1. By Dr Aijaz Ahmed Sohag
MSc (Env:Sc),M.A.S(H.S.A.),MBA(Health
Mgt),MPH , PhD
Prep by: Abdul Wasay Baloch
Amna Inayat Medical College
Statistic Test

2. Test of Significance ‘t’ Test
Summary points about ‘t’ Test
Gosset in Dublin (1908) discovered it and called it ‘Student’
test later as ‘t’ Test
To compare the means b/w groups t test is used
Used if sample size is less than 30
If sample size is 30 or more than Z test is used
Paired t ; when there is only one sample group is used and
we take the means before and after interventions
Unpaired ‘t’ test ; where two sample groups are used
Formula of t or Z test is=X1-X2/SE, where X1=mean of group
1, and X2=mean of group 2

3. Indication of ‘t’ Test
Quantitative data
To compare two Means
 Random samples
Normal distribution
Sample size is less than 30
“S” unknown
Continuous Data
Parametric test

4. Types of ‘t’ Test
One sample ‘t’ Test
Two sample ‘t’ Test
Paired Sample ‘t’ test

5. Level of Significance
Alpha value:
It gives probability of incorrectly rejecting the null hypothesis
when it is actually true
Traditional values are used as 0.05,0.01 + 0.001
When a test statistics falls in the area of critical region the
result is referred to as SIGNIFICANT

6. Conventions for Interpreting P values
P Value Interpretation
P> 0.05 Result not significant
P<0.05 Result significant
P<0.01 Result highly significant
P<0.001 Result is very highly significant

7. Testing Null Hypothesis
In testing null hypothesis we have two decisions
It is false – consequently rejected
It is true – we fail to reject it
If we do decisions as above – we do a correct decision
If we commit a mistake to decide incorrectly – then we
make/commit errors called alpha error and beta error

8. Errors of Hypothesis Testing
Two types of Errors
1. Type 1 or α error : when we decide the null hypothesis is
false, when it is actually true (no difference between two
variables)
 Rejecting the null hypothesis when it is true
 Type 1 or alpha error(it is dangerous error)
1. Type 2 or β error: when we decide that null hypothesis is
true when it is actually false
 Not rejecting the null hypothesis when it is actually false

9. inference Accept it Reject it
Null Hypothesis Correct decision Type 1 error
NH is false Type 2 Error Correct Decision
In Medical studies Type 1
error is more serious as
compared to Type 2 errors

10. Chi Square Test
Advantages/Rationale
a) Alternate method: to testify significance of difference between
two proportions
b)To determine whether there is some association between two
variables
c) It is applicable to qualitative data (where ‘t’ is not applicable)

11. Basis of Chi Square Test X2
Most tests involving quantitative data depend on x2
In x2 we can test significance for many groups at the same
time
In x2 actual no are used
The steps are
Stating null hypothesis
Calculating x2 value
Finding degree of freedom
Looking for P value from x2 table
Acceptability or rejecting the hypothesis

12. Chi Square Tests
Test of significance of the difference b/w
two proportion

13. An Example:Trial of 2 whooping cough vaccines
Vaccine No of
vaccinated
No of cases Non Attacked Total
A 2400 22 68 90
B 2300 14 72 86
Total 4700 36 140 176
•Apparently vaccine was B was superior to Vaccine A, to
know whether the vaccine was really superior to vaccine A
OR whether the diff was merely due to chance

14. Firstly we assume or test the hypothesis in following ways
Considering the Null Hypothesis , that there was no
differences b/w the effect of the two vaccines

15. Test the Null Hypothesis
 proportion of people attacked will be 36/176=0.204
 Proportion of people not attacked will be 140/176=0.795
 From these proportion we calculate the expected no. of
people attacked or cases by vaccine A
90*0.024=18.36
 Expected not attacked by vaccine A 90*0.795=71.55
 Similarly expected no. of attacked by Vaccine B 86*
0.204=17.544
 Expected no of non attacke by vaccine B 86*0.795=68.37

