Multivaria Nitra 2013

Transcription

1 Multivaria Nitra 2013

2 523 Recenzenti: doc. RNDr. Michal Munk, PhD. Katedra matematiky Trieda Andreja Hlinku 1, Nitra Nitra ISBN

3 Predhovor k ich pravdepodobnosti. u SPSS.

4 Obsah T-testy test testu v SPSS test test v SPSS test test v SPSS interakcie v SPSS SPSS Zhlu Podstata a Aglo SPSS SPSS SPSS SPSS Dodatok a ich charakteristiky Dodatok Vektory a matice

5 Text obsahuje -testom SS i z Vektory a matice v dodatku tohto textu 5

6 1 T-testy 1.1 -test x 1, x 2,..., x n. Na odhad strednej hodnoty za a rozptylom 2 /n n a rozptylom X 2. Dostali sme N(0, 1). na odhad rozptylu 1 n 2 s n 1 i 1 xi X 2 2, s 2, t-rozdelenie s df = n t (n 1) rozdelenie). Graf funkcie hustoty t- parameter df n je hustota t-rozdelenia hustotou N(0, 1) rozdelenia Obr. 1: Funkcia hustoty t (10) rozdelenia t (n 1)-rozdelenia t (n 1) N(0, 1) rozdelenia, Interval P( t > t (n 1)) =. s s X t n 1, X t n 1. n n 6

7 1.1. (Pozeranie TV, Karpinski [3, str. 2-31]). V 21,96 19,38 23,69 26,11 18,82 22,81 21,98 25,79 21,67 24,35 28,18 18,69 21,23 18,37 25,6 23,87 25,11 24,23 20,9 19,51 22,65 20,9 21,2 28,04 16,77 25,39 26,89 21,61 20,14 20,75 23,81 21,74 23,68 23,80 21,40 18,36 24,12 25,4 23,36 26,46 20,20 20,82 21,11 20,76 23,16 22,69 24,51 25,21 24,5 14,68. overovanie predpokladov v, na Variable View a Excelu), prepneme V ponuke Graphs Histogram, Variable a klepneme na OK. Podobne v Graphs vyberieme BoxPlot, vyberieme Simple, Summaries of separate variables. Klepneme na Define a presunieme do Boxes represent a OK. 7

8 Dostali sme histogram a boxplot. V Analyze vyberieme Descriptive Statistics a klepneme na Options Descriptives 8

9 Descriptive Statistics N Range Minimum Maximum Mean Std. Deviation Variance Skewness Kurtosis Statistic Statistic Statistic Statistic Statistic Std. Error Std. Std. Statistic Statistic Statistic Error Statistic Error CAS 50 13,50 14,68 28,18 22,5272, , ,115 -,294,337,103,662 Valid N (listwise) 50 hodnota t a p- t- 9

10 Ale t- okolo priemeru, hodnota t a p- priemeru. a Testovanie k testovaniu. t- n = 50. p- df = n 1 = 49, napr. v Exceli pomocou funkcie TDIST(3,25;49;2) = 0, p-hodnotu s p = 0,002,89 < 0,05 =, H 0 zamietame. roku rozdelenia pre df = n 1 = 49, napr. v Exceli TINV(0,05;49) = 2,0096. t- N, 10

11 s s 2,85 2,85 X t0,05 49 ; X t0, ,53 2,01 ;22,53 2,01 21,72; 23,34 n n t-testu v SPSS Analyze Compare Means One-sample T-test Test Variables, Test Value klepneme OK. priemeru a v prvej je priemer, smerod t-testu. One-Sample Statistics N Mean Std. Deviation Std. Error Mean CAS 50 22,5272 2,84866,

12 One-Sample Test Test Value = % Confidence Interval of the Difference t df Sig. (2-tailed) Mean Difference Lower Upper CAS 3,245 49,002 1,30720,4976 2,1168 pre rozdiel, t = 3,245, p H 1 H 0 a H 0 by sme zamietli v t hodnotu p- polovica dvojstrannej p-hodnoty, = 0,05. V t = 3,245 > 1,6765 =, p = 0,001 < 0,05. H 0 malo by a H 0 by sme zamietli v t ia ako - p- p- 0,05. 10,2 12,5 12,3 15, , ,5 12, ,1 16, ,9 11, ,5 11,6 15,2 11,1 15,7 12

13 1.2 -test (t- n X Vy (x 1, y 1 ), (x 2, y 2 ),..., (x n, y n ). z 1 = (x 1 - y 1 ), z 2 = (x 2 - y 2 ),..., z n = (x n - y n ). strednou hodnotou z 1, z 2,..., z n a rozptylom 2. Na odhad strednej hodnoty, hodnotou smerodajn a rozptylom 2 /n N(0, 1). na odhad rozptylu 1 n 2 s n 1 i 1 zi z 2 2, s 2, t-rozdelenie s df = n test v SPSS kontexty v 13

14 Rozdiel bodov overovanie predpokladov i, a Data View BODY1, BODY2. do Excelu), prepneme na Variable View pomenujeme ju ROZDIEL. Vyberieme Transform, Compute Variable. Do Target Variable ROZDIEL, do Numeric Expression presunieme BODY1 presunieme BODY2 do Numeric Expression. ROZDIEL. Vyberieme Analyze, Descriptive Statistics, Explore. ROZDIEL presunieme do Dependend list. Klepneme na Plots a v Explore Plots Normality Plots with tests a Histogram. Klepneme na Continue a potom OK. 14

