One rock hold whole hunt

Ugg sit by fire. Big test come in two sun-rises. Ugg no need learn all fourteen hunts again — Ugg need retrieve, pull old knowing from head, fast. Test give little story ("men taller than women?") and ask the same thing over and over: which spear you throw, why, what you promise, how you tell the kill. Run the map under thirty breaths — half the meat already yours.

The decision tree — four questions pick the spear

Decision tree — four questions Ugg ask in order. They point to the right test like footprints point to the mammoth.

One: how many things you measure? The measured thing is the dependent variable (DV) — thing that change when you poke. One DV → ANOVA family. Many DV at once → MANOVA.

Two: what kind is the DV?

• Name-boxes (red/blue, yes/no) → chi-square (χ²) family, or logistic regression when you guess a yes/no from stuff.
• Rank-order, or lumpy-not-bell → rank spears: Mann-Whitney U, Wilcoxon, Kruskal-Wallis, Friedman, Spearman.
• Smooth number with nice bell shape → t-test / ANOVA / regression.

Three: how many groups? One, two, or three-plus.

Four: same tribe or different tribe? Different people in each group = between-subjects (independent). Same people measured again = within-subjects (paired/repeated). The pokey thing you change is the independent variable (IV).

Four questions funnel any story into one spear.

The spear grid — carve in cave wall

| | 2 different | 2 same | 3+ different | 3+ same | |---|---|---|---|---| | Bell-smooth | indep t | paired t | one-way ANOVA | RM-ANOVA | | Rank/lumpy | Mann-Whitney U | Wilcoxon | Kruskal-Wallis | Friedman | | Name-box | χ² | McNemar | χ² big | (rare) |

Extra spears in the margin: one IV plus a nuisance-number to hold still → ANCOVA. Two+ IV all different tribes → factorial ANOVA (hunt the interaction — when one poke change how the other poke work). Mix same-and-different people → mixed ANOVA. Two smooth things together → Pearson r. Ugg know the secret: all these one big family (GLM) wearing different fur.

Bad words that lose meat

Test love to catch you saying the wrong thing. Say the right thing:

p-value — NOT "3% chance the no-effect story is true." RIGHT: "IF no-effect story true, only 3% chance to see data this wild." Ugg warn: no flip the arrow!

Confidence interval (CI) — NOT "95% chance the true number sit inside this fence." RIGHT: "if we hunt many many times, 95% of such fences catch the true number." We no know if THIS fence one of the lucky ones.

Big p (not significant) — NOT "no effect." RIGHT: "not enough proof to throw out the no-effect story." No footprint is not proof the mammoth gone.

Correlation — NOT "A make B happen." RIGHT: "A and B move together; make-happen needs an experiment." Ugg warn: maybe a third thing push both.

Big tribe + tiny p — NOT "huge effect!" RIGHT: "we can see it, but maybe too small to matter — check the size."

Every spear promise — and the checking-stone

Bell-spears (t, ANOVA, regression) only work if you promise things. Each promise has one stone to check it. Memorize the pairs:

• Bell shape of leftovers → Shapiro-Wilk, Q-Q picture.
• Groups spread the same amount → Levene's.
• Same-people ANOVA, even spread across pairs → Mauchly (this is sphericity; broke → Greenhouse-Geisser fix).
• Regression line straight → leftover-vs-guess picture.
• Regression predictors not twins → VIF, ${\text{VIF}}_j=1/(1-R_j^2)$, over 5–10 is bad.
• One weird point drag the whole line → Cook's distance, over 1 is bad.
• χ² boxes → every expected count must be 5 or more, else use Fisher's exact.

Slides SHOUT this: name your promises for every spear. Big marks.

How big the mammoth — effect size

Effect size — not "did we see it" but "how big." Always tell it beside p, or p is only half the kill.

• Cohen's d: 0.2 / 0.5 / 0.8 = small / medium / big. $d=(M_1-M_2)/{\text{SD}}_{\text{pooled}}$.
• η² (eta-squared): .01 / .06 / .14. ${\eta }^2={\text{SS}}_B/{\text{SS}}_T$.
• Pearson r: 0.1 / 0.3 / 0.5. Odds ratio (logistic): 1.5 / 2.5 / 4.

Tell the kill right — five numbers

Every result needs five numbers: test statistic, degrees of freedom, p, effect size, 95% CI. Like: "paired t-test show anxiety drop after fix, $t(29)=4.2$, $p<.001$, Cohen's $d=0.77$, 95% CI [0.45, 1.08]."

For big story-questions, use the 10-point framework:(1) question,(2) H₀ and H₁,(3) IV/DV/scale,(4) design,(5) test + why,(6) promises,(7) how to check each,(8) backup spear if a promise breaks,(9) effect size,(10) reporting sentence. Ugg secret: even with wrong numbers, every step still wins marks. Write all ten!

Rocks to carve in head

• Distance from middle: $z=(x-\mu )/\sigma$ — how many spreads from center.
• Steadiness of the mean: $\text{SEM}=s/\sqrt{n}$ — bigger tribe, steadier mean. Ugg warn: SEM is NOT SD! SD is spread of the data; SEM is spread of the mean.
• ANOVA: ${\text{SS}}_T={\text{SS}}_B+{\text{SS}}_W$, and $F=\text{MSB}/\text{MSW}$ — between-noise over within-noise.
• Name-box test: ${\chi }^2=\sum (O-E{)}^2/E$, with $E_{ij}=r_i{c}_j/n$, and $df=(r-1)(c-1)$.
• Many tests make many false alarms: $\text{FWER}=1-(1-\alpha {)}^m$. Twenty tests at .05 → 64% chance of one false alarm! Fix with Bonferroni: use ${\alpha }_{\text{new}}=\alpha /m$.

Two things look same, but not same

• Reliability (same answer every time) vs validity (right answer). Ugg can be wrong the same way every time — reliable but not valid.
• Type I error (cry mammoth, none there) vs Type II error (miss a real mammoth). Power $=1-\beta$.
• PCA (squash many things into few) vs FA (find the hidden cause underneath).
• FWER (chance of ANY false alarm) vs FDR (share of alarms that are false). FWER stricter.
• One-tailed spear must be promised BEFORE the hunt. Switch after, to grab significance → p-hacking.

Ugg remember

• Run the decision tree every time: DV kind → IV kind → how many groups → same or different tribe → spear. Even the easy-look ones.
• Always tell five numbers: statistic, df, p, effect size, 95% CI. p alone is half a kill.
• Say the trap-words RIGHT — p-value, CI, "not significant," correlation-not-cause. These four hide on every paper.
• Big tribe makes tiny thing look big. Statistical significance is NOT the same as mattering in real life.
• Name the promises for every spear, and write all ten framework points — partial meat is still meat.