Test of significance
The test which is done for
testing the research hypothesis
against the null hypothesis.
• Why it is done?
To assist administrations and
clinicians in making decision.
• The difference is real ?
• It is happen by chance ?
• Due to study design and nonsampling errors ?
 steps
in doing significance
test:
Statement of the problem.
 Formulation of hypothesis, null and
alternate
 Decide upon a significant level, α of the
test.
 Choose a test statistic, t, z
 Compare test-statistics with relevant
tabulated value
 Make statistical decision

Research hypothesis: It is the
conjecture or supposition that motivates
the research.
 Statistical hypothesis: are hypothesis
that are stated in such a way that they
may be evaluated by appropriate
statistical techniques.

Null Hypothesis
 Null Hypothesis (symbolized as H0) can be
defined as the statistical hypothesis of no
difference.
 H0 is an artificial ‘ straw man” that provides a
reference for examining the departure of data
actually obtained from the data that would be
expected under the null hypothesis.
Alternate hypothesis(Ha ) : Is any
other hypothesis which we are willing to
accept when the H0 is rejected.
How to write a null hypothesis.
Alternative hypothesis (Ha ) guides the
writing of the null hypothesis(H0 ).
 So consider the form of the alternative
hypothesis first.
 remember Ha is the reflection of your
Research hypothesis.
 The Research hypothesis is usually written
in narrative form while the Ha is written in
algebraic form of inequality.


In testing population mean μ about a
given mean μ0 , Ha can be written as
follows,
H
Ha
0
when the test is done between two
sample
μ1 -μ2 =0
μ1 -μ2 ≠ 0
when sample mean with a known
standard
μ =μ0
μ ≠ μ0
for one tailed test, Right tail,greater than
μ  μ0
μ  μ0
for one tailed test, Left tail, lesser than
 level

of Significance
In hypothesis testing, the null
hypothesis is either accepted or
rejected, depending on whether
the p value is above or below a
predetermined cut-off
point,known as the Significance
level of the test, usually it is
taken as 5% level.
P value
P is the probability of being wrong
when H0 rejected .
 When the level of Significance is
set at 5% and the test statistics fall
in the region of rejection, then the p
value must be less than 5% i.e
.(p<.05).
 When we will accept H0 (p>.05).

Cont…..

It is a number that tells us how unusual
our sample results are, given that the
null hypothesis is true. A p value
indicating that the sample results are
not likely to have occurred, if the null
hypothesis is true.
Calculated value:
 tabulated value: for a certain degree of
freedom highest value of test statistics
obtainable by chance corresponding to
probability of .05 or .01.

Example of t test
The average temp. of a group of 100
persons was calculated to be 98.90 with
a SD of 1.10 . We wish to test this mean
against the known standard of 98.60.

chi square test

In a random sample of 200 people there were
50 smokers and 150 non-smokers. of the 50
smokers 15 had lung cancer and of the 150
non smokers lung cancer was found in 15.
can we conclude, on the basis of this data,
that smoking is associated with lung cancer?
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Important points for chi square test
sample must be random
data qualitative and discrete
overall total is 40 or more, or
overall total is between 20 and 40, and none
of the four expected values is less than 5.
in 2/2 table ,if the expected frequency in any
cell is less than 5, needs Yates’ correction(
subtraction of 0.5from each cell).
in more than 2/2 table, test cannot be done.