Statistics in orthodontics

STATISTICS IN
ORTHODONTICS
www.indiandentalacademy.com

INTRODUCTION
• STATISTICS
• “STATISTICA”-an italian word meaning
STATESMAN

What is statistics?
• It is defined as –principles and means of
collection,presentation,analysis &
interpretation of numerical data of different
kinds and expressing the results in a
mathematical or graphical form.

Need for statistics
• It is the scientific solution to the problem of
incoherence and arbitrary judgment.
• Helps convert hypothesis to theories and
later as principles
• To evaluate unproven beliefs of clinical
practice

BELIEFS & HYPOTHESIS
Epidemological statistical
survey analysis
THEORIES & PRINCIPLES

STATISTICAL
DEFINITIONS

• SAMPLE: group of individuals who are
actually available for investigation.
• RANDOMIZATION;Procedure for
allocating experimental subjects to
eliminate investigator-induced bias.
• DATA:compilation of facts and findings.
– Data is classified as:
1.geographical
2.chronological
3.qualitative
4.quantitative

PRESENTATION OF DATA
• Data compiled can be summarized and
presented in the form of:
-Bar diagrams
multiple bar
proportional bar
-pie diagram
-histogram
-line diagram
-frequency polygon

• MEASURES OF TENDENCY:
MEAN: It is a mathematical estimate,a
simple measure of tendency.
mean =
sum of all observations of data
-----------------------------------------
no. of observations

• MEDIAN:middle value in a distribution.
it is a positional estimate.
• MODE: that value in a series of
observations which occurs with the greatest
frequency.

Eg: consider the no. brackets that got
debonded from the first visit to the sixth to
be as:
10,7,5,3,3,2
Here mean is 30 divided by 6 = 5.
median is 8 div. By 2 =4
mode is 3.

MEASURES OF DISPERSION
DISPERSION is the degree of variation about
a central value.
It consists of:
RANGE
STANDARD DEVIATION
COEFFICIENT OF VARIATION

• RANGE: it is the difference between the smallest
and largest value tabled in a given sample.
• STANDARD DEVIATION: it is the root mean
square deviation from the arithmetic mean.
S.D. = square root of{sum of “d2
”/(n-1)}
where n is the no. of trials, d is the deviation from
mean.
• COEFFICIENT OF VARIATION: It is used to
compare 2 or more series of data with marked
difference in mean
C.V. =( S.D. X 100 ) / -
X, -
X is arithmetic mean.

TESTS OF SIGNIFICANCE
These tests are to test if the difference
between the different samples is due to
sampling variation or otherwise.
it includes:
NULL HYPOTHESIS
LEVEL OF SIGNIFICANCE
DEGREE OF FREEDOM
STANDARD ERROR

NULL HYPOTHESIS
• asserts that there is no real difference in the
sample(s) and the population under
consideration and that the difference found
is accidental and arises out of sampling
variation.
• eg: If a survey is conducted to find out the
correlation between extent of occurrence of
bi-maxillary protrusion in kerala population
- null hypothesis states that no real
correlation exists between the two and the
findings were due sampling variation.

LEVEL OF SIGNIFICANCE
• It is a probability level that helps us decide
upon the magnitude of risk in accepting or
rejecting the null hypothesis.
-if the probability value is small, then the
null hypothesis is rejected.

• DEGREE OF FREEDOM: it is the no. of
independent samples in a population.
It is denoted by (n-1)
• STANDARD ERROR: it is the standard
deviation of a statistic like mean.
S.E. = S.D. /square root of “n”

STATISTICAL TESTS
TESTS OF MEAN AND VARIATION
-PAIRED “t” TEST
-ANALYSIS OF VARIANCE(ANOVA)
-BARTLETT’S TEST
TESTS OF ASSOCIATION
- r
- REGRESSION
-SPEARMAN

TESTS OF RANKS:
-WILCOXON
-MANN WHITNEY U
-KRUSKAL-WALLIS
POST-HOC TESTS:
-NEWMAN-KEULS
-SCHEFFE
-DUNCAN
-DUNNETT www.indiandentalacademy.com

• PARAMETRIC TESTS:
series of tests that require testing of parameters as
mean, or variation.
eg: t-tests
analysis of variance
• NON-PARAMETRIC TESTS:
Tests that do not require any assumptions about
the distributions nor require testing of distribution
parameters.
eg:
wilcoxon
chi square test

PAIRED “t” TEST:
• The test is used to test for the difference in
two similar sets of observations.
Eg: if the comparitive force levels between
preformed NiTi intrusion arches and
burstone three piece intrusion arches were
compared and results were tabulated.
To find out the effective difference between
the two set of observations is determined
using the t test as:

1. State NULL HYPOTHESIS
2.determine d = Xi – X
3.Determine S.D. & S.E.
4.test statistic “t”: d / S.E.
5.Compare ‘t’ value with table value for (n-1)
degree of freedom to find ‘P’ value.
IF ‘t’ VALUE IS LESS THAN ‘t’ VALUE AT
0.1% PROBABILITY THEN THE MEAN
DIFFERENCE BETWEEN THE TWO ARCHES
IS NOT SIGNIFICANT.

ANALYSIS OF VARIANCE:
(ANOVA)
• PARAMETRIC TEST
• Ideally used when the no. of groups is
more than two and and thus more than two
means to compare are present.
• the analysis of variance statistic,F,
indicates whether any of the means
compared are significantly different from
each other, but it does not indicate which
pair of means differ.

CHI SQUARE TEST:
Determines whether the difference in distribution
of qualities in different groups is due to sampling
variation or not.
it is determined by
sum of {(observed freq.-expected freq.)2
expected freq.
WILCOXON SIGNED RANKS TEST:
• NON-PARAMETRIC counter part of paired ‘t’
test
• used to compare a single sample with a
hypothetical median two related groups.

• MANN WHITNEY TEST
Nonparametric test to compare the medians
of two independent samples
useful alternative to the parametric t test
when measurement is on an ordinary scale.
• KRUSKAL-WALLIS TEST;
Non-parametric test to compare the medians
of several independent samples. It is the
nonparametric equivalent of one-way
analysis of variance.www.indiandentalacademy.com

ERRORS IN STATISTICAL
ANALYSIS:
• FAILURE TO INCLUDE A CONTROL
GROUP
• IMPROPER RANDOMIZATION
METHODOLOGY
• FAILURE TO LIST THE STATISTICAL
TESTS USED
• FAILURE TO COMPLETELY
SUMMARIZE THE RESULTS
• USE OF S.E. INSTEAD OF S.D.

• INAPPROPRIATE USE OF
PARAMETRIC TESTS
• FAILURE TO INCLUDE
MULTICOMPARISON CORRECTION
• IMPROPER USE OF STATISTICS TO
TEST DIFFERENCES OTHER THAN
THOSE THE EXPERIMENT WAS
DESIGNED FOR.

CONCLUSION

To conclude statistics might not be of much
significance in clinical practice but when it
comes to pursuing newer techniques and
principles, scientific substantiation can be
obtained only with statistical verification
and interpretation.
Thus Statistical substantiation can be
termed as the “VISA” for any new
methodology to enter into the ever
widening arena of ORTHODONTICS !

Statistics in orthodontics

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Statistics in orthodontics