ch- Sample (Typeset by TYINDEX, Delhi) of May , :

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SIGNIFICANTTESTS

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After any experiment we get some results, but we are not sure about thisresult 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’.

S S T :.................................................................................................................................

The selection of the appropriate statistical test is depends upon:

. The scale of measurement e.g. Ratio, Interval.. The number of groups e.g. One, Two or More.. Sample size e.g. If the sample size is less than . Students ‘t’ test is to be

used.. Measurements e.g. Repeated or Independent measurements.

S T S :.................................................................................................................................

For application of test sample should be selected randomly. Thus we have inthis case degree of freedom ‘n’ = – = Now, table value of x2 is . t .

ch- Sample (Typeset by TYINDEX, Delhi) of May , :

SIGNIFICANT TESTS

Table 13.1 This is Example of Table Sample.

Scale Two groups Three/More groups

Independent Repeated Independent Repeated

Intervaland Ratio

Z testt test

Z testt test

ANOVA test(F test)

ANOVA(F test)

Ordinal Median testMannWhitney

Wilcox antest

MedianKruscal test

Friedman test

Nominal X2 test Me Nemartest

Chi–SquareTest

Cochron’s test

for degree of freedom, which is much less than the obtained value that is.

T :.................................................................................................................................

. Parametric Tests. Non – Parametric Tests

. P T :.................................................................................................................................

When quantitative data like Weight, Length, Height, and Percentage is givenit is used. These tests were based on the assumption that samples were drawnfrom the normally distributed populations.

E.g. Students t test, Z test etc.

. N – P T :.................................................................................................................................

When qualitative data like Health, Cure rate, Intelligence, Color is given it isused. Here observations are classified into a particular category or groups.

E.g. Chi square (x2) test, Median tests etc.

ch- Sample (Typeset by TYINDEX, Delhi) of May , :

SIGNIFICANT TESTS

Table 13.2 This is Example of Table Sample.

Patients Before Aftertreatment (B) treatment (A)

1 2.4 2.22 2.8 2.63 3.2 3.04 6.4 4.25 4.3 2.26 2.2 2.07 6.2 4.88 4.2 2.4

I. T – T :.................................................................................................................................

W.S. Gosset investigated this test in . It is called Student t – Test becausethe pen name of Dr. Gosset was student, hence this test is known as student’st – test. It is also called as ‘t- ratio’ because it is a ratio of difference betweentwo means.

Aylmer Fisher (–) developed students ‘t’ test where samples aredrawn 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 theNormal, Binomial and Poisson distributions and Comparison of a samplevariance with population variance.

S:

Here, ∑D = 8.3

N = 8∑D2 = 14.61

D =8.3

8= 1.0375

ch- Sample (Typeset by TYINDEX, Delhi) of May , :

SIGNIFICANT TESTS

∴ Standard deviation of the different between means. Here, the calculatedvalue for ‘t’ exceeds the tabulated ‘t’ value at p = 0.05 level with df. Thereforethe glucose concentration by the patients after treatment is not significant.

=

√∑D2 − (

∑D)2

n

N − 1

=

√14.61 − (8.3)2

8

7

=

√14.61 − 68.89

8

7

∴ S.D. =

√14.61 − 8.6112

7

=√

0.8569

∴ S.D. = 0.9257

Now, standard error of the difference (SED)

. =SD√

N=

0.9257√8

=0.9257

2.8284

∴ S.E. = 0.3272

∴ t =D

SED=

1.0375

0.3272= 3.1708

Here, the calculated value for ‘t’ exceeds the tabulated ‘t’ value at p = 0.05level with df. Therefore the glucose concentration by the patients after treat-ment is not significant.

U:

It is widely used in the field of Medical science, Agriculture and Veterinary asfollows:

� To compare the results of two drugs which is given to same individualsin the sample at two different situations? E.g. Effect of Bryonia and Ly-copodium on general symptoms like sleep, appetite etc.

� It is used to study of drug specificity on a particular organ / tissue / celllevel. E.g. Effect of Belberis Vulg. on renal system.

ch- Sample (Typeset by TYINDEX, Delhi) of May , :

SIGNIFICANT TESTS

� It is used to compare results of two different methods. E.g. Estimation ofHb% by Sahlis method and Tallquist method.

� To compare observations made at two different sites of the same body.E.g. compare blood pressure of arm and thigh.

� To study the accuracy of two different instruments like Thermometer, B.Papparatus etc.

� To accept the Null Hypothesis that is no difference between the twomeans.

� To reject the hypothesis that is the difference between the means of thetwo samples is statistically significant.