CEDZO

T-TESTt-test (kim nh t) c s dng trong kim nh s khc bit v gi tr trung bnh ca tng th () vi mt gi tr (0) cho trc, hoc kim nh s khc bit v gi tr trung bnh gia hai tng th (1 v 2). Thc hin kim nh v chng ta nghin cu cho tng th da trn quan st mu c chn ra t tng th. Nguyn tc ca kim nh cc gi thuyt ca tng th l : a ra cc gi thuyt v cc tham s (trung bnh, phng sai, t l), tin hnh thu thp thng tin t mu kim nh gi thuyt a ra.

Cc bc tin hnh kim nh gi thuyt (5 bc):

1. Bc 1: t gi thuyt: gm cp gi thuyt H0 (null hypothesis) v gi thuyt i H1; trong , H0 (gi thuyt khng l gi thuyt m chng ta mun kim nh).2. Bc 2: Chn mc ngha kim nh (thng l 1%, 5% hay 10%); l mc chp nhn sai lm ca nh nghin cu.3. Bc 3: Chn php kim nh thch hp (kim nh t hay z) v tnh gi tr thng k .4. Bc 4: Xc nh gi tr ti hn ca php kim nh.5. Bc 5: So snh gi tr ti hn vi gi tr kim nh quyt nh chp nhn hay bc b gi thuyt H0. Ty thuc vo cch t gi thuyt m chng ta c kim nh hai bn (two tailed test) hay kim nh mt bn (one-tailed test).H0: 0 = 0

H1: 0 < 0H1: 0 0H1: 0 > 0

Pr(T < t)Pr(|T| > |t|)Pr(T > t)

Kim nh bn triKim nh hai bnKim nh bn phi

l trung bnh ca tng th.

0 gi tr so snh.

Khi s dng phn mm thng k, chng ta s dng cch tip cn p value quyt nh chp nhn hay bc b gi thuyt khng (H0, null hypothesis). P-value l mc ngha quan st (observed significance level) tng ng vi gi tr thng k kim nh. V d, khi chng ta dng kim nh t (hnh di) th gi tr p ng bng din tch pha di ca ng cong tnh t gi tr thng k t (ng thng t=t) n v cng ().

Khi tip cn p-value ra quyt nh chp nhn hay bc b gi thuyt H0, chng ta ch cn i chiu gi tr p theo nguyn tc sau:1. Nu p ( chp nhn H0 (t chi H1)

2. Nu p < ( bc b H0 (chp nhn H1)

Nu gi thuyt H0 ng v chng ta chp nhn H0 ( chng ta c quyt nh ng vi xc sut l (1 ). Ngc li, khi chng ta bc b gi thuyt H0 (trong khi n ng) th chng ta gp phi sai lm vi xc sut l .C 2 trng hp: t-test mt mu (one sample t test) v t-test 2 mu (2 mu c lp v mu phi hp tng cp).By gi chng ta tin hnh vic kim nh gi thuyt v trung bnh tng th.

1. t-test mt mu (one-sample t-test) ( kim nh gi thuyt v tr trung bnh ca mt tng th.Chng ta thc hnh trn file data c tn : JobSurveyRawData.sav;Pht biu 1: c ngi cho rng thu nhp trung bnh l 18.000, chng ta kim nh gi thuyt ny?Trong SPSS: Analyze > Compare Means > One-Sample T Test.One-Sample Test

Test Value = 18000

tdfSig. (2-tailed)Mean Difference95% Confidence Interval of the Difference

LowerUpper

Thu nhap-9.75867.000-2361.765-2844.87-1878.66

P value (Sig.) = 0.000 rt nh so vi 5% ( p-value < ( bc b gi thuyt H0. bng chng ni rng thu nhp trung bnh ca tng th l khc 18.000.Pht biu 2: c ngi cho rng thu nhp trung bnh l 12.000, chng ta kim nh gi thuyt ny?

One-Sample Test

Test Value = 12000

tdfSig. (2-tailed)Mean Difference95% Confidence Interval of the Difference

LowerUpper

Thu nhap15.03267.0003638.2353155.134121.34

P value (Sig.) = 0.000 rt nh so vi 5% ( p-value < ( bc b gi thuyt H0. bng chng ni rng thu nhp trung bnh ca tng th l khc 12.000.