16. The expose (E) and Observed (O) are
Vaccine A Attacked Non Attacked
O=22
E=18.36
O-E=22-18.36= 3.64
O=68
E=71.55
O-E = 68-71.55= -3.55
Vaccine B Attacked Non Attacked
O=14
E=17.54
O-E=14-17.54= -3.54
O=72
E=68.37
O-E= 72-68.37= 3.63

17. By applying the Chi Square test
X2 = ∑ (O-E)/ E
Combining O-E attacked case & non attacked case
= 3.64^2/18.36 + 3.55^2/71.55 + 3.54^2 / 17.54 + 3.36^2/68.37
=0.72+0.17+0.71+0.19+1.7
B)Finding the degree of Freedom (d.f)- depends on no. of
columns and rows in a table
d.f=(c-1) (r-1)
= (2-1) (2-1)
=1
c) Referring Probability Table
 by referring Chi Square Probable table having d.f 1 against probability of
0.05
=3.84

18. Since the observed value in Chi Square table is much lower so
the null hypothesis is true, hence Vaccine B is not superior to
Vaccine A
This test is valid only if the expected no.of each cell is not less
than 2

19. Pakistan Demographic & Health Survey
06-07
 About apprehension/non fulfillment of MDG on improved maternal health
 96% women know about contraceptive knowledge, 22% using that
 One in four unmarried women has unmet need for family planning
 Most widely used method is Male Sterilization
 In Sindh women of age 15-49 is 27%
 Drop in total fertility rate from 5.4 children born to mother 90-91 to 4.1 children in
2006-07
 1/3rd
birth taken place within 24 months of previous birth which can be cited for
increased Child Mortality
 More than 9 of every 100 children die before 5th
birthday
 IMR in Sindh 8.1% while 7.8% in rest of country
 MMR in Sind ¾ deaths in every 100,000. 20% of female deaths due to Maternal
causes

20. Half of birth by DAI, 39% by skilled doctor, nurse, midwife, LHV
47% children between 12 and 23 months receive all vaccines
02%of children under 5
02% pregnant women sleep under net
The global population is growing by 80 miion people per year, 90%
of it in poorer countries
In past 50 years extraction from rivers, lakes and aqiofers has
tripled to help meet population growth and demand for water
intensive food such as rice cotton, dairy and meat products
Agriculture accounts for 70% of the withdrawals, a figure that
reaches more than 90% in some developing countries

21. PROBABILITY
The probability of an event is denoted by P
Probabilities are usually expressed as decimal fractions, not
as percentages and must lie b/w zero (zero probability) and
one (absolute probability)
If the event is sure to occur, than p-value is 1(absolute
probability), for e.g. all men sure to die. So probability is P
= 100/100= 1(standard)
5 chances in 100=5/100 OR 1/20 OR 0.05. We can also say
I chance in 20 is taken as cut off value

22. Example : FREQUENCY RATE OF DIABETES WAS DEFINITELY HIGHER
AMONG OBESE
By calculating P-value, the statistical association between exposure status and
occurrence of diabetes is ascertained
Test of significance will depend upon the variables under investigation
If we are dealing with discrete variables(cannot be expressed in decimals), the
results are usually presented as rates and proportion, THAN test of significance
usually adopted is the STANDARD ERROR OF DIFFERENCE BETWEEN TWO
PROPORTION or CHI-SQARE TEST.
However, if we are dealing with continuous variables(can be expressed in
decimals e.g., age, blood pressure), the data will have to be grouped and test of
significance used will be STANDARD ERROR OF DDIFFERENCE BETWEEN
TWO MEANS, or t- test
If p- value is less than or equal to equal to 0.05, it is regarded as “statistically
significant”

23. Smaller the p- value , the greater the statistical significance
The smaller the P value, the greater the statistical
significance or probability that the association is not due to
chance alone.
However, statistical association (P value) does not imply
causation.

P= 0.05 ( just significant at 5 percent level)
P<0.05 (significant at 5 percent level)
P>0.05 (not significant at 5 percent level)