15 Case Processing Summary Cases Valid Missing Total N Percent N Percent N Percent ROZDIEL ,0% 0,0% ,0% Descriptives Statistic Std. Error ROZDIEL Mean -1,5333, % Confidence Interval for Mean Lower Bound -3,1117 Upper Bound,0451 5% Trimmed Mean -1,4815 Median -1,0000 Variance 8,124 Std. Deviation 2,85023 Minimum -7,00 Maximum 3,00 Range 10,00 Interquartile Range 5,00 Skewness -,312,580 Kurtosis -,613 1,121 Tests of Normality Kolmogorov-Smirnov a Shapiro-Wilk Statistic df Sig. Statistic df Sig. ROZDIEL,108 15,200 *,974 15,913 a. Lilliefors Significance Correction *. This is a lower bound of the true significance. nezamietame. p-hodnota Shapirovhov 15

16 Normalitu rozdelenia potvrdzuje Q-Q Symetria 16

17 H 0 proti H 1 -testu Klepneme na Analyze, Compare Means a vyberieme Paired Samples T Test. BODY1, BODY2. Klepneme na OK. Dosta T-Test Paired Samples Statistics Mean N Std. Deviation Std. Error Mean Pair 1 BODY1 28, , ,65378 BODY2 29, , ,87154 Paired Samples Correlations N Correlation Sig. Pair 1 BODY1 & BODY2 15,968,000 Paired Samples Test Paired Differences 95% Confidence Interval of Std. Std. Error the Difference Sig. (2- Mean Deviation Mean Lower Upper t df tailed) Pair 1 BODY1 - BODY2-1, ,85023, ,11174, ,084 14,056 nuly, p- 17

18 V - hodno - H V sa testov s Test F A rozpore s 1.3 -test (t- X, X,..., X n z rozdelenia, z rozdelenia. Testujeme: = kde t S X1 X2, 2 n1 n2 S. nn. 1 2 ( n 1) S ( n 1) S ( n n 2)

19 , t t-rozdelenie s df = n 1 + n 2 W = (-, - t (df)) (t (df), ). H 0, alebo p- H 0 nezamietame test v SPSS 1.3. a skupina Skupina s nedostatkom H 0 H 1 NS (skupina s SKUPINA s SKORE K Vyberieme Analyze, Descriptive Statistics, Explore. SKORE presunieme do Dependend list a Factor list. Klepneme na Plots a v Explore Plots a Histogram. Klepneme na Continue a potom OK. SKUPINA do Normality Plots with tests 19

20 Case Processing Summary Cases Valid Missing Total SKUPINA N Percent N Percent N Percent SKORE K ,0% 0,0% ,0% NS ,0% 0,0% ,0% Tests of Normality Kolmogorov-Smirnov a Shapiro-Wilk SKUPINA Statistic df Sig. Statistic df Sig. SKORE K,129 12,200 *,954 12,702 NS,162 12,200 *,939 12,490 20

21 Predpoklad normality (p-hodnoty (Sig.) pre Shapirov- -test (t-test vzorky). Vyberieme Analyze, Compare Means, Independent Samples T test. (Test Variable) je SKORE a (Grouping Variable) je SKUPINA. V Define Groups K a NS. T-Test Group Statistics SKUPI NA N Mean Std. Deviation Std. Error Mean SKORE K 12 48,9167 9, ,61539 NS 12 46, , ,89200 Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means F Sig. t df Sig. (2- tailed) 95% Confidence Interval of the Difference Mean Std. Error Difference Difference Lower Upper SKORE Equal variances assumed,256,618,748 22,462 2, , , ,

22 Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means F Sig. t df Sig. (2- tailed) 95% Confidence Interval of the Difference Mean Std. Error Difference Difference Lower Upper SKORE Equal variances assumed Equal variances not assumed,256,618,748 22,462 2, , , ,00315,748 21,781,462 2, , , ,00786 p- h H 0 -testu s p- -testu s r

23 z rozsiahlej v. sex), poradie por.por), vek matky (vekmat), vek otca (vekotca), vyska4). Pohlavie Poradie p rodu Vek matky Vek otca V ka vekom otca. matky v 2. a 1. Data View v SPSS. Vo Variable View por.por, vekmat, vekotca, vyska4. sex, rozdiel veku otca a veku matky a pomenujeme ju roz. Vyberieme Transform, Compute Variable. Definujeme roz = vekotca vekmat. 23

24 Explore. roz. Vyberieme Analyze, Descriptive Statistics, roz presunieme do Dependend list. Klepneme na Plots a v Explore Plots Normality Plots with tests a Histogram. Klepneme na Continue a potom OK. Case Processing Summary Cases Valid Missing Total N Percent N Percent N Percent roz ,0% 0,0% ,0% Descriptives Statistic Std. Error roz Mean 3,8000 1, % Confidence Interval for Mean Lower Bound,8533 Upper Bound 6,7467 5% Trimmed Mean 2,8333 Median 2,5000 Variance 39,642 Std. Deviation 6,29620 Minimum -2,00 Maximum 27,00 Range 29,00 Interquartile Range 4,75 Skewness 2,874,512 Kurtosis 10,044,992 Tests of Normality Kolmogorov-Smirnov a Shapiro-Wilk Statistic df Sig. Statistic df Sig. roz,237 20,004,692 20,000 a. Lilliefors Significance Correction 24

25 Plot. p- H 0 : v zamietame. ne ne t-test As Q-Q Klepneme na Analyze, NonparametricTests a vyberieme Related Samples., vyberieme vekmat, a vekotca, Wilcoxon a Sign, klepneme na OK. Dosta Testuje H 0 : Rozdelenie veku otca je v rozdelenie premennej rozdiel veku matky a veku otca je 0.) 25