Pht biu 3: c ngi cho rng thu nhp trung bnh l 15.500, chng ta kim nh gi thuyt ny?One-Sample Test

Test Value = 15500

tdfSig. (2-tailed)Mean Difference95% Confidence Interval of the Difference

LowerUpper

Thu nhap.57167.570138.235-344.87621.34

P value (Sig.) = 0.570 ln hn 5% ( p-value > ( chp nhn gi thuyt H0. bng chng ni rng thu nhp trung bnh ca tng th l bng 15.500.

2. Kim nh 2 mu

2.1. t-test hai mu c lp (independent-samples t-test) ( kim nh gi thuyt v s bng nhau gia hai trung bnh tng th V d v hai mu c lp: Quan tm v mc chi tiu hc ngoi ng tui 10 30 gia Tp. HCM v Tp. Cn Th.

Quan tm kt qu hc mn kinh t chnh tr gia trng H Kinh t v Hc vin Chnh tr quc gia.

Quan tm v s tin s dng dch v in thoi di ng ca khch hng gia Mobifone v S-fone.

H0: 1 2 = 0

H1: 1 2 < 0H1: 1 2 0H1: 1 2 > 0

Pr(T < t)Pr(|T| > |t|)Pr(T > t)

1, 2 l trung bnh ca tng th th nht v th hai.

Trong thc tin, chng ta thng khng bit phng sai ca hai tng th. Khi thc hin t-test trng hp hai mu c lp (independent-samples t-test) chng ta cn tin hnh kim nh phng sai ca hai tng th l bng nhau hay khng bng nhau. Trong SPSS, kim nh ny c tn l Levene test. H0 ca Levene test l phng sai ca hai tng th bng nhau. Kt qu ca vic chp nhn hay bc b gi thuyt H0 s thay i vic la chn k tip v kim nh gi thuyt bng nhau v trung bnh gia hai tng th. Quy tc chp nhn hay bc b H0 ca kim nh Levene cng nh tng t khi xem xt gi tr p value m chng ta bit.Pht biu 4: C pht biu ni rng l khng c s khc bit v thu nhp gia gii nam v gii n.Trong SPSS: Analyze > Compare Means > Independent Samples T Test.

Group Statistics

Gioi tinhNMeanStd. DeviationStd. Error Mean

Thu nhapNam3715708.111829.143300.709

Nu3115554.842206.481396.296

Independent Samples Test

Levene's Test for Equality of Variancest-test for Equality of Means

FSig.tdfSig. (2-tailed)Mean DifferenceStd. Error Difference95% Confidence Interval of the Difference

LowerUpper

Thu nhapEqual variances assumed.614.436.31366.755153.269489.275-823.5991130.138

Equal variances not assumed.30858.367.759153.269497.470-842.3921148.930

Sig. = 0.436 > 0.05 nn chp nhn gi thuyt H0: ngha l phng sai ca hai tng th (tng th nam v tng th n) l bng nhau, mc ngha 5%. Do , chng ta s s dng kt qu kim nh t phn Equal variances assumed. Chng ta thy gi tr sig. trong kim nh t > 0.05 nn chng ta chp nhn gi thuyt H0 : cho rng, thu nhp gia hai gii nam v n l bng nhau mt cch c ngha thng k.Chng ta cn kim nh c khc bit v thu nhp trung bnh gia cc nhm dn tc?2.2. t-test hai mu ph thuc hay phi hp tng cp (paired-samples t-test) ( kim nh tr trung bnh ca hai mu ph thuc hay mu phi hp tng cpH0: 1 2 = 0

H1: 1 2 < 0H1: 1 2 0H1: 1 2 > 0

Pr(T < t)Pr(|T| > |t|)Pr(T > t)

1, 2 l trung bnh ca tng th th nht v th hai.

V d v hai mu phi hp tng cp: Ci tin phng php dy ngoi ng.

Hiu qu trc v sau c chng trnh khuyn mi.

Khc bit trong cht lng sn phm trc v sau ci tin.

V d: Thiviet.sav ( kim nh c hay khng c s ci thin v k nng vit lun nh tham gia kha o to. Ngha l chng ta cn kim nh gi thuyt H0 rng s k nng vit lun ca sinh vin trc v sau khi tham gia kha o to k nng l bng nhau (H0:1 = 2), vi mc ngha l = 5%.

Trong SPSS, Analyze > Compare means > Paired-Samples T testPaired Samples Statistics

MeanNStd. DeviationStd. Error Mean

Pair 1So cau viet truoc khi tham gia khoa hoc10.79244.606.940

So cau viet sau khi tham gia khoa hoc26.38248.2981.694

Paired Samples Correlations

NCorrelationSig.

