S&DS-1000

Sample mean

x-bar

Population mean

mu

Sample standard deviation

s

Population standard deviation

sigma (lower-case)

Sample proportion

p-hat

Population proportion

pi

Sample correlation

r

Population correlaton

rho

Sample regression slope

b

Population regression slop

beta

Sampling distribution

Distribution of sample statistics computed from different samples of the same size (n) from the same population; samples from the whole population, centered at the population parameter

Confidence Intervals

Another measurement of inference, states the possible range of values that the parameter could lie → the higher the confidence interval, the larger the range (includes less data, less confident)

3 Major CI Levels

99.7-statistic lies at most 3 SE away from the parameter; 95-statistic lies at most 1.96 SE away from the parameter; 68-statistic lies at most 1 SE away from the parameter

Bootstrap distribution

Method of est the standard error, sampling with replacement (proxy for sampling dist w/o continuous resampling; sample sample pop); relies on the plug in principle

Bootstrap Steps

1-start with sample; 2-repeat steps 10k times; 3-get SE*

Plug-in principle

We pretend that our sample is the population → allows us to continuously sample with replacement to compute stat of interest + create boot dist

SE vs STD

We use the standard error (SE) instead of the standard deviation (STD) when calculating confidence intervals because a confidence interval measures the uncertainty around a sample estimate (like the sample mean) rather than the spread of individual data points in a sample

Null hypothesis (H0)

Claim that there is no effect or no difference

Alternative hypothesis (HA)

Claim for which we seek significant evidence; est by observing evidence that is inconsistent with null

Null vs alternative hypothesis

H0 states no effect; HA states claim of interest

P-value

Probability of obtaining a statistic as (or more) extreme than the observed sample if the null hypothesis was true; small p is strong evidence against the null (less likely that something as extreme would happen; indication of some effecy)

Hypothesis Testing Steps

1-State the hypotheses (null and alternative); 2-Calculate the observed stat; 3-Create a null dist that is consistent with H0, 4-Calculate the p-valaue; 5-Make a judgement

Central Limit Theorem

For random sample with a sufficiently large sample size (n), the distribution of the sample statistics for a mean (x-bar) or a proportion (p-hat) is

Effect of n increasing for distributions

As n increases, accuracy increases --> distribution should "shrink" & become more narrow; indicates more precision

Line of Best Fit

Line which minimizes sum of squared residuals

Five Number Summary

Min, Q1, Median, Q3, Max; Helps describe the spread of the data + key summary statistics of a data sample

Measures of Spread

Range, interquartile range, five number summary

z-score

Show how many standard deviations a point is from the mean

Boxplot

Visualization of the five number summary

Quantile

Value (v) which is greater than P percent of the data; 90th percentile of test scores is 92

Percentile

Percentage of values in a data set that are less than or equal to a value x; Scoring a 92 gives you a percentile rank of 90% (you beat 90% of test-takers)

Sampling Distribution vs Bootstrap Distribution

Sampling Dist: Take multiple samples from the true population to get results about a parameter vs Bootstrap: Takes multiple samples with replacement from one sample of the pop to get results for SE*

Outlier Rule of Thumb

Q1-1.5*IQR __or__ Q3 + 1.5*IQR