Applied Statistics - Chapter 8: Two-sample tests for differences between means

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8 Terms

1
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Why do we do two-sample tests?

To determine if the samples were drawn from two different populations or from the same population, regardless of the parameter

e.g. Mean, variance, correlation, etc.

<p>To determine if the samples were drawn from two different populations or from the same population, regardless of the parameter</p><p>e.g. Mean, variance, correlation, etc.</p>
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Why are we interested two-sample tests?

We’re interested in whether the value of a parameter is the same (or different) for two populations

3
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What does the e estimated variance of the sampling distribution of the difference between means depend on?

  • Whether the sample sizes, n1 and n2 , are equal or not

  • What information is given to you in the problem.


4
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Assumptions for the Independent Samples t-Test

  • The observations within each sample must be independent

  • The two populations from which the samples are selected must be normal

  • The two populations from which the samples are selected must have equal variances


5
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Sample size and the means

The larger the sample size (n):

  • The smaller the critical value of t that’s required for statistical significance

  • The smaller the standard error of the difference between means


6
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Sample size and the means (con’t)

The smaller the standard error – the smaller the difference between the means has to be to be statistically significant

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When to reject the null for a lower-tailed u1 - u2 test

Reject the null if tobs < -tcrit

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When to reject the null for a upper-tailed u1 - u2 test

Reject the null if tobs > tcrit