Cumulative for STATSSSSSSSSS

Categorical Data

Grouped in categories

Quantitative Data

Group by numerical values

Frequency Table

Number of individuals in a table

Relative Frequency Table

The proportion/percentage of individuals having each value

Marginal distributions

Shows the probability of a single variable (pass/total)

Conditional distributions

Shows the probability of one variable given a specific condition on another variable (pass/didn’t study)

Categorical Data Plos

Side by side graphs and segmented bar plots

Quantitative Data Plots

Dot plots, histogram, stem and leaf plot, box plots

Measures of center

Mean: Add and divide

Median: Middle

Modes: Unimodal or bimodal

Measures of spread

Range: Max-min

IQR: Q3-Q1

Standard Deviation

Describe 1 variable data

CSOCS

Context

Shape

Outliers

Center

Spread

Percentiles

Percent of data less than or equal to a certain data value

Z-score

(data point - mean) / standard deviation, is # standard deviations away from the mean

Graph 2 variable quanatative data

Scatterplots: shows correlation with LSRL

Explain 2 variable quanatative data

CDOFS

Context

Direction (pos/neg)

Outliers

Form (linear or non)

Strength (correlation)

Least Square Regression Line

Y=a+bx

a=y intercept

b= slope

The sum of square residuals between the data and model “line of best fit” essentially

Residuals

Actual - predicted

LSRL outliers

High leverage

Influenciable outliers

Coefficient of Determination

Square rooting the r-sq

If R² = 0.75, it means that 75% of the variation in the dependent variable is explained by the independent variable(s) in the regression model

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

What does bias lead to

Over or undercoverage of a population

Retrospective study

Examines existing data on individuals

Prospective study

Follows individuals to gather future data (overtime)

Key Components of an Experiment

Experimental Units: The objects or subjects to which treatments are randomly assigned.

Explanatory Variable: The variable that is purposely manipulated in the experiment.

Treatments: The different levels or conditions of the explanatory variable that are applied to the experimental units.

Response Variable: The measured outcome of the experiment, used to compare treatment effects.

Confounding Variable: A factor that may influence the response variable but is not accounted for in the study, potentially skewing results.

Completely randomized design

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

Completely randomized 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

Matched Pairs

Assigning which goes first but measuring with both

Probability formulas ∩ U

Intersection (A ∩ B): Outcomes common to both events (INTERSECTION/ADD)

Union (A U B): Outcomes in A, B, or both (UNION/OR)

Mutually Inclusive Events Formula

Events that can occur at the same time and share at least one outcome

P(A U B)=P(A)+P(B)-P(A ∩ B).

Mutually Exclusive Events

Are events that cannot occur at the same time

P(A ∪ B) = P(A) + P(B)

Test for Independence

P(A∩B) = P(A) P(B)

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

Conditional Probability

P(A|B)=P(A∩B)/P(B)=P (both events occur)/P(given event occurs)

Geometric Distribution

Number of trials needed to achieve the first success in a series of independent trials

Binomial Distribution

Number of trials until the first success

CDF

Probability that a random variable is less than or equal to a specific value

PDF

Probability that a random variable, say X, will take a value exactly equal to x

Proportions (𝑝̂) tests

1. Random sample (unbiased)

2. 10% Condition (independence)

3. Large counts condition: Np≥10 and n(1−p)≥10 (approx normality)

Means (𝑥̄) tests

1. Random sample (unbiased)

2. 10% Condition (independence)

3. Central Limit Theorem (𝑛 ≥ 30 ensures normality)

Confidence Level

If we were to repeat this process many times, about __% of the confidence intervals we create would contain the true [parameter]

Confidence Interval

"We are __% confident that the true [parameter] is between bound] and [bound]."

Type I Error

Rejecting Ho when it’s actually true.

Type II Error

Fail to reject Ho when it’s actually false