# Lec9 - Comparing two samples Two approaches to comparing...

This preview shows pages 1–7. Sign up to view the full content.

Comparing two samples Two approaches to comparing two means: 1. Using confidence intervals 2. By hypothesis testing

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
A. (23, 170) B. (6, 191) C. (21, 172) ? Use the liberal approx. of the df to calculate the 90% confidence interval for the difference between the means: Another confidence interval example df = ( SE 1 2 + SE 2 2 ) 2 SE 1 4 n 1 1 + SE 2 4 n 2 1 SE ( y 1 y 2 ) ( y 1 y 2 ) ± t .05 SE ( y 1 y 2 ) 90% confidence interval = μ 1 2 y 1 y 2 SE ( y 1 y 2 ) = SE 1 2 + SE 2 2 = s 1 2 n 1 + s 2 2 n 2 (540.8 444.2) ± (1.833) 27 2 + 31 2 ( ) Concentration of a brain chemical norepinephrine (NE) in rats with and without exposure to toluene 31 27 SE 69.6 66.1 s 444.2 540.8 y 5 6 n 549 387 564 412 635 502 431 385 523 535 543 Control Toluene
Comparing two samples Two approaches to comparing two means: 1. Using confidence intervals 2. By hypothesis testing

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
In the toluene example, we may be interested in whether or not toluene has an effect on brain function: H 0 * =Toluene has no effect on NE concentration in rat medulla H A * =Toluene has some effect on NE concentration in rat medulla These are informal statements of what is truly being tested, the differences between the means. Hypothesis testing Generally, we will be using our data to test the hypothesis that μ 1 and 2 are not different NULL HYPOTHESIS : The hypothesis that the two means are equal H 0 : 1 = μ 2 ALTERNATIVE HYPOTHESIS : The hypothesis that the two means differ H A : 1 2 FORMALLY INFORMALLY STATISTICAL TEST OF A HYPOTHESIS: A procedure for assessing the compatibility of the data with H 0 .
The t test H 0 : μ 1 2 = 0 H A : 1 2 0 and t test: a standard method for choosing between the two hypotheses H 0 : 1 = μ 2 H A : 1 2 and FIRST STEP : Compute the test statistic for the t test t s = ( y 1 y 2 ) 0 SE ( y 1 y 2 ) This stands for sample and reminds us that we are making a calculation based on data This reminds us what we are testing A difference between the sample means, expressed in relation to the SE of the difference t s = (540.8 444.2) 0 41.195 = 2.34 Example: For the toluene data set, the value of t s is 31 27 SE 69.6 66.1 s 444.2 540.8 y 5 6 n Control Toluene

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
The t test SECOND STEP : Use the test statistic ( t s ) to assess whether the data are consistent with H 0 t s = ( y 1 y 2 ) 0 SE ( y 1 y 2 ) H 0 : μ 1 2 = 0 H A : 1 2 0 =0 BUT, H 0 can be true and we can still get sample means that differ from each other because of sampling variability SO, just because our sample means differ, we cannot necessarily conclude that H 0 is false.
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 11/04/2009 for the course BIO 50935 taught by Professor Bryant during the Fall '09 term at University of Texas at Austin.

### Page1 / 20

Lec9 - Comparing two samples Two approaches to comparing...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online