Assumptions for Inference

Proportions(z)

• one sample

1. Individuals are independent → SRS and <10% of population

2. Sample is sufficiently large → Successes and failures ≥ 10

• two sample

1. Samples are independent → (How was the data collected)

2. Data in each sample are independent → Both SRS and <10% of populations

3. Both samples are sufficiently large → Success and failures ≥ 10 for both

Means(t)

• One sample
  (df = n-1)

1. Individuals are independent → SRS and <10% of population

2. Population has a Normal model → Histogram is unimodal and symmetric*

• Matched pairs
  (df = n-1)

1. Data are matched → (think about design)

2. Individuals are independent → SRS and <10% of population

3. Population of differences is Normal → Histograms of differences is unimodal and symmetric

• 2 independent samples
  (df from calculator)

1. Samples are independent → (think about design)

2. Data in each sample are independent → SRSs and < 10% of populations

3. Both populations are Normal → Both histograms are unimodal and symmetric*

Distributions (Chi-square)

• Goodness of fit
  (df = #cells - 1)

1. Data are counts → (yes/no)

2. Data in sample are independent → SRS and <10% of population

3. Sample is sufficiently large → All expected counts ≥ 5

• Homogeneity
  (df = (r-1)(c-1))

1. Data are counts → (yes/no)

2. Data in groups are independent → SRS and <10% of population

3. Groups are sufficiently large → All expected counts ≥ 5

• Independence
  (df = (r-1)(c-1))

1. Data are counts → (yes/no)

2. Data are independent → SRS and <10% of population

3. Sample is sufficiently large → All expected counts ≥ 5

Regression
(df = n-2)

• Association
  ß = 0?

1. Form of relationship is linear → Scatterplot look approx. linear

2. Errors are independent → No apparent pattern in residuals plot

3. Variability of errors is constant → Residuals plot has consistent spread

4. Errors have a Normal model → Histogram of residuals is approximately unimodal and symmetric