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Comparing Two Groups

This article explores the comparison of two groups using statistical tests, specifically focusing on t-tests and matched pairs t-tests. We detail the rationale behind testing whether group means are significantly different, illustrated with a practical example involving educational methods. Learn how to set up hypotheses, calculate test statistics, and interpret results while considering assumptions such as homogeneity of variance and independence of observations. Gain insights into the power of these tests and their implications in real-world scenarios, enhancing your statistical toolkit.

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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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