Pair 1So cau viet truoc khi tham gia khoa hoc & So cau viet sau khi tham gia khoa hoc24.578.003

Paired Samples Test

Paired DifferencestdfSig. (2-tailed)

MeanStd. DeviationStd. Error Mean95% Confidence Interval of the Difference

LowerUpper

Pair 1So cau viet truoc khi tham gia khoa hoc - So cau viet sau khi tham gia khoa hoc-15.5836.7751.383-18.444-12.722-11.26823.000

Sig.= 0.000 < 0.05 ( kt lun rng c s khc bit c ngha thng k v ci thin k nng vit lun khi tham gia kha o to.

C th so snh trn nhiu cp bin a vo. V d: kh nng vit lun ca sinh vin th hin qua vit cu v vit on .Paired Samples Statistics

MeanNStd. DeviationStd. Error Mean

Pair 1So cau viet truoc khi tham gia khoa hoc10.79244.606.940

So cau viet sau khi tham gia khoa hoc26.38248.2981.694

Pair 2So cau doan truoc khi tham gia khoa hoc2.29241.488.304

So cau doan sau khi tham gia khoa hoc5.42241.530.312

Paired Samples Correlations

NCorrelationSig.

Pair 1So cau viet truoc khi tham gia khoa hoc & So cau viet sau khi tham gia khoa hoc24.578.003

Pair 2So cau doan truoc khi tham gia khoa hoc & So cau doan sau khi tham gia khoa hoc24.517.010

Paired Samples Test

Paired DifferencestdfSig. (2-tailed)

MeanStd. DeviationStd. Error Mean95% Confidence Interval of the Difference

LowerUpper

Pair 1So cau viet truoc khi tham gia khoa hoc - So cau viet sau khi tham gia khoa hoc-15.5836.7751.383-18.444-12.722-11.26823.000

Pair 2So cau doan truoc khi tham gia khoa hoc - So cau doan sau khi tham gia khoa hoc-3.1251.484.303-3.751-2.499-10.31923.000

Ph lc:

Ti liu tham kho

1. Hamilton (2006), Statistics with Stata 9, Pub. Thomson.

2. J. Scott Long (2007), Regression Models for Categorical and Limited Dependent Variables, A Stata Press Publication.

3. Woolbridge, J.M. (2005) Introductory Econometrics A Modern Approach, South-Western College Pub.

4. James H. Stock & Mark W. Watson (2006) Introduction to Econometrics (second edition), Addison-Wesley Pub.

5. Christopher Dougherty (2007), Introduction to Econometrics (third edition), Oxford Pub.6. Alan C.Ellicot & Wayne A. Woodward (2007), Statistical Analysis Quick Reference Guidebook with SPSS Examples, Sage Pub.Chp nhn H0

t = (0; t)

0

t

Bc b H0

t = (t; +)

t1 hay t2 chnh l t tnh ton

ng vi t1 c P1; t2 c P2

t chnh l gi tr t tra bng

t

p1

t1

p2

t2

t

Trong thc tin, kim nh t c dng thay cho kim nh z v chng ta thng khng bit trc phng sai tng th. V khi kch thc mu ln th hai php kim nh t v z l nh nhau.

Vi cc phn mm thng k, dng cch tip cn p-value trong quy tc bc b hay chp nhn gi thuyt khng H0 (Null Hypothesis), gi thuyt lun cha du =.

V d: nu p-value = 20% m chng ta vn bc b H0 th chuyn g s xy ra? Khi thc hin kim nh, chng ta chn mc ngha kim nh 5% (c th 1% hay 10%), ngha l chng ta chp nhn phm sai lm bc b H0 trong khi thc s H0 ng (gi l sai lm loi I) ti a ch 5%. Nu ta bc b gi thuyt H0 ti mc ngha quan st 20% (ln hn nhiu so vi 5%) tc l kh nng phm sai lm bc b H0 trong khi thc s H0 ng ti 20%, ln hn nhiu so vi ngng cho php ti a m chng ta chn. V vy, chng ta khng nn bc b H0 (v i mt vi nguy c phm sai lm qu ln). Nh l, khi bc b hay khng bc b ga thuyt H0 chng ta u c nguy c mc phi sai lm. l xc sut ti a mc phi sai lm bc b H0 trong khi H0 thc s ng. l xc sut ti a mc phi sai lm khng bc b H0 trong khi H0 thc s sai.

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