ST1131 Cheat Sheet Page 1

Chapter 1: Intro     

Chapter 5: Probability

Graphs for Categorical: Pie / Bar Graphs for Quantitative(Discrete / Continuous) : Dot Plot / Stem & Leaf / Histogram / Timeplot Describe: Centre/Mode, Spread, Shape, Outlier Perfect bell-shaped: Mean = Median = Mode Skewed Data: Mode > Median > Mean

Chapter 2: Representation of Data -

Midrange =

-

Range = Highest value – Lowest value

-

Mid-quartile =

-

∑

=

VS

- SR VS LR, Cumulative Freq fluctuates in Short Run - P( ) = 1 – P(A) - P(A OR B) = P(A) + P(B) – P(A ∩ B), where P(A ∩ B) = 0 if disjoint - P(A ∩ B) = P(A) x P(B|A) = P(B) x P(A|B) - If independent, P(A ∩ B) = P(A) x P(B)

=∑

s2 =

∑

̅

, k = s.d.

= √∑

p= ̂ -

⁄

CI for Means (with δ VS w/o δ) µ= ̅

-

√

⁄

VS µ = ̅

√

Sample Survey: Simple Random, Cluster, Stratified, Systematic Experiment: Control, Random, Blinding, Large Observational Studies: Sample Survey, Retrospective, Prospective

Avoid Convenience Sampling Statistical Significance ≠ Practical Significance

⁄

√

, df = n–1

Pooled p, ̂

-

Derive Sample Size: ̂̂

⁄

, ̂

̂

Binomial µ = np δ = √ - Each trial has only 2 outcomes - Each trial has same probability, p - Trials are independent of each other - No. of successes, X is an integer from [0, n] Binomial close to bell-shape if np & nq ≥ 15 - P( ) = nCx.Px.(1-P)n-x

Chapter 4: Gathering Data

 

-

Point Estimate: Single value of best guess Interval Estimate: Interval of numbers which parameter believed to fall in Interval = point estimate ± margin of error Sample size ↑, SE ↓ despite high CI CI for Proportions:

̂ δ = √∑

µ = E(X)

Chebyshev’s Inequality: At least (1 -



-

Discrete

1.5IQR below Q1 OR 1.5IQR above Q3: Outliers Relation ≠ Causation, as one ↑, the other ↑ Response Variable (Dependent Variable, y) VS Explanatory Variable (Independent Variable, x) Population Variance VS Sample Variance: δ2

Probability is the relative frequency with which the event occurs

Chapter 6: Probability Distribution (Experiment)

Chapter 3: Descriptive Analysis -

Chapter 8: Statistical Inference(One Population)

Chapter 7: Sampling Distributions (Sample) Mean = p ; standard error = √ Central Limit Theorem applies when n ≥ 30 X ~ N(µ, δ2)  Z ~ N(0, 1)  Probability When and are given: Find: Use:

P(X) Z=

P( ̅ ) Z=

⁄√

Incorrect Error P Correct Type P Reject true H₀ Type I α True H₀ A 1-α Fail to reject H₀ Type II β False H₀ B 1-β

Chapter 9: Hypothesis Step 1: H₀: µ = µ₀

VS

Hₐ: µ ≠ µ₀

Step 2: Variable is quantitative/categorical Data obtained randomized? Population distribution approximately normal (SIZE)? Step 3 / 4: Compute test statistic Derive p-value Step 5: Small p, reject H₀ and conclude that… Large p, evidence to support H₀