Boost Fertility New Invention Ups Success Rates.pdf
Z test
1. Dr. Muhammedirfan H. Momin
Assistant Professor
Community Medicine Department
Government Medical College, Surat.
DR IRFAN MOMIN
2. INTRODUCTION
The use of any statistical method for
analyzing data is based on the objectives
of the study, the hypothesis to be tested
and type of available statistical data
which is to be analyzed to answer the
research questions
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3. Statistical Tests
How to tell if something (or somethings) is different
from something else
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4. TYPES OF DATA
It can be
-Primary or Secondary
-Qualitative or Quantitative
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5. • Primary data is that which is collected by the
researcher to address the current research.
• Secondary data refers to data gathered by
others or from other studies like official
records, publications, documents etc.
• Qualitative data refers to data having
counting of the individuals for the same
characteristic and not by measurement.
• Quantitative data refers to data having
magnitude and the characteristic is measured
either on an interval or on a ratio scale.
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6. Qualitative ( Sex, Religion)
• Data types
Quantitative
Continuous Discrete
(measurable) (countable)
Age No. of. Children
Hb No. of Cases
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10. Table 1 Risk factors for Myocardial Infarction for patients (n=57)
admitted to the Kilpauk Medical College Hospital,
Chennai, Jan- Sep 1998
Risk factor MI Patients
No %
Hypertension 24 42.1
Smoking 20 35.1
Diabetes 13 22.8
CAD 9 15.8
Hyperlipedemia 2 3.5
None 8 14.0
DR IRFAN MOMIN
11. Steps in Test of Hypothesis
1. Determine the appropriate test
2. Establish the level of significance
3. Formulate the statistical hypothesis
4. Calculate the test statistic
5. Compare computed test statistic against a
tabled/critical value
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12. 1. Determine Appropriate Test
• Z Test for the Mean
• (Standard error of difference between two means)
• Z Test for the Proportion
• (Standard error of difference between two proportions)
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13. 2. Establish Level of Significance
p is a predetermined value
The convention
p = .05
p = .01
p = .001
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19. A sampling distribution for
H0 showing the region of
rejection for = .05 in a
2-tailed z-test.
2-tailed regions
Fig 10.4 (Heiman
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20. A sampling distribution for
H0 showing the region of
rejection for = .05 in a
1-tailed z-test.
1-tailed region, above mean
Fig 10.7 (Heiman
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21. A sampling distribution for
H0 showing the region of
rejection for = .05 in a
1-tailed z-test where a
decrease in the mean is
predicted.
1-tailed region, below mean
Fig 10.8 (Heiman
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23. If P < 0.05, the observed difference is
‘SIGNIFICANT (Statistically)’
P< 0.01, sometimes termed as ‘Highly Significant’
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24. INTERPRETATION OF SIGNIFICANCE
SIGNIFICANT Does not necessarily mean that the
observed difference is REAL or
IMPORTANT. Only that it is unlikely
(< 5%) to be due to chance.
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25. INTERPRETATION OF NON - SIGNIFICANCE
NON - SIGNIFICANT Does not necessarily mean that
there is no real difference; it means
only that the observed difference
could easily be due to chance
(Probability of at least 5%)
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26. 3. Determine The Hypothesis:
Whether There is an Association
or Not
Write down the NULL HYPOTHESIS and
ALTERNATIVE HYPOTHESIS and set the LEVEL
OF SIGNIFICANCE.
Ho : The two variables are independent
Ha : The two variables are associated
We will set the level of significance at 0.05.
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27. For Example
Some null hypotheses may be:
‘there is no relationship between the height of the land
and the vegetation cover’.
‘there is no difference in the location of superstores and
small grocers shops’
‘there is no connection between the size of farm and the
type of farm’
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29. STANDARD ERROR OF DIFFERENCE
BETWEEN TWO PROPORTIONS
P1 - P2
Z = ------------------
SE (P1 - P2)
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30. STANDARD ERROR OF DIFFERENCE
BETWEEN TWO PROPORTIONS
SE (P1 - P2) = P1Q1 + P2Q2
n1 n2
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31. EXAMPLE
If swine flu mortality in one sample of 100 is 20% and in
another sample of 100 it is 30%. Is the difference in
mortality rate is significant?
