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Comparing Two Groups

Comparing Two Groups. Statistics 2126. So far. We have been able to compare a sample mean to a population mean z test t test Often times though we have two groups to compare Is Group 1 different from Group 2. Matched pairs or correlated t test. AKA dependent sample t test

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Comparing Two Groups

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  1. Comparing Two Groups Statistics 2126

  2. So far.. • We have been able to compare a sample mean to a population mean • z test • t test • Often times though we have two groups to compare • Is Group 1 different from Group 2

  3. Matched pairs or correlated t test • AKA dependent sample t test • When subjects are matched on a variable or are used as their own controls, a sort of before and after thing if you will • Be very careful with this • But it is way powerful and easy to do

  4. Back to our mythical IQ course..

  5. A couple of summary statistics

  6. Now it is a simple t test

  7. And now for the decision • t(6) = 2.447 • tobt = 2.95 • Reject H0 • Our IQ course works!!

  8. Two sample problems • While is is useful to know how to compare a sample mean to a population mean and check for significance it is not all that common • We rarely know μ • Sometimes we do • IQ • Differences • Theoretical values

  9. The much more common question is… • Does one group differ from another? • Let’s say we had two classes with different teaching methods • Is there an effect of teaching method?

  10. Some (made up) data

  11. Our hypotheses • Are the two classes different? • H0μ1 = μ2 • HAμ1 ≠ μ2 • Or we could restate them like this: • H0μ1 - μ2 = 0 • HAμ1 ≠ μ2 ≠ 0

  12. Let’s go back to the original t formula Statistic ↓ H0 ↓ ← Error

  13. Figure it out

  14. Now about that error… • We cannot just add the values of s for each group • They must be weighted

  15. So the formula is

  16. Degrees of freedom • With a one sample t test we lose one degree of freedom • Because we calculated one standard deviation • Here was have calculated 2 • So we lose 2 df • In our case we have 99 df

  17. Sub in the values

  18. conclusions • All t tests are based on the same formula • Keep the assumptions in mind • SRS • Homogeneity of variance • Independence of observations

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