This document discusses different types of data and statistical tests used in orthodontics. It outlines categorical (qualitative) and numerical (quantitative) data, including nominal, ordinal, discrete, and continuous variables. Appropriate statistical tests are described for each data type, such as chi square tests for categorical data and t-tests or ANOVA for numerical data. Key concepts in data summarization are also covered, including measures of central tendency, variability, normal distribution, correlation, and hypothesis testing. The importance of selecting the right analysis method based on data type is emphasized.

1. Statistic and Orthodontic
Types of data
1. Categorical (qualitative) data
2. Numerical (quantitative) data
Categorical data
A. Nominal
Categories with no particular order, e.g. gender or colour
B. Ordinal
Categories with some order, e.g. IOTN uses:
• no treatment need
• little treatment need
• moderate treatment need
• great treatment need
• very great treatment need
Tests for categoricaldata
1. Wilcoxon one rank test
2. Wilcoxon two rank test
3. Chi square test
Features for categorical data
• Less powerful than parametric tests
• Tend to be more limited (than parametric tests) in terms of the predictions that
can be made from them, e.g. they cannot describethe variance in observations
in terms of standard deviation

2. Numerical data
A. Discrete:Discrete numerical data can only take a fixed number of values
e.g. whole numbers
B. Continuous: Continuous numerical data is quoted to greater precision e.g.
using decimal places; in principle, any number across somerange
Tests for numerical data:
1. Two sample (unpaired) t test for independent samples
2. One sample (paired) t test
3. Two way analysis of variance (ANOVA)
4. One way analysis of variance (F test) using total sum of squares
Why the type of data is important?
The type of data (categorical or numerical) is crucial in determining which
methods of analysis are appropriate and valid
1. Statisticalsteps in summarising data
1. Measurement of central tendency (Normal distribution )
2. Measurement of the spread of data (i.e. the variability)
Normal distribution
 Represented by a family of curves - NOT a single unique curve
 Curves are characteristically bell shaped and symmetrical, but vary in height
 The exact distribution is determined by the mean and standard deviation

3. 2. Measurementof the variability (spread of data)
Descriptive analysis include:
1) Mean
 average value in a population
2) Median
 middle value in a population
3) Mode
 most common value
4) Range
The values at the top and bottomdenote the findings furthest from the mean.
However quoting the range fails to give an indication of the spread of
observations about the mean
a. Interquartile Range
values that capture the middle 50% of the distribution
b. Upper and lower quartiles
values that capture the (75th - 25th percentile)
5) Standard deviation (SD)
•This describes the spread of observations either side of the mean
•SD should only be used when the population or data sample has a normal
distribution

4. •It is also known as the Standard Error of the Mean (SEM)
•SEM provides an indication of the precision of the sample mean
•Within the first standard deviation 68.2% of the sample located within this SD
•Within the second standard deviation 27.2% of the sample located within this
SD
•Within the third standard deviation 4.2% of the sample located within this SD
•Within the fourth standard deviation 0.2% of the sample located within this
SD
6) Correlation (r)
Way of quantifying the degree of association between two or more variables
I. if r= +1 there is perfect positive correlation between the variables so that as
one variable increases so does the other
II. if r= 0 there is no correlation between the variables or a correlation may exist
but it is non linear
III. if r= -1 there is prefect negative correlation between the variables so that as
one variable increases the other one decreases
•Pearson's correlationcoefficient:the correlation coefficient used for
parametric data
•Spearman's correlationcoefficient:the non-parametric equivalent of
Pearson's correlation coefficient
7) Confidence limits
A 95% confidence interval implies that there is a 95% chance that the true
population mean lies within a given range of values

5. 8) Kappa statistic (k):
Used to measure level of agreement, Kappa (k) is measured from -1 through 0
to +1 so that:
•If k = +1, this represents perfect agreement
•If k = 0, agreement is no better than chance
•If k = -1, worse than chance agreement
Very useful statistic for measuring the diagnostic consistency between
examiners
9) Null hypothesis
No difference between the populations is tested, i.e. if there is no difference
between the populations then the hypothesis is accepted.
Statistical methods for parametric data
•One sample (paired) t test: Compares two sets of observations on a single
sample eg, To compare weight of infants before and after a feed
•Two sample (unpaired) t test: Compares two sets of observations on a two
sample.
•Two way analysis of variance (ANOVA): used for comparing three or more
independent sample means. It is essentially a significance test which compares
the 'within group' variance and the 'between group' variance
Statisticalmethods for non-parametric data (categorical)
•Wilcoxon's one sample rank test: non-parametric equivalent of the t test for
paired data
•Wilcoxon's two sample rank test non-parametric equivalent of the t test for
unpaired data
•Chi Sample: non-parametric equivalent of the ANOVA test for unpaired data