Statistics

StatisticsThe science of collecting, organizing, presenting, analyzing and interpreting data to assist in making more effective decisions.Types of Sta

Graphically1\. Frequency distribution(table)2\. Bar chart(discrete)3\. Histogram(continuous)4\. Frequency polygon5\. Dot plot6\. Pareto chartPareto ch

1\. Random ExperimentConsider an Action or a Process that will have the following characteristics.Two or more outcomesUncertainty as to which outcome

Discrete Probability Distributionmean = μ = ∑x · p(x) = E(x) = expected value of xvariance = sd^2 = ∑(x-μ)^2 · p(x) Binomial Probability DistributionE

Normal Distribution1\. Bell Shaped2\. Symmetrical3\. AsymptoticParametres of Normal Distributionmu, standard deviationStandard Normal DistributionNorm

In stratified sampling, the strata must be homogenous and also collectively exhaustive, and mutually exclusive as well. The strata must define a part

Sampling distribution Sampling distribution is the distribution of the means of sample statistics where the samples are taken from a particular popul

Margin of errorMargin of error is calculated by a z score times standard error. It expresses the maximum expected difference between the true populati

Via simulation (Unit 1)Via theoretical methods that rely on the CLT (this Unit)Null hypothesisOften either a skeptical perspective or a claim to be te

The likelihood of making a type 1 error and likelihood of making a type 2 error are actually inversely proportional. So, it's actually not that easy t

The interplay between significance levels used in hypothesis testing as well as confidence levels used in construction of confidence intervals.So far,

Statistical vs Practical SignificanceIncrease in sample size -> decrease in standard error -> increase test statistic -> smaller p valueA z-score of 2

Review: What purpose does a large sample serve?With independent observations and not extremely skewed population distribution, a large sample would en

T - distribution Review: What purpose does a large sample serve? With independent observations and not extremely skewed population distribution, a l

2 Steps: Construct a confidence Interval, Conduct a hypothesis testConditions1) IndependenceWithin groups: sampled observations must be independento R

(much like the ‘inference of a mean’ with a new column of difference)Paired DataWhen two sets of observations have this special correspondence (not in

Type 1 error is rejecting H0 when you shouldn’t have, and the probability of doing so is alpha (significance level)Type 2 error is failing to reject H

Comparing Many Means(ANOVA)These plots show how much groups with means are likely to be significant from each other.There are more than two means to c

Sampling Variability and CLT for Categorical DataSampling Distribution for Categorical DataRemember a sampling distribution is different from a sample

Estimating a ProportionParameter of Interest p \- eg. Percentage of all Americans who have good intuition about experimental design.Point Estimate p

INSTRUCTIONSSet the hypothesisH0 : p = null valueH1 : p < or > or != null valueCheck conditionsIndependence: Sampled observations must be independe

Estimating the Difference Between Two ProportionsParameter of Interest: pA - pBPoint Estimate: p̂A - p̂BDifference between the proportions of sampled

Working with One Proportion: p̂ vs p (Review)When working with one proportion, we had different formulae for success-failure condition and standard er

Chi-Square GOF testUsed to evaluate the distribution of one categorical variable with more than 2 levels.Evaluating by comparing the distribution of t

The Chi-square Independence TestEvaluating the relationship between two categorical variables, at least 1 categorical variable with more than 2 levels

Measurement of the relationship1\. Covariance2\. CorrelationCoefficient of Determination\*

For two numerical variables, we use Pearson's correlation to measure the strength of the relationship between the variables.Cramer's V is something eq

상관관계수치형 vs 수치형 \- 피어슨 상관계수(correlation coefficient) 범주형 vs 범주형 \- 분할표 범주형 vs 수치형 \- group by - boxplot/violin chart다변수 시각화 \- 조건화를 통한 그룹 별 차트

정의상관관계가 매우 높은 독립변수들이 동시에 모델에 포함될 때 발생문제같은 변수를 두 번 넣은 것임최소제곱법 계산이 어려워짐.회귀 계수를 구할 때, Standard Error가 비정상적으로 커지고, t-test statistic이 작아지고, p-value가 커지면서 유