What parameter is being tested? Categorical  proportionNumeric  mean

How many samples are being tested? 1 Sample2 Samples multiple

Is the data normally distributed? Normally distributedNon-normal distribution

Do you know the true population variance? I know what σ 2 isNo, σ 2 is unknown

1-sample z-test or confidence interval

1-sample t-test or confidence interval

How large is the sample? n < 30 n > 30 so the Central Limit Theorem holds

Non-parametric Model! Best advice: ask a statistician!

Use the Central Limit Theorem approx z-test = large sample t test

Are the two samples related? They are independentThey are dependent

How are the samples distributed? They are normally distributed They are non-normal

How are the sample variances related? They are equalThey are not equal

Pooled t-test (where Sp is the pooled standard deviation)

2-sample t-test

How large is the sample size? n < 30n > 30

Use Central Limit Theorem 2-sample t-test

Paired t-test

How many samples are being tested? 1 Sample2 Samples multiple

Can we use the normal approximation for p? n*π > 10 and n*(1-π) > 10 No, either n*π ≤ 10 or n*(1-π) ≤ 10

Use the normal approximation

This is an exact Binomial(n,π)

Are the two samples related? They are independentThey are dependent

Does the normal approximation hold? n*π > 10 and n*(1-π) > 10 No, either n*π ≤ 10 or n*(1-π) ≤ 10

2-sample proportions p 0 is the pooled sample proportion since we are assuming that the π’s are equal.

STOP Go ask a statistician!

Test for multiple means Ho: μ1 = μ2 = μ3 = … = μk Assume: 1)Each of the k population or group distributions is normal 2)Distributions have identical variances 3)Each of the k samples is a random and independent sample

 2 test for multiple proportions Or the Test for Independence Assumptions: 1)Expected cell count is ≥ 5, with individual expected counts ≥ 1 2)For 2x2 tables, all expected counts ≥ 5