Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

History of statistics wikipedia, lookup

Student's t-test wikipedia, lookup

Taylor's law wikipedia, lookup

Bootstrapping (statistics) wikipedia, lookup

Resampling (statistics) wikipedia, lookup

Misuse of statistics wikipedia, lookup

Degrees of freedom (statistics) wikipedia, lookup

Transcript

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 • 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 Back to our mythical IQ course.. Before After Difference 103 98 -5 100 107 7 111 119 8 97 100 3 133 134 1 106 111 5 87 85 -2 A couple of summary statistics d 27 d d n 27 d 7 d 3.86 sd 3.48 Now it is a simple t test d t sd / n 3.86 0 t 3.48 / 7 3.86 t 3.48 / 2.65 3.86 t 1.31 t 2.95 And now for the decision • • • • t(6) = 2.447 tobt = 2.95 Reject H0 Our IQ course works!! 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 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? Some (made up) data Statistic Class 1 Class 2 Mean 77 71 Standard deviation 6.2 6.7 Number of students 49 52 Our hypotheses • • • • • • Are the two classes different? H 0 μ1 = μ2 H A μ1 ≠ μ2 Or we could restate them like this: H 0 μ1 - μ2 = 0 H A μ1 ≠ μ2 ≠ 0 Let’s go back to the original t formula Statistic H0 ↓ ↓ x t s/ n ← Error Figure it out ( x1 x2 ) ( 1 2 ) t error practicall y.... ( x1 x2 ) t error Now about that error… • We cannot just add the values of s for each group • They must be weighted 2 1 2 2 s s n1 n2 6.2 2 49 6.7 2 52 So the formula is t x1 x2 2 1 2 2 s s n1 n1 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 Sub in the values t 77 71 2 2 6.2 6.7 49 52 6 t 1.65 t 4.67 rejectH0 conclusions • All t tests are based on the same formula • Keep the assumptions in mind – SRS – Homogeneity of variance – Independence of observations