Parametric test with t test and ANOVA on the bases of Biostatistics subject. The slide contains definition of particular test with their sums. Comparison of tests and some terminologies used in hypothesis testing. Useful for Pharmacy students.

1. Parametric test

2. - used to evaluate hypotheses
- Types of Parametric test
• t-test
• Z-test
• F-test
• Analysis of variance (ANOVA)
- Parametric tests assume a normal distribution of values
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P a r a m e t r i c t e s t
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3. 3
T t e s t
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4. 4
T t e s t
3 types of t-test
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5. 5
T t e s t
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6. 6
Two-tailed One-tailed
For α=0.05 For α=0.05
left-tailed
right-tailed
T t e s t
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7. Case I
- After A large amount of data was collected for the content of drug in the tablet formulation during
a period of several years , The manufacturing process showed an average
potency of 5.01 mg and a standard deviation of 0.11, both values
considered to be equal to the true process parameters.
- A new batch was made with a modification of the usual
manufacturing procedure. And assay of 20 tablets give bellow..
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O n e - s a m p l e t e s t
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8. 8
O n e - s a m p l e t e s t
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9. 2. The null hypothesis and alternative hypothesis
two sided hypothesis testing
- Alternative hypothesis suggest that the average drug potency of the
new batch can conceivably be smaller as well as greater than the
historical process average of 5.01 mg.
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O n e - s a m p l e t e s t
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10. 3. The level of significance is specified
1
Z ≤ -1.96 or Z ≥ 1.96 then reject H0
O n e - s a m p l e t e s t
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11. 4. Selection of sample
5. Experiment trials
6. After the experiment is completed , Statistical calculations are
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12. One-sample test, variance unknown. two-sided test
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O n e - s a m p l e t e s t
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13. 1
O n e - s a m p l e t e s t
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14. 1
O n e - s a m p l e t e s t
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15. Case II
- A pharmaceutical company places A new compound on an
“antihypertensive” screening. Experience has shown that a blood
pressure reduction of more than 15 mm Hg in hypertensive animals.
since such testing is expensive, the researchers wish to be reasonably
sure that statistically the compound truly reduces the blood pressure
by more than 15 mm Hg before testing is continued. The level of
significance of 10% was chosen
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O n e - s a m p l e t e s t
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16. 1
O n e - s a m p l e t e s t
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17. 1
O n e - s a m p l e t e s t
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18. What difference (reduction) would have been needed to show a significant
reduction in this clinical trial ?
1
O n e - s a m p l e t e s t
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19. 1
U n p a i r e d s a m p l e t e s t
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20. 2
U n p a i r e d s a m p l e t e s t
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21. - Statement of hypothesis
2
U n p a i r e d s a m p l e t e s t
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22. 2
U n p a i r e d s a m p l e t e s t
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23. 2
U n p a i r e d s a m p l e t e s t
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24. 2
U n p a i r e d s a m p l e t e s t
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25. 2
U n p a i r e d s a m p l e t e s t
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26. 2
U n p a i r e d s a m p l e t e s t
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27. 2
U n p a i r e d s a m p l e t e s t
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28. 2
U n p a i r e d s a m p l e t e s t
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29. Synonym:
2
U n p a i r e d s a m p l e t e s t
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30. P a i r e d s a m p l e t e s t
3
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31. 3
P a i r e d s a m p l e t e s t
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32. 3
P a i r e d s a m p l e t e s t
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33. 3
P a i r e d s a m p l e t e s t
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34. EXCERSIZE
- A certain stimulant drug is administered to each of 12 patients resulted in
the following change in blood pressure 5, 2, 8, -1, 3, 0, -2, 1, 5, 0, 4, 6
Can it be concluded that the stimulant will in general be accompanied by an
increase in blood pressure with ( = 0.05 )
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P a i r e d s a m p l e t e s t
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35. 3
P a i r e d s a m p l e t e s t
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36. 3
P a i r e d s a m p l e t e s t
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37. 3
P a i r e d s a m p l e t e s t
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38. Full form : Analysis of variance
Defination :
ANOVA is a statistical technique specially designed to test whether the
means of more than 2 quantitative populations are equal.
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A N O V A
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39. 3
A N O V A
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40. 4
O N E - W A Y A N O V A
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41. 4
O N E - W A Y A N O V A
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42. 4
O N E - W A Y A N O V A
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43. 4
O N E - W A Y A N O V A
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44. Calculation steps
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O N E - W A Y A N O V A
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45. 4
O N E - W A Y A N O V A
Calculation steps
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46. 4
O N E - W A Y A N O V A
Calculation steps
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47. 4
O N E - W A Y A N O V A
Calculation steps
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48. 4
O N E - W A Y A N O V A
Calculation steps
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49. 4
O N E - W A Y A N O V A
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50. 5
O N E - W A Y A N O V A
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51. - statement of hypothesis
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O N E - W A Y A N O V A
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52. 5
O N E - W A Y A N O V A
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53. 5
O N E - W A Y A N O V A
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54. 5
O N E - W A Y A N O V A
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55. ANOVA table
5
O N E - W A Y A N O V A
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56. 5
L S D t e s t
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57. 5
L S D t e s t
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58. - Finding LSD in EXCERSIZE 2
- t = 2.306
- S2 = 4
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L S D t e s t
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59. 5
L S D t e s t
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60. 6
T W O - W A Y A N O V A
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61. 6
T W O - W A Y A N O V A
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62. 6
T W O - W A Y A N O V A
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63. 6
T W O - W A Y A N O V A
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64. 6
T W O - W A Y A N O V A
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65. 6
T W O - W A Y A N O V A
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66. 6
T W O - W A Y A N O V A
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67. 6
ANOVA table
T W O - W A Y A N O V A
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68. 6
T W O - W A Y A N O V A
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69. 6
T W O - W A Y A N O V A
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70. 7
T W O - W A Y A N O V A
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71. 7
T W O - W A Y A N O V A
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72. 7
O N E - W A Y v s T W O - W A Y
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73. 7
S t u d y q u e s t i o n s
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74. 7
S t u d y q u e s t i o n s
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75. 7
S t u d y q u e s t i o n s
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76. 7
S t u d y q u e s t i o n s
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77. 7
S t u d y q u e s t i o n s
Ans.
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78. 7
S t u d y q u e s t i o n s
Ans.
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79. 7
S t u d y q u e s t i o n s
Ans.
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80. 8
S t u d y q u e s t i o n s
Ans.
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81. End
Reference:
Ph’ceutical statistics- Practical and clinical
applications –Sanford Bolton
Fundamental of Statistics –S.C. Guptha
Net Source
of the topic