• basics
  • sample vs. population
    • in experiment, the data is the sample, all possible experiments is the population
    • in bio, usually population is infinite/big relative to sample
  • statistical modeling: how well experiment fits math model (eg linear regression - best fit line)
  • descriptive stats (describe study/experiment) vs. inferential stats (extrapolate to pop. eg hypothesis testing, stats modeling)
  • variable is the property being measured
  • data types: quantitative (continuous vs. discrete) vs qualitative
    • 4 levels in reverse hierarchy: nominal (qual, no order), ordinal (qual, no ratio), interval (quan, no zero-point), ratio (quan)
  • accuracy (close to truth) vs. precision (close to each other)
    • good precision to use: between range/30 & range/300
  • derived variable: function(2+ vars) eg ratio

• hypothesis testing
  • hypthesis: rejected or not rejected; divide into null (H₀) and alternative (H₁)
  • statistical test: p=probability(H₀=true)
  • errors: Type 1 (reject H₀ when true), Type 2 (don't reject H₀ when false)
    • p(T1 occurring) = α (usually 0.05)     p(T2) = β     α, β, and n all related

• experiments: mensurative vs. manipulative
  • manipulative control: procedural (non-manipulated group for comparison), temporal (eg measure before & after)
  • statistical control: measure factor instead of fixing it

• nominal, ordinal, interval, ratio
• Type 1: reject H₀
  • α T1 rate
• variable=property
• precision=close together
• p p(H₀=true)
• CV = SD as % of mean (compare SDs even w/ diff means)
• skew g₁; kurtosis g₂
• CI range (around μ), w/ d.confidence (1-α; that % of CIs would contain true value)
  • need μ, variability, n, d.c
  • assume random (independent & from same pop.) sample, normal
• t-dist assume pop. normal; d.f=n-1 less flat (more normal) w/ n (n>30 approx normal)
• χ² to estimate SD (vs z/t for μ & proportions) d.f=n-1
• H₀ always includes =; p<=α is significant
• critical region: tail(s) where reject H₀
• parametric = assumed normal
• test μ 1-sample test (p or CI (adjust if 1-tailed))
• compare 2 μs
  • paired (d.f=pairs-1, assume duh) parametric (paired t-test (use difference)), non-parametric (Wilcoxon Signed Ranks H₀:medians =)
  • unpaired (d.f=Σ(n-1)) parametric (independent t-test (pooled if assume =SD, n<=30)), non-parametric (Mann-Whitey U, W.R sum)
• comparing SD²
  if normal Leven's test (1 is 1 w/ > variance) d.f=d.f 1/2
• test normality
  • graphs: histogram, normal quantile (Q-Q; n<50 use Rankits), normal prob (P-P)
  • formal: Kolmogorov-Smirnov (unknown μ), Shapero-Wilk (n<50), skew, kurtosis, g test, chi² test
• ANOVA (>2 μs) d.f=groups-1,groups×(n-1) (assume normal, =variances, independent; 1 diff factor; 1st,2nd assumptions relaxed in 1-way)
  • sum of squared: variance before ÷n-1; MS(mean squares) = SS/d.f
  • F MS_treatment/MS_error (>F = more group diff; F=1 is = means)
  • Kruskal-Wallis (K in SPSS)= non-parametric equivalent (assume independent, same distribution shapes)
  • post-hoc: share α among comparisons

lec 7 includes testing sample proportions...

r2 is fraction of variance that's shared

aka % of one due to the other