Københavns Universitet Statistik for Biokemikere Det naturvidenskabelige fakultet Inge Henningsen Afdeling for Anvendt Matematik og Statistik December 2006 i SAS (Zar kapitel 23) PROC FREQ PROC CATMOD 1
Eksempel 23.1 i ZAR DATA zar23_1; INPUT haar $ sex $ antal; CARDS; sort m 32 brun m 43 blond m 16 roed m 9 sort k 55 brun k 65 blond k 64 roed k 16 ; PROC FREQ ORDER=DATA; TABLES sex*haar/nopct NOCOL CHISQ CELLCHI2 EXPECTED; UDSKRIFT til Eksempel 23.1 i ZAR Sex Table of sex by haar Haar Frequency Expected Cell Chi-Square Row Pct sort brun blond roed Total m 32 29 0.3103 32.00 k 55 58 0.1552 27.50 43 36 1.3611 43.00 65 72 0.6806 32.50 16 26.667 4.2667 16.00 64 53.333 2.1333 32.00 9 8.3333 0.0533 9.00 16 16.667 0.0267 8.00 100 200 Total 87 108 80 25 300 Statistics for Table of sex by haar Statistic DF Value Prob Chi-Square 3 8.9872 0.0295 Likelihood Ratio Chi-Square 3 9.5121 0.0232 Mantel-Haenszel Chi-Square 1 2.6155 0.1058 Phi Coefficient 0.1731 Contingency Coefficient 0.1705 Cramer's V 0.1731 Sample Size = 300 2
Eksempel 23.2 i ZAR DATA zar23_2; INPUT hand $ sex $ antal; CARDS; venstre m 6 hojre m 28 venstre k 12 hojre k 24 ; PROC FREQ ORDER=DATA; TABLES hand*sex/nopct NOROW CHISQ CELLCHI2 EXPECTED MEASURES; UDSKRIFT til Eksempel 23.2 i ZAR hand Table of hand by sex Sex Frequency Expected Cell Chi-Square Col Pct m k Total venstre 6 8.7429 0.8605 17.65 hojre 28 25.257 0.2979 82.35 12 9.2571 0.8127 33.33 24 26.743 0.2813 66.67 18 52 Total 34 36 70 Statistics for Table of hand by sex Statistic DF Value Prob Chi-Square 1 2.2524 0.1334 Likelihood Ratio Chi-Square 1 2.2896 0.1302 Continuity Adj. Chi-Square 1 1.5061 0.2197 Mantel-Haenszel Chi-Square 1 2.2202 0.1362 Phi Coefficient -0.1794 Contingency Coefficient 0.1766 Cramer's V -0.1794 3
UDSKRIFT til Eksempel 23.2 i ZAR (fortsat) Fisher's Exact Test Cell (1,1) Frequency (F) 6 Left-sided Pr <= F 0.1095 Right-sided Pr >= F 0.9631 Table Probability (P) 0.0726 Two-sided Pr <= P 0.1748 Statistic Value ASE Gamma -0.4000 0.2403 Kendall's Tau-b -0.1794 0.1150 Stuart's Tau-c -0.1567 0.1021 Somers' D C R -0.2051 0.1309 Somers' D R C -0.1569 0.1022 Pearson Correlation -0.1794 0.1150 Spearman Correlation -0.1794 0.1150 Lambda Asymmetric C R 0.1176 0.1992 Lambda Asymmetric R C 0.0000 0.0000 Lambda Symmetric 0.0769 0.1333 Uncertainty Coefficient C R 0.0236 0.0307 Uncertainty Coefficient R C 0.0287 0.0371 Uncertainty Coefficient Symmetric 0.0259 0.0336 Estimates of the Relative Risk (Row1/Row2) Type of Study Value 95% Confidence Limits Case-Control (Odds Ratio) 0.4286 0.1396 1.3154 Cohort (Col1 Risk) 0.6190 0.3074 1.2467 Cohort (Col2 Risk) 1.4444 0.9310 2.2410 Sample Size = 70 4
Eksempel 23.4 i ZAR DATA zar23_4; INPUT parasit $ art $ antal; CARDS; ja 1 18 nej 1 6 ja 2 10 nej 2 15 ; PROC FREQ ORDER=DATA; TABLES parasit*art/nopct NOROW CHISQ CELLCHI2 EXPECTED; UDSKRIFT til Eksempel 23.4 i ZAR Table of parasit by art parasit Art Frequency Expected Cell Chi-Square Col Pct 1 2 Total ja 18 13.714 1.3393 75.00 nej 6 10.286 1.7857 25.00 10 14.286 1.2857 40.00 15 10.714 1.7143 60.00 28 21 Total 24 25 49 Statistics for Table of parasit by art Statistic DF Value Prob Chi-Square 1 6.1250 0.0133 Likelihood Ratio Chi-Square 1 6.2823 0.0122 Continuity Adj. Chi-Square 1 4.7792 0.0288 Mantel-Haenszel Chi-Square 1 6.0000 0.0143 Phi Coefficient 0.3536 Contingency Coefficient 0.3333 Cramer's V 0.3536 5
