Two Sample T-Tests and Power

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

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14 Terms

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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.

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Paired Data

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

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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.

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Hypotheses for Two Sample Means (Null)

H0: μ1 = μ2 (or H0: μ1 − μ2 = 0)

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Hypotheses for Two Sample Means (Alternative)

HA: μ1 ≠ μ2 (or HA: μ1 − μ2 ≠ 0)

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Test Statistic (Unpaired Data)

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

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Degrees of Freedom (Unpaired Data)

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

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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.

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Test Statistic

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

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Power of a Test

The probability that we detect an effect.

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Effect Size

The difference that we are looking for.

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Type I Error

Reject the null hypothesis when it’s actually true.

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Type II Error

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

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Beta

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