ch-13 Sample (Typeset by TYINDEX, Delhi) 1 of 4 May 31, 2009 18:1
A fter any experiment we get some results, but we are not sure about
this result whether the result occurred by chance or a real difference.
That time to ﬁnd truth we will use some statistical tests, these tests are
termed as, ‘Tests of Signiﬁcance’.
Selection of Statistical Tests:
The selection of the appropriate statistical test is depends upon:
1. The scale of measurement e.g. Ratio, Interval.
2. The number of groups e.g. One, Two or More.
3. Sample size e.g. If the sample size is less than 30. Students ‘t’ test is
to be used.
4. Measurements e.g. Repeated or Independent measurements.
Selection of Test of Signiﬁcance:
For application of test sample should be selected randomly. Thus we have
in this case degree of freedom ‘n’ = 4 – 1 = 3 Now, table value of x2 is 7.815
t 0.05 for 3 degree of freedom, which is much less than the obtained value
that is 20.554
There are two types of tests:
1. Parametric Tests
2. Non – Parametric Tests
ch-13 Sample (Typeset by TYINDEX, Delhi) 2 of 4 May 31, 2009 18:1
Table 13.1. This is Example of Table Sample.
Scale Two groups Three/More groups
Independent Repeated Independent Repeated
Interval Z test Z test ANOVA test ANOVA
and Ratio t test t test (F test) (F test)
Ordinal Median test Wilcox an test Median Friedman test
Mann Whitney Kruscal test
Nominal X2 test Me Nemar test Chi–Square Cochron’s test
1. Parametric Test:
When quantitative data like Weight, Length, Height, and Percentage is
given it is used. These tests were based on the assumption that samples
were drawn from the normally distributed populations.
E.g. Students t test, Z test etc.
2. Non – Parametric Test:
When qualitative data like Health, Cure rate, Intelligence, Color is given
it is used. Here observations are classiﬁed into a particular category or
E.g. Chi square (x2 ) test, Median tests etc.
I. T – Test:
W.S. Gosset investigated this test in 1908. It is called Student t – Test
because the pen name of Dr. Gosset was student, hence this test is known
as student’s t – test. It is also called as ‘t- ratio’ because it is a ratio of
difference between two means.
Aylmer Fisher (1890–1962) developed students ‘t’ test where samples are
drawn from normal population and are randomly selected.
After comparing the calculated value of ‘t’ with the value given in the
‘t’ table considering degree of freedom we can ascertain its signiﬁcance.
Is the testing reliable? It is used for comparisons with expectations of
the Normal, Binomial and Poisson distributions and Comparison of a
sample variance with population variance.
ch-13 Sample (Typeset by TYINDEX, Delhi) 3 of 4 May 31, 2009 18:1
Table 13.2. This is Example of Table Sample.
Patients Before After
treatment (B) treatment (A)
1 2.4 2.2
2 2.8 2.6
3 3.2 3.0
4 6.4 4.2
5 4.3 2.2
6 2.2 2.0
7 6.2 4.8
8 4.2 2.4
D = 8.3
D2 = 14.61
D= = 1.0375
∴ Standard deviation of the different between means. Here, the calculated
value for ‘t’ exceeds the tabulated ‘t’ value at p = 0.05 level with 7df.
Therefore the glucose concentration by the patients after treatment is not
D2 − ( n
14.61 − 8
14.61 − 68.89
14.61 − 8.6112
∴ S.D. =
∴ S.D. = 0.9257
ch-13 Sample (Typeset by TYINDEX, Delhi) 4 of 4 May 31, 2009 18:1
Now, standard error of the difference (SED )
SD 0.9257 0.9257
.= √ = √ =
N 8 2.8284
∴ S.E. = 0.3272
∴t= = = 3.1708
Here, the calculated value for ‘t’ exceeds the tabulated ‘t’ value at p =
0.05 level with 7df. Therefore the glucose concentration by the patients
after treatment is not signiﬁcant.
It is widely used in the ﬁeld of Medical science, Agriculture and Veterinary
r To compare the results of two drugs which is given to same individ-
uals in the sample at two different situations? E.g. Effect of Bryonia
and Lycopodium on general symptoms like sleep, appetite etc.
r It is used to study of drug speciﬁcity on a particular organ / tissue /
cell level. E.g. Effect of Belberis Vulg. on renal system.
r It is used to compare results of two different methods. E.g. Estimation
of Hb% by Sahlis method and Tallquist method.
r To compare observations made at two different sites of the same body.
E.g. compare blood pressure of arm and thigh.
r To study the accuracy of two different instruments like Thermometer,
B.P apparatus etc.
r To accept the Null Hypothesis that is no difference between the two
r To reject the hypothesis that is the difference between the means of
the two samples is statistically signiﬁcant.