Chi Square Test - Analysis of Biological Data - Lecture Slides, Slides of Biological Systems

Download Chi Square Test - Analysis of Biological Data - Lecture Slides and more Slides Biological Systems in PDF only on Docsity! 1 Analysis of Frequencies So far --> response variable (Y) - continuous Now look at response variable that is discrete/categorical eg presence-absence or yes-no --> ask questions about frequencies in each category Chi -Square Test - compare OBSERVED frequency of a trait to EXPECTED frequency of a trait Testing for randomness Let’s say we’re interested in the ratio of females to males in this class. Is the composition a RANDOM sample of the UWO population? I will have two observed frequencies, one for each of females and males, And two expected frequencies, one for each of females and males. Where do the frequencies come from? Observed: Count all females and males Count Females 132 Males 76 Total 208 Where do the frequencies come from? Expected: Let’s say females:males at UWO is 50:50, half are females and half are males. So, in a RANDOM sample, expect 50% female and 50% male. Observed Expected Females 132 Males 76 Total 208 Docsity.com 2 Observed Expected Females 132 Males 76 Total 208 χ 2 2 1 = − = ∑ ( )exp exp f f f observed ected ectedi k χ 2 2 2 2 2 132 104 104 76 104 104 28 104 28 104 7 5 7 5 15 = − + − = + − = + = ( ) ( ) . . Expected: Let’s say females:males at UWO is 60:40. So, in a RANDOM sample, expect 60% female and 40% male. Observed Expected Females 132 Males 76 Total 208 Observed Expected Females 132 Males 76 Total 208 124.8 83.2 208 χ 2 2 2 2 2 1 3 2 1 2 4 8 1 2 4 8 7 6 8 3 2 8 3 2 7 2 1 2 4 8 7 2 8 3 2 0 4 2 0 6 2 1 0 4 = − + − = + − = + = ( . ) . ( . ) . . . . . . . . Testing to see if your data fit a theoretical distribution Hardy-Weinberg expectations for Mendel’s Peas Dihybrid cross testing for independent assortment of traits smooth-yellow 9 smooth-green 3 wrinkled-yellow 3 wrinkled-green 1 Count smooth-yellow 152 smooth-green 53 wrinkled-yellow 39 wrinkled-green 6 TOTAL 250 Observed Docsity.com 5 Soil Type Serpentine Non-serpentine Total Pubescent 9.52 18.48 28 Leaf Morphology Smooth 24.48 47.52 72 Totals 34 66 100 Expected Soil Type Serpentine Non-serpentine Total Pubescent 12(9.52) 16 (18.48) 28 Leaf Morphology Smooth 22(24.48) 50 (47.52) 72 Totals 34 66 100 χ 2 2 1 615 9 52 615 18 48 615 24 48 615 47 52 0 6461 0 3328 0 2512 01294 13595 = − = + + + = + + + = = ∑ ( ) . . . . . . . . . . . . . exp exp f f f observed ected ectedi k For example, varieties of tiger beetles found during four times of the year Colour Pattern Season Bright Red Not Bright Red Total Early Spring 29 11 40 Late Spring 273 191 464 Early Summer 8 31 39 Late Summer 64 64 128 Totals 374 297 671 Ho: The occurrence of tiger beetle colour types is not dependent upon time of year HA: The occurrence of tiger beetle colour types is dependent upon time of year Colour Pattern Season Bright Red Not Bright Red Total Early Spring 29(22.3) 11 (17.7) 40 Late Spring 273(258.6) 191 (205.38) 464 Early Summer 8(21.74) 31 (17.26) 39 Late Summer 64(71.34) 64 (56.66) 128 Totals 374 297 671 Docsity.com 6 χ 2 2 1 2 2 2 229 223 223 273 258 6 258 6 8 217 217 64 56 66 223 2 01 08 8 68 095 27 68 = − = − + − + − + + − = + + + + = = ∑ ( ) ( . ) . ( . ) . ( . ) . ... ( . ) . . . . ... . . exp exp f f f observed ected ectedi k Logistic Regression --> used to describe the relationship between Examples of dichotomous Y variable Smoker Group n Absent Present Proportion 0-9 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 2 2 3 3 3 2 3 1 1 2 2 2 2 1 0 1 0 0 0 0 1 1 2 2 2 1 1 0.0 0.0 0.33 0.33 0.66 1.0 0.67 1.0 1.0 Total Docsity.com 7 )(# )(# 10 10 1 )( Cigs Cigs e eLC ββ ββ π + + + = Variables in the Equation .110 .024 20.784 1 .000 -5.275 1.140 21.410 1 .000 V2 Constant Step 1 a B S.E. Wald df Sig. Variable(s) entered on step 1: V2a )(#11.03.5 )(#11.03.5 1 )( Cigs Cigs e eLC +− +− + =π Docsity.com