Stats Rules

Z-Test (means or proportions)

• Random sample or randomized experiment

• Independence (10% condition: n≤0.1Nn \le 0.1Nn≤0.1N)

• Normality:

  • Means: population normal OR n≥30n \ge 30n≥30

  • Proportions: success-failure condition → np≥10np \ge 10np≥10, n(1−p)≥10n(1-p) \ge 10n(1−p)≥10

T-Test (means) 1-sample

• Random

• Independent (10% condition)

• Nearly normal (no strong skew/outliers OR n≥30n \ge 30n≥30)

T-Test (means) 2-sample

• Two independent random samples

• Independence within each sample (10% condition)

• Both groups nearly normal OR large samples

T-Test (means) paired

• Data are paired (before/after, matched)

• Differences are:

  • Random

  • Independent

  • Nearly normal

Z-Test for 1 Proportion

• Random

• Independent (10% condition)

• Success-failure:

  • np≥10, nq≥10

Z-test for 2 Proportion

• Two independent random samples

• Independence (10% condition for both)

• Success-failure for BOTH groups

Chi Goodness of Fit

• Random

• Independent (10% condition)

• Expected counts ≥ 5 in ALL categories

Chi Test for Independence/ Homogeneity

• Random samples or random assignment

• Independence (10% condition)

• ALL expected counts ≥ 5

Linear Regression

• Linear: relationship looks linear

• Independent: observations independent (watch for time data!)

• Normal: residuals roughly normal

• Equal variance: constant spread (no funnel shape)

• Random: data from random sample or experiment

Confidence Interval (means=T-interval)

• Random

• Independent (10%)

• Nearly normal

Confidence Interval for Proportion

• Random

• Independent

• np≥10, nq≥10