🌳 Which Test Do I Use?

Conditions:
• Random — random sample or randomly assigned
• 10% — n < 10% of population
• Large Counts — np₀ ≥ 10 and n(1−p₀) ≥ 10

Conditions:
• Random — both groups randomly sampled/assigned
• 10% — n₁ < 10% and n₂ < 10% of their populations
• Large Counts — n₁p̂₁, n₁(1−p̂₁), n₂p̂₂, n₂(1−p̂₂) all ≥ 10

Conditions:
• Random — random sample
• Large Counts — all expected counts ≥ 5
• No 10% condition needed

Conditions:
• Random — independent random samples from each group
• Large Counts — all expected counts ≥ 5

Conditions:
• Random — one random sample from the population
• Large Counts — all expected counts ≥ 5

Conditions:
• Random — random sample or randomly assigned
• 10% — n < 10% of population
• Normal/Large Sample — n ≥ 30, or population Normal, or graph looks roughly symmetric with no strong skew

Conditions:
• Random — both groups randomly sampled/assigned
• 10% — both n < 10% of their populations
• Normal/Large Sample — both groups meet the condition independently

Key step: Compute the differences first (d = x₁ − x₂), then treat as a 1-sample t-test on the differences.

Conditions: Random pairing, 10%, Normal/Large Sample — all applied to the differences.

Conditions (LINER):
• Linear — scatterplot looks linear
• Independent — observations independent (10% if sampling)
• Normal — residuals roughly Normal
• Equal variance — residual plot has consistent spread
• Random — random sample or assignment