Eksempel 23.5 i ZAR DATA zar23_5; INPUT modstand $ snegl $ antal; CARDS; ja 1 12 nej 1 7 ja 2 2 nej 2 9 ; PROC FREQ ORDER=DATA; TABLES snegl*modstand/nopct NOCOL CHISQ CELLCHI2 EXPECTED; UDSKRIFT til Eksempel 23.5 i ZAR Table of snegl by modstand snegl modstand Frequency Expected Cell Chi-Square Row Pct Ja nej Total 1 12 8.8667 1.1073 63.16 2 2 5.1333 1.9126 18.18 7 10.133 0.9689 36.84 9 5.8667 1.6735 81.82 19 11 Total 14 16 30 Statistics for Table of snegl by modstand Statistic DF Value Prob Chi-Square 1 5.6622 0.0173 Likelihood Ratio Chi-Square 1 6.0162 0.0142 Fisher's Exact Test Cell (1,1) Frequency (F) 12 Left-sided Pr <= F 0.9979 Right-sided Pr >= F 0.0212 Table Probability (P) 0.0191 Two-sided Pr <= P 0.0259 Sample Size = 30 6
DATA zar23_8; INPUT gruppe hand $ sex $ antal; CARDS; 1 venstre m 6 1 hojre m 28 1 venstre k 12 1 hojre k 24 2 venstre m 4 2 hojre m 25 2 venstre k 7 2 hojre k 13 3 venstre m 7 3 hojre m 27 3 venstre k 10 3 hojre k 18 4 venstre m 4 4 hojre m 22 4 venstre k 7 4 hojre k 14 ; Eksempel 23.8 i ZAR /*Model 1: Fuld model*/ PROC CATMOD DATA=zar23_8; MODEL gruppe*hand*sex=_response_/nodesign NOITER NOPARM NOPROFILE NORESPONSE; LOGLIN gruppe hand sex; /* Model 2: ingen 3. ordens vekselvirkning*/ PROC CATMOD; MODEL gruppe*hand*sex=_response_/nodesign NOITER NOPARM NOPROFILE NORESPONSE; LOGLIN gruppe hand sex @2; /*Model 3: ingen vekselvirkning mellem gruppe og hand*/ PROC CATMOD; MODEL gruppe*hand*sex=_response_/nodesign NOITER NOPARM NOPROFILE NORESPONSE; LOGLIN gruppe sex hand sex; /*Model 4: ingen vekselvirkning mellem gruppe og hand og mellem gruppe og sex. Modellen kan også formuleres som samme fordeling i de fire tabeller*/ PROC CATMOD; MODEL gruppe*hand*sex=_response_/nodesign NOITER NOPROFILE NORESPONSE; /*parameter inkl.*/ LOGLIN gruppe hand sex; 7
/*Model 5: Samme fordeling i de fire tabeller og lige mange i hver tabel*/ PROC CATMOD; MODEL gruppe*hand*sex=_response_/nodesign NOITER NOPARM NOPROFILE NORESPONSE; LOGLIN hand sex; /*Model 6:Fuld model i marginal tabel over gruppe*/ PROC CATMOD; MODEL hand*sex=_response_/nodesign NOITER NOPARM NOPROFILE NORESPONSE; LOGLIN hand sex; /*test for uafhængighed i marginal tabel*/ UDSKRIFT TIL MODEL 1 i Eksempel 23.8 i ZAR De to følgende tabeller gentages i alle udskrifterne, men er ikke medtaget i notatet Data Summary Response gruppe*hand*sex Response Levels 16 Weight Variable Antal Populations 1 Data Set ZAR23_8A Total Frequency 228 Frequency Missing 0 Observations 16 Maximum Likelihood Analysis Maximum likelihood computations converged. Source DF Chi-Square Pr > ChiSq Gruppe 3 5.71 0.1265 Hand 1 48.37 <.0001 gruppe*hand 3 0.41 0.9391 Sex 1 0.15 0.6979 gruppe*sex 3 0.70 0.8731 hand*sex 1 8.74 0.0031 gruppe*hand*sex 3 0.28 0.9646 Likelihood Ratio 0.. 8
UDSKRIFT TIL MODEL 2 i Eksempel 23.8 i ZAR Source DF Chi-Square Pr > ChiSq Gruppe 3 5.60 0.1330 Hand 1 48.91 <.0001 gruppe*hand 3 0.35 0.9495 Sex 1 0.11 0.7409 gruppe*sex 3 1.31 0.7264 hand*sex 1 8.58 0.0034 Likelihood Ratio 3 0.28 0.9642 UDSKRIFT TIL MODEL 3 i Eksempel 23.8 i ZAR Source DF Chi-Square Pr > ChiSq Gruppe 3 6.48 0.0903 Sex 1 0.10 0.7462 gruppe*sex 3 1.41 0.7043 Hand 1 49.93 <.0001 hand*sex 1 8.67 0.0032 Likelihood Ratio 6 0.63 0.9959 9
UDSKRIFT TIL MODEL 4 i Eksempel 23.8 i ZAR Source DF Chi-Square Pr > ChiSq Gruppe 3 6.22 0.1014 Hand 1 49.93 <.0001 Sex 1 0.22 0.6390 hand*sex 1 8.67 0.0032 Likelihood Ratio 9 2.04 0.9908 Parameter gruppe Analysis of Maximum Likelihood Estimates Estimate Standard Error Chi- Square Pr > ChiSq 1 0.2191 0.1079 4.12 0.0424 2-0.1376 0.1213 1.29 0.2567 3 0.0977 0.1121 0.76 0.3834 hand hojre 0.5578 0.0789 49.93 <.0001 sex k 0.0370 0.0789 0.22 0.6390 hand*sex hojre k -0.2325 0.0789 8.67 0.0032 UDSKRIFT TIL MODEL 5 i Eksempel 23.8 i ZAR Source DF Chi-Square Pr > ChiSq Hand 1 49.93 <.0001 Sex 1 0.22 0.6390 hand*sex 1 8.67 0.0032 Likelihood Ratio 12 8.28 0.7632 UDSKRIFT TIL MODEL 6 i Eksempel 23.8 i ZAR Source DF Chi-Square Pr > ChiSq Hand 1 49.93 <.0001 Sex 1 0.22 0.6390 hand*sex 1 8.67 0.0032 Likelihood Ratio 0.. 10