This document provides an overview of tests of significance, including: 1) Tests of significance are mathematical methods to determine the probability of an observed difference occurring by chance. They are used to compare sample means, proportions, and associations between attributes. 2) Tests are classified as parametric (follow normal distribution) or non-parametric. Common parametric tests include t-tests and ANOVA, while common non-parametric tests include chi-square, Mann-Whitney U, and Wilcoxon. 3) Key steps in performing a test of significance are stating hypotheses, selecting the appropriate test, calculating test criteria, determining significance level, and interpreting results to draw conclusions.

1. GOOD MORNING

2. TESTS OF SIGNIFICANCE
Dr.Nagappan.N
Department of public health dentistry
Saveetha dental college

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.

22. THANK U