli (trials with two possible outcomes) trials.

z-test

Only used if standard deviation is known

one-sample t-test

Only used if experiment has only one independent variable and one group/condition

t-test for independent means

Only used if there is one independent variable and two groups/conditions

Pooled variance