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T- Test

T- Test. Prof. Dr. Ramez Bedwany. Comparison of two independent samples t- Test. = mean of the first simple = mean of the second sample = pooled Variance. = pooled Variance. Critical t from table at degree of freedom = n1+ n2-2 If n1+ n2 < 120 use t test

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T- Test

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  1. T- Test Prof. Dr. Ramez Bedwany

  2. Comparison of two independent samplest- Test = mean of the first simple = mean of the second sample = pooled Variance

  3. = pooled Variance

  4. Critical t from table at degree of freedom = n1+ n2-2 • If n1+ n2 < 120 use t test • If n1+ n2 ≥120 use z test with the same formula

  5. Example (1) Sample of size 25 was selected from healthy population , their mean BP 125 mm Hg with standard deviation of 10 mm Hg. another sample of size 17 was selected from population of diabetics their mean BP was l32mmHg, with standard deviation of 12 mm Hg Test whether there is significant difference in mean BP of diabetics and healthy individual at I % level of significance

  6. Answer • n1=25 X1=125 S1=10 • n2=17 X2=132 S2=12 • df= n1+n2-2 = 25+17-2=40 • Critical t at 40, 1% level of significance 2.704

  7. Decision: Since the computed t is smaller than critical t so there is no significant difference between mean BP of healthy and diabetic samples at 1 %

  8. Exercise • Example 2 and 3

  9. t- test for paired observation (t- difference) • Uses: To compare the means of two pairedsamples • Example: Mean pulse rate before and after intake of drug

  10. di = difference (after-before) Sd = standard deviation of difference n = sample size Critical t from table at df = n-1

  11. Example (1) The following data represents the reading of Systolic BP before and after administration of certain drug. Test whether the drug has an effect on BP at 1% level of significance

  12. Serial number BP BP Before after I 200 180 2 160 165 3 190 175 4 185 185 5 210 170 6 175 160

  13. ANSWER

  14. = -14.17 = 15.942

  15. Critical t at df=6-1=5 and 1% level of significance = 4.032 Decision Since the computed t is smaller than critical t so there is no significant difference between mean BP before and after administration of drug so the drug has no effect on BP at 1% level of significance

  16. Assignment

  17. Outcomes • By the end of this lecture, the student will be able to Know definition, uses and types of statistics.

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