Two Sample T-Tests and Power

Flashcards covering key vocabulary and concepts related to Two Sample T-Tests and Power.

Central Limit Theorem (for means)

If we have a random and independently selected sample with a large sample size (more than 30) that takes up less than 10% of the population, the distribution of the sample mean is approximately Normal with a mean equal to the population mean, and standard deviation equal to the population standard deviation divided by the square root of the sample size.

Paired Data

Observations in each dataset are paired in some way, and the two samples will always have the same sample size.

Central Limit Theorem (for means)

If we have a random and independently selected sample with a large sample size (more than 30) that takes up less than 10% of the population, the distribution of the sample mean is approximately Normal with a mean equal to the population mean, and standard deviation equal to the population standard deviation divided by the square root of the sample size.

Paired Data

Observations in each dataset are paired in some way, and the two samples will always have the same sample size.

Unpaired Data

Observations in each dataset don’t need to have a natural pairing, and the sample sizes don’t need to be the same.

Hypotheses for Two Sample Means (Null)

H0: μ1 = μ2 (or H0: μ1 − μ2 = 0)

Hypotheses for Two Sample Means (Alternative)

HA: μ1 ≠ μ2 (or HA: μ1 − μ2 ≠ 0)

Test Statistic (Unpaired Data)

Use the difference in their sample means (x̄1 − x̄2) as the point estimate.

Degrees of Freedom (Unpaired Data)

Use the smaller of n1 − 1 and n2 − 1 (a more conservative approach).

Standard Error for the Difference of Two Means

sqrt((s1^2 / n1) + (s2^2 / n2)), where s1 and s2 are the standard deviations of the two samples and n1 and n2 are their sample sizes, respectively.

Test Statistic

(x̄1 - x̄2) / SE, where x̄1 and x̄2 are the sample means, and SE is the standard error.

Power of a Test

The probability that we detect an effect.

Effect Size

The difference that we are looking for.

Type I Error

Reject the null hypothesis when it’s actually true.

Type II Error

Fail to reject the null hypothesis when it’s not true.

Beta

The probability of making a Type II error; the power of a test is equal to 1 – β.