PDB_Stat_100_Lecture_21_Printable

PDB_Stat_100_Lecture_21_Printable - STA 100 Lecture 21 Paul...

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Unformatted text preview: STA 100 Lecture 21 Paul Baines Department of Statistics University of California, Davis February 25th, 2011 Admin for the Day I Homework 6 posted, due Wednesday at 5pm! I Midterms are ready for pickup. . . I Project groups assigned I Project Proposals due Monday! I Possible project datasets will be posted shortly References for Today: Rosner, Ch 8.4, 8.7, 10.1-10.3 (7th Ed.) References for Monday: Rosner, Ch 10.6, Ch 11 (7th Ed.) Two-Sample Tests We have covered methods for answering questions about one set of data. Last time we saw some methods if we want to compare two sets of data. . . If have two sets of data, we can formulate a hypothesis test to compare them. Two-Sample Examples 1. Recall the sloth example from the midterm. Two different populations, living in different regions. Do they have the same characteristics? e.g., do they have same rates of injury? Q: Previously we did: We know the probability in region 2 is 0.06. Do sloths in region 1 have a probability 0.06 of being injured? Q: More realistically: We have data on sloth injuries in both regions. Do the two regions have the same probability of injury? Two-Sample Examples 2. Recall the ozone example on the homework. Two periods of time (1970-1985) and (1986-1995). Are ozone levels lower in the second period? Q: Previously we did: We know the mean for 1970-1985 is 1.66 ppm. Is the mean for 1986-1995 the same, or lower? Q: More realistically: We have have data on ozone levels in both time periods. Do they have the same mean ozone level? Pooled t- tests For continuous data, sometimes it is reasonable to assume that the two groups have the same variance i.e., 2 1 = 2 2 = 2 . In this case we can pool all of the data (from both groups) to estimate 2 . Hence, this is called a pooled t- test . Again, we still require that the two groups are independent! It is usually safer to do an unpooled t-test, but we include this for completeness. Pooled t- tests Steps for Performing a Two-Sample Pooled t- test: 1. Compute the pooled variance: s 2 p = ( n 1- 1) s 2 1 + ( n 2- 1) s 2 2 n 1 + n 2- 2 2. Compute the test statistic: t = x 1- x 2 s p q 1 n 1 + 1 n 2 3. Compute the degrees of freedom: d p = n 1 + n 2- 2. 4. Compute the p- value by comparing to t to a t d p-distribution. 5. Decide whether to reject H or not, based on the p- value. 6. Interpret what this means for your example. Pooled t- tests Example: We are interested in whether HDL (Good) Cholestrol levels differ between men and women. For both sexes, HDL levels can be assumed to be independent and normally distributed. We will also assume that they have the same variance. Let X m 1 . .. , X mn 1 N ( 1 , 2 ) and X f 1 , .. . , X fn 2 N ( 2 , 2 ) be the HD levels of men and women respectively. Note: Both have variance 2 ....
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This note was uploaded on 03/09/2011 for the course STAT 100 taught by Professor drake during the Spring '10 term at UC Davis.

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PDB_Stat_100_Lecture_21_Printable - STA 100 Lecture 21 Paul...

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