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# T-Test

T-Test. Faisal Aziz. T-Test. William S. Gosset discovered T-distribution in 1906 T-distribution is similar to normal distribution Used when sample size &lt;30. T-Test. To compare means Numerical Data Comparing the Mean of two groups Also referred as student t-test. Degrees of Freedom.

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## T-Test

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1. T-Test Faisal Aziz

2. T-Test • William S. Gosset discovered T-distribution in 1906 • T-distribution is similar to normal distribution • Used when sample size <30.

3. T-Test • To compare means • Numerical Data • Comparing the Mean of two groups • Also referred as student t-test

4. Degrees of Freedom Minimum number of information required to estimate the population variance One sample • n-1 Two sample • n1+n2-2

5. 1) Determine the type of hypothesis Right sided Steps of T-Test

6. Steps of T-Test 1) Determine the type of hypothesis • Left sided

7. Steps of T-Test 1) Determine the type of hypothesis • Two sided

8. Steps of T-Test 2) Determine level of significance • Level of Significance= α

9. Steps of T-Test 3) Apply T-Test • Compute t- calculated (Formula) by choosing best statistical test • Compute t- tabulated…… (T- Table)

10. T-table

11. 4) Make an inference….. Reject H0 if t cal >t α/2 Reject H0 if t cal < -t α /2 Reject H0 if t cal >t α Reject H0 if t cal < -t α Steps of T-Test

12. Steps of T-Test 5) Conclusion • Accept or reject H0

13. One sample T-test To compare population mean with sample mean

14. One sample T-Test df = n-1

15. Example • The average Hb level of normal woman is 13. The doctor at clinic A feels that the pregnant women coming at clinic are mostly anemic. She takes a random sample of 25 pregnant women and looks at their Hb. The data is given below • Sample mean X=11.8 • Sample SD s=2.6 • Sample size n=25 • Level of significance α = 0.05 Hypothesis ???

16. Example • 1) H0= µ>13 Ha= µ<13 • 2) α = 0.05 • 3) t cal= -2.32 T tabulated(0.05’24)= -1.711

17. Example 4) Reject H0 if t cal < -t tab • Hence t cal < -1.711 5) Conclusion • Therefore we reject H0 at 5% significance level. • Average Hb of pregnant women at clinic A is less than that of normal women

18. Two Independent Samples t-test

19. Two Independent Samples t-test • For comparison of two means • To compare one group with other

20. Example

21. Example Null Hypothesis (Ho): H1 = H2 Alternative hypothesis (Ha): H1 = H2 α = 0.05

22. t cal= 2/0.56=3.6

23. T- tabulated • α = 0.05 • D.F= n1+n2-2 60+52-2= 110 • Look into T- Table • T tabulated= 1.98

24. Inference • T calculated=3.6 > t tabulated=1.98 Conclusion ???

25. How to do ‘Independent Sample t-test’ by SPSS