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  1. t-test Dr. Tipsuda Janjamlha 23 Aug 08

  2. t-test :Compute mean differences 1 one group t-test. 2 two independent groups t-test 3 two paired (dependent) groups t-test

  3. 1 one group t-test compare ‘gr. mean’ with ‘constant’ A class of 30 students is given special training to improve intelligence. After training, are their IQ significantly different from 100 ? • 112 128 98 98 • 116 124 98 97 • 125 106….. 100

  4. 2 two independent groups t-test • To compare means of two independent samples. • Ex. Measurements on the two difference samples • Analysis performed on differences between group means • 112 128 98 • 116 124 98 • 125 106….. • 112 128 98 98 • 124 98 97 • 125 ….. GROUP 1 GROUP 2

  5. 3 two paired (dependent) groups t-test • To compare means of two non-dependent samples. • Ex. Measurements on the same individuals before and after a treatment • Analysis performed on differences between individual pairs of observations • 112 128 98 • 116 124 98 • 106….. • 112 128 98 98 • 124 98 97 • 125 ….. GROUP 1 GROUP 2

  6. 3 two paired (dependent) groups t-test SUBJECT Data1 Data2 Difference 1 105 112 -7 2112 128 -16 3 128 98 -30 4 98 98 0 5106 105 1 6 124 124 0 798 98 0 etc. etc.etc. etc.

  7. A Comparison of one or two group’s means

  8. Question-naire: 9 items 1.. 2.. … 9.. male Space satisfaction gender female natural Illness recover duration Window views building

  9. The type of data depend on your measurement A Thai identity Roof characteristics B low Well-being Crowing experiences high

  10. building natural natural building natural building ASSUMPTION: Normality distribution Mean, SD., n Mean, SD., n

  11. ผู้ชายเก็บความลับเก่งกว่าผู้หญิงผู้ชายเก็บความลับเก่งกว่าผู้หญิง ผู้ใช้ครีมหน้าเด้งยี่ห้อ A มีความพึงพอใจระดับมากในความเด้ง คนอายุมากกับคนอายุน้อยมีความขี้บ่นแตกต่างกัน ปริมาณผมบนศีรษะมีความสัมพันธ์กับอาการใจน้อย วัยรุ่นมักจะขับรถเร็วกว่าที่กฎหมายกำหนด (90 km/hr) นักศึกษา APTU ใช้เวลานอนแตกต่างจากนักศึกษาคณะอื่น มีค่าเฉลี่ยเวลานอนอย่างน้อย 1 คู่ที่แตกต่างกัน

  12. Steps in t-test Is the DV : interval/ratio and IV : nominal level? No Find other methods Yes Assumption of normality To test assumption of normality: - Explore the skewness, and kurtosis (-1 and + 1) - Kolmogorov – Smirnov and Shapiro – Wilk test No Non-parametric stat. Yes Is there a pair or independent gr.? Independent Pair Compute the independent t test Compute the pair t test

  13. Assumption of Equal Variances: See the p-value for the Levene’s test for equality of variances p-value < alpha: not assumed p-value > alpha: assumed Equality not assumed Equality assumed Decision about Hypotheses: Is the p-value for the t test <= alpha? Yes No Not reject Ho, no difference at all Reject Ho, difference between group

  14. Case1: 1 group t-test The researcher wants to examine ‘the personal space bubble’ of the TU students. Sample: 24 TU students. The international standard of the student space is 454 cm2/person Do the data provide sufficient evidence to conclude that the personal space bubble of the TU students is different from the international standard (454 cm2/person).

  15. Test of normality: analysis > descriptive statistics > explore…

  16. 1 2 3 • Interpretation • The TU student personal space is 450 cm2,SD =8.663 • t =-2.262 ,df=23,p=.033 ,so the TU space mean is not equal to 454 cm2 (standard) • ‘TU space is less than the standard space’

  17. Case2 : independent groups t-test Crowding perception of 30 apartment residents and house residents in Bangkok. apartment Crowing perception (Quantitative data) Resident types house

  18. Test of normality: analysis > descriptive statistics > explore…

  19. 1. การทดสอบ Levene test for Equality Ho : Ha : F=0.052, p=.820 p> α(.05), so equal variances assumed 1 1 2

  20. interpretation mean difference testing:Ho : Ha : 2 t = -.635 , p = .529 p > α(.05),so not reject Ho. There is no significant difference in crowding perception mean between apartment and house residents. คนที่อาศัยในอพาร์ทเมนท์มีการรับรู้ความหนาแน่นเฉลี่ยไม่แตกต่างจากคนที่อาศัยในบ้าน

  21. Case3 : pair (dependent) groups t-test Car mileages , before and after added a new gasoline.

  22. t =4.714 , p= .001 p < α (.05),so reject Ho. There is a .05 significant difference in car mileage mean between before and after added a new gasoline. After adding the gas, the car has a shorter mileage. ค่าเฉลี่ยระยะทางก่อนและหลังเติมgasoline แตกต่างกันอย่างมีนัยสำคัญทางสถิติที่ระดับ .05 โดยหลังเติม gasoline รถมีระยะทางการวิ่งลดลง