3. DEFINITION
It is a mathematical methods by
which the probability (P) or
relative frequency of an observed
difference, occurring by chance is
found
4. Objective of using tests of
significance
To compare – sample mean with
population
Means of two samples
Sample proportion with population
Proportion of two samples
Association b/w two attributes
5. CLASSIFICATION
TESTS IN TEST OF SIGNIFICANCE
Parametric
(normal distribution & Normal curve )
Non-parametric
(not follow normal distribution)
Quantitative data
Student ‘t’ test
Paired
Unpaired
Z test (for large samples)
One way ANOVA
Two way ANOVA
Qualitative data
Z – prop test
χ² test
Qualitative
(quantitative converted
to qualitative )
Mann Whitney U test
Wilcoxon rank test
Kruskal wallis test
Friedmann test
6. Parametric Uses Non-parametric
Paired t test Test of diff b/n
Paired observation
Wilcoxon signed
rank test
Two sample t test Comparison of two
groups
Wilcoxon rank sum test
Mann Whitney U test
’s s test
One way Anova Comparison of
several groups
Kruskal wallis test
Two way Anova Comparison of groups
values on two variables
Friedmann test
Correlation
Coefficient
Measure of association
B/n two variable
Spearman’s rank
Correlation
’s rank
correlation
Normal test (Z test ) Chi square test
7. The paired t test is used to determine
the single sample correlated
observations
The unpaired t test is to determine
the two independent samples
8. Criteria for applying ‘t’
test
Random samples
Quantitative data
Variable follow normal
distribution
Sample size less than 30
9. Application of ‘t’ test
Two means of small independent
sample
Sample mean and population
mean
Two proportions of small independent
samples
10. Z test (Recapitulate normal
deviate)
Large samples ( > 30)
Difference observed b/w sample estimate
and that of population is expressed in
terms of SE
Score of value of ratio b/w the observed
difference & SE is called ‘Z’
To test difference b/w sample mean &
population mean Z = diff in means / SE
of mean
Z = X - µ/ SE
11. Z = observed diff b/w 2 sample
means
SE of difference b/w 2
σ =Σ (xi-x)/ n-1
If the distance in terms of SE or Z
falls within mean +- 1.96 SE , Ho is
accepted
Distance from mean at which Ho is
rejected – level of significance
12. Chi square test ( χ² test )
Non parametric test
Developed by Karl Pearson
Not based on any assumption or
distribution of any variable
Used for qualitative data
To test whether the difference in
distribution of attributes in different
groups is due to sampling variation or
otherwise.
13. Used as a test of : proportion
association
goodness of fit
14. Test of proportions
Find the significance of difference in
two or more than two proportions.
To compare values of two binomial
samples even when they are very
small (< 30)
To compare the frequencies of two
multinomial samples
15. Test of association
Association b/w two events in
binomial or multinomial samples
Measures the probability of
association b/w two discrete variables
Assumption of independence made
unless proved otherwise by χ² test
16. Test of goodness of fit
It is to determine if the actual
numbers are similar to the expected
or theoretical numbers
Check whether the observed
frequency distribution fits in a
hypothetical or theoretical or
assumed distribution
Test the difference b/w observed &
assumed is by chance or due to a
particular factor
17. Restrictions in applications of χ² test
When applies in fourfold table –
results not reliable . Yates correction
=[O-E] -1/2
Test maybe misleading when f < 5
Tables larger that 2 x 2 , yates
correction cannot be applied
χ² values interpreted with caution
when sample < 50
Does not measure strength of
association
Does not indicate cause & effect
18. Steps & procedure of test of
significance
State null hypothesis
State alternate hypothesis
Selection of the appropriate test
to be utilized & calculation of test
criterion based on type of test
Fixation of level of significance
19. Select the table & compare the
calculated value with the critical
value of the table
If calculated value is > table
value, is rejected
If calculated value is < table
value, is accepted
Draw conclusions
20. Non parametric tests
Friedman’s test – nonparametric equivalent of analysis of
variance
Kruskal – Wallis test – to compare medians of several
independent samples equivalent of one –way analysis of variance
Mann – Whitney U test – compare medians of two independent
samples. Equivalent of t test
a family of statistical tests also called as distribution free tests
that do not require any assumption about the distribution the data
set follows and that do not require the testing of distribution
parameters such as means or variances
21. References
Sundar Rao Richard, An introduction to Biostatistics 3RD
Edition,2011
Dr Mahajan B K Methods in Biostatistics,5th edition 2010.