Lecture16 - BIOL 361 Final Exam Friday April 24th...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
BIOL 361 Final Exam Friday April 24 th 12:30 -3:00 pm in PAC 11,12 Duration = 2.5 hours
Background image of page 1

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

View Full DocumentRight Arrow Icon
Lecture 16: Categorical Data Analysis II (Two-Way Designs - Contingency Tables) Sources of Information Triola: Chapter 10 Motulsky: Chapters 26-29 Sokal & Rohlf: Chapter 17 Dytham: p. 60-64, 147-154 OUTLINE : 1. 1-Way GOF test - Intrinsic hypothesis 2. 2 x 2 Contingency Tables 3. R x C Contingency Tables
Background image of page 2
• So far, for our examples the expected frequencies were determined on the basis of some extrinsic hypothesis – balanced sex ratio (based on chromosome sorting during meiosis) or phenotype frequencies followed expectations based on principles of Mendelian genetics, etc. • Sometimes, no a-priori basis for expected frequencies • Instead, parameters are estimated from the data themselves • Most common in GOF testing involving statistical distributions. 1-Way GOF Tests for Intrinsic Hypotheses
Background image of page 3

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

View Full DocumentRight Arrow Icon
Houseflies, when at rest, fold their wings over their abdomen. A student determined that this behavior was consistent in individual flies – they always had the left wing over the right wing, or vice versa. That is, flies exhibit “wingedness” similar to “handedness” in humans. Q: The student wanted to determine whether the distribution of wingedness in a laboratory colony was binomially distributed. Example (Intrinsic Hypothesis, Binomial data) :
Background image of page 4
Left wing over right Frequency 0 out of 8 42 15 2 23 8 31 2 44 50 62 70 80 To fit a binomial distribution to these data, we need an estimate of p , the population proportion of left-winged flies. Since there is no a-priori biological rationale for specifying p , we estimate it from the data Æ intrinsic parameter estimates for the model She examined 150 random samples, each of 8 flies. Results :
Background image of page 5

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

View Full DocumentRight Arrow Icon
Can compute that p = 0.16 (= proportion who are left ‘winged’). Then, can use p = 0.16 and the binomial distribution to compute the expected frequencies. Doing this we get the following table. But, to avoid cells with unacceptably small frequencies (< 5), we pool adjacent cells. Summing the individual chi-square values for each cell yields χ 2 = 2.4048. The degrees of freedom are not k -1 (5-1 = 4), as you might expect, but rather k- 2 (5 -1-1 = 3). Left Winged Observed frequency Expected Frequency χ 2 0 42 37.1814 0.6246 1 52 56.6753 0.3828 2 38 37.7716 0.0014 3 12 14.3892 0.3967 4+ 6 4.006 0.9993
Background image of page 6
Reason for the loss of an additional degree of freedom • we used the data to estimate p , the binomial parameter. • Every parameter that is estimated costs you a degree of freedom. • We don’t lose a degree of freedom for q (the proportion of flies that are ‘right winged’) because once p is known, q is automatically determined.
Background image of page 7

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

View Full DocumentRight Arrow Icon
Nominal Data: 2-way Designs (= Contingency Tables) So far, • considered one variable at a time Æ 1-way GOF tests • data could been presented in 1-way frequency tables Æ Observed data (values & categories) could be listed in a single row or column.
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 07/10/2010 for the course BIOL 361 taught by Professor Hall during the Winter '08 term at Waterloo.

Page1 / 36

Lecture16 - BIOL 361 Final Exam Friday April 24th...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online