Stats Cumulative

Stratified Random Sample

Divides the population into homogeneous groups (e.g., grade levels) and selects a few individuals from each group.

Systematic Sample

Selects individuals at fixed intervals (e.g., every 3rd person).

Simple Random Sample (SRS):

Every individual has an equal chance of being selected

Cluster Sample

The population is divided into groups called "clusters," and then a random selection of those clusters is chosen, with data collected from every member.

1. Assign labels to population or treatments

2. Randomly sample or assign by RNG

3. Stopping Rule

4. Correspondence

How to do random sampling or assignment

1. Context and variables

2. State how sample is not representative of population

3. Over or underestimate

Identify bias steps

1. Experimental units

2. Explanatory variable

3. Response variable

4. Treatments

Types of experiment units

Completely randomized block design

An experimental design in which experimental units are assigned to treatments completely at random.

Randomized Complete Block Design

Experimental units are first blocked (grouped) by a similar trait that may affect response. Then, units from each block are randomly assigned to treatment

Random sampling removes bias, random assignment removes confounding

What reduces bias, what removes confounding

Described by categories, uses side by side or segmented bar chart

Describe categorical and graph

Describe by numericals, uses dot plots, histogram, or stem leaf plot

Describe quantitive and graph

1. Context

2. Make claim

3. Compare percentages

How to describe associations

1. Context

2. Shape: skew, uni, bi

3. Outliers (1.5x IQR rule)

4. Center (mean/median)

5. Spread (range, IQR, SD)

Describing Distributions

1. Range (Max-Min)

2. IQR (Q3-Q1)

3. SD (use calc)

How to calculate spread

1. Mean (add and divide)

2. Median (center)

How to calculate center

Z-score measures how many standard deviations a data point is above/below the mean

= (data point - mean) / standard deviation

What does Z score show?

1. Center changes by constant

2. Spread has no change

Adding/sub a constant by data value

1. Center changes by constant

2. Spread changes by constant

Multiplying by a constant

CDOFS

1. Context

2. Direction (pos, negative)

3. Outliers (influenceable, high leverage)

4. Form (linear)

5. Strength (app strong, moderate, weak)

Compare relationship between bivariate quantitative data

1. How strong two variables are to each other

2. Variation with LSRL

3. How off the regression line fits with residuals

Explain correlation, coefficient of determination, and standard deviation of residuals

Actual-predicted

Calculate residuals

ŷ=a+bx

Equation of regression line ŷ

b= r (response y /explanatory x)

Formula for slope

a=mean of response - b(mean of explanatory)

Formula for y-intercept

Estimating unknown values

Extrapolation

1. Assign labels to population or treatments

2. Randomly sample or assign like RNG

3. Stopping Rule

4. Correspondance

How to format a simulations

Can occur at same time

P(A∪B)=P(A)+P(B)-P(A∩B)

Mutually Inclusive Events and Formula ∪ ∩

Cannot occur at same time

P(A ∪ B) = P(A) + P(B)

P(A ∩ B) = 0

Mutually Exclusive Events and Formula ∪ ∩

P(A∩B) = P(A) P(B) or P(A)=P(A|B)

Solve for Independence ∩

One event happens given that another event is already known to have happened

P(A|B)=P(A∩B)/P(B)

Conditional Probability and formula ∩

The first success of a probability event happening

Geometric distribution

The number of successes of a probability event happening in a number of trials

Binomial distribution

Random variable will be less than or equal to a specific value within a given distribution

CDF

Probability of a continuous random variable taking on a specific value within a given range

PDF

1. Normality is law of large counts np>_10 n(1-p)>_10

2. Mean is by unbiased random sampling

3. SD/spread is 10% condition for independence

Conditions for Using Sampling Distributions

1. Normality by CTL n>30

2. Mean is unbiased sampling

3. SD is 10% conditition for independence

Conditions for Sample Means (X-bar)