statistics

Fisher’s LSD and Tukey’s HSD aren’t enemies; they’re personalities. LSD is powerful and liberal… great at finding differences with three simple groups, riskier with many. Tukey balances caution and power… steady, trusted, and happiest with equal sample sizes. Bonferroni is the seatbelt you never unbuckle; Sidak, a sleeker cousin. Games-Howell is your friend when variances […]

Significance tests don’t create meaning… your design does. If your factor levels are cosmetic, ANOVA will dutifully compare cosmetics. The craft is identifying the construct that actually moves outcomes… then operationalizing it cleanly. Don’t toggle the nearest proxy; name the lever and build conditions that differ on that lever (not five things at once). Before

Tools don’t fail us; we fail to set them up for success. Any stats package will happily scramble your analysis if you paste unlabeled columns and hope for the best. Try this instead: keep tidy data, and dependent-variable columns and numeric factor columns with human-readable labels (e.g., “1=High-Impact, 2=No-Impact, 3=Personal Baseline”). Before any test, run

Every dataset whispers two stories. “Within” is the human noise floor: mood, sleep, coffee, quirks. “Between” is what your design invited to happen. ANOVA’s brilliance is ratio, not rhetoric: mean square between/mean square within. High ratio? Your manipulation likely mattered. Low ratio? Your signal is still stuck in the room hum. Build the craft by

ANOVA isn’t the hero because it tells us everything… it’s the hero because it tells us whether there’s a “there” there. Before we chase pairwise stories, we ask: did something happen worth explaining? Think of it like a detective board (strings, pins, notes)… impressive, but meaningless if no crime occurred. The F-test is that threshold.

One Big Question  Rewrite your study to ask a single, modelable question. If you hear yourself listing pairwise comparisons, you need ANOVA or a planned-contrast design. Define “Meaningful” First  Pick the smallest effect worth acting on. Decisions beat declarations; a tiny, “significant” blip may be operationally irrelevant. Visual First Pass  Plot group distributions and intervals. If the picture

Pre-register the primary question and outcomes. Define the minimal meaningful effect. Plan the model that answers the one big question (ANOVA for multi-group means; chi-square for categorical links; regression when predictors stack). Set your alpha and power targets. Specify how you’ll handle multiple comparisons (or avoid them with planned contrasts). Commit to reporting effect sizes

Statistics is an act of humility: say what the sample shows, then bound what you can infer about the population. Confidence intervals are your friend… they frame plausibility, not certainty. Replication is your ally… one sample is a clue; multiple, independent samples sketch the map. Effect sizes carry weight… small effects can matter, but only

You won’t always have the toolset to fit a model… but you can still read one. Start with the claim: “There is (or isn’t) an association/effect.” Translate it: if the null were true, how surprising is the observed pattern? That’s the p-value, not a truth meter but a rarity meter. Then anchor on effect size

t-tests are great at one thing: two-group comparisons. The moment you care about three or more conditions, t-tests turn into a whack-a-mole of pairwise guesses, each swing adding error. ANOVA reframes the puzzle. Instead of asking six small questions, it asks one: do these group means differ more than we’d expect from within-group noise? That