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@jemoka / Jemoka Knowledge Base / wiki/concepts/crap_to_remember_for_ap_stats.md
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--- title: "crap to remember for AP Stats" type: concept related: [Apstats, Crap To Remember For Ap Stats, Binomial Distribution] source: https://www.jemoka.com/posts/kbhcrap_to_remember_for_ap_stats/ confidence: high status: active --- crap to remember for AP Stats is a cram sheet for the AP Statistics exam. 95% confidence: \(z^*=1.96\) \(r=1\): perfect positive correlation \(r=-1\): perfect negative correlation \(r=0\): no correlation S: standard deviation of residuals R-sq: how much of varience in dep. var can be explained by indp. var SE: estimate of standard deviation of the random var. that is slope. For lines: Note that p value from regression outputs are two-tailed. So divide by 2 if you want a one-tail result. Multiplication changes mean as well as well as standard deviation. Adding changes mean but not standard deviation. Expected value of the sum and differences of random variables are just the sums and differences of their expected value. \(S = X+Y, \bar{S} = \bar{X}+\bar{Y}\). Variance of random variables are just the sum and differences of their variance. \(S=X+Y,{\sigma^2}_S = {\sigma^2}_X+{\sigma^2}_Y\). #WHAPS what test what hypothesis and what significance level assumptions and conditions; state! random independent: \(\le 10\%\) of population. t and z special: normal (z tests: \(np, n(1-p) \geq 10\), t tests: \(n>30\) or given) chi-square special: \(\forall\ EV > 5\) p: z-statistic that would XD: Control (control for confounding and bias, placebo, etc.), Randomization (spread uncontrolled variability), Replication (need to have adequate units and ability to be repeated) => Describing a distribution Center: Mean, Median, or Mode? figure by skew Shape: Symmetric vs Skewed? Unimodal vs Bimodal Spread: Range and Inter-Quartile Range Outlier: anything more than 1.5*IQR away Context: what the distribution shows “Experimental Unit”: a physic entity that’s the primary unit of interest in a research objective. Conditions for binomial distribution: Binary Independent Fixed number of trials All trials with same probability Conditions for geometric distrubiton Binary Independent Fixed number of successes All trials with same probability state the thing, state the conditions: “normal distribution with n= s=”, binomial distribution with n= p= etc.