P1= 20 q1 = 80 n1 = 100
P2= 30 q2 = 70 n2 = 100
P1 - P2
Z = ------------------
SE (P1 - P2)
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32. STANDARD ERROR OF DIFFERENCE
BETWEEN TWO PROPORTIONS
SE (P1 - P2) = 20x80 + 30x70
100 100
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33. STANDARD ERROR OF DIFFERENCE
BETWEEN TWO PROPORTIONS
SE (P1 - P2) = 37
= 6.08
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34. EXAMPLE
If swine flu mortality in one sample of 100 is 20% and in
another sample of 100 it is 30%. Is the difference in
mortality rate is significant?
P1= 20 q1 = 80 n1 = 100
P2= 30 q2 = 70 n2 = 100
P1 - P2
Z = ------------------
SE (P1 - P2)
DR IRFAN MOMIN
35. EXAMPLE
If swine flu mortality in one sample of 100 is 20% and in
another sample of 100 it is 30%. Is the difference in
mortality rate is significant?
P1= 20 q1 = 80 n1 = 100
P2= 30 q2 = 70 n2 = 100
20-30
Z = --------- = -1.64
6.08
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36. Z value and probability
z 1.96 2.58
p 0.05 0.01
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37. Obtained z value (1.64) is less than critical z value
(1.96) , so P >0.05, hence difference is insignificant at
95 % confidence limits.
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38. STANDARD ERROR OF DIFFERENCE
BETWEEN TWO MEANS
X1 - X2
Z = ------------------
SE (X1 - X2)
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39. STANDARD ERROR OF DIFFERENCE
BETWEEN TWO MEANS
SE (X1 - X2) = SD12 + SD22
n1 n2
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40. EXAMPLE
In a nutritional study, 100 children were given usual diet and 100
were given vitamin A and D tablets. After 6 months, average
weight of group A was 29kg with SD of 1.8kg and average
weight of group B was 30kg with SD of 2kg. Is the difference
is significant?
SD1= 1.8 n1 = 100
SD2= 2 n2 = 100
X1 - X2
Z = ------------------
SE (X1 - X2)
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41. STANDARD ERROR OF DIFFERENCE
BETWEEN TWO MEANS
SE (X1 - X2) = SD12 + SD22
n1 n2
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42. STANDARD ERROR OF DIFFERENCE
BETWEEN TWO MEANS
SE (X1 - X2) = (1.8)2 + (2)2
100 100
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43. STANDARD ERROR OF DIFFERENCE
BETWEEN TWO MEANS
SE (X1 - X2) = (1.8)2 + (2)2
100 100
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44. STANDARD ERROR OF DIFFERENCE
BETWEEN TWO MEANS
SE (X1 - X2) = 3.24+4
100
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45. STANDARD ERROR OF DIFFERENCE
BETWEEN TWO MEANS
SE (X1 - X2) = 0.0724
=0.27
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46. EXAMPLE
In a nutritional study, 100 children were given usual diet and 100
were given vitamin A and D tablets. After 6 months, average
weight of group A was 29kg with SD of 1.8kg and average
weight of group B was 30kg with SD of 2kg. Is the difference
is significant?
SD1= 1.8 n1 = 100
SD2= 2 n2 = 100
X1 - X2
Z = ------------------
SE (X1 - X2)
DR IRFAN MOMIN
47. EXAMPLE
In a nutritional study, 100 children were given usual diet and 100
were given vitamin A and D tablets. After 6 months, average
weight of group A was 29kg with SD of 1.8kg and average
weight of group B was 30kg with SD of 2kg. Is the difference
is significant?
SD1= 1.8 n1 = 100
SD2= 2 n2 = 100
29 - 30
Z = ---------------- = -3.7
0.27
DR IRFAN MOMIN
48. A sampling distribution for
H0 showing the region of
rejection for = .05 in a
2-tailed z-test.
2-tailed regions
Fig 10.4 (Heiman
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49. Z value and probability
z 1.96 2.58
p 0.05 0.01
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50. As obtained value of z (-3.7) is higher than critical
value (-1.96 or -2.58), the observed difference is highly
significant, vitamins played a role in weight gain .
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