t Test. Abhishek

7/30/2019 t Test. Abhishek

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A thorough background in craniofacial growth and development is necessary for

every dentist. An important concept in the study of growth & development is

variability. Populations differ in their character, size, growth and shape. These

differences are due to complicated interaction of genetic and enviormental factors.

Indian children do differ from western population groups in physical growth,

maturation, dentition etc, due to factors like morphogenetic pattern and nutritional

status therefore the cephalometric standards for one ethnic and racial group or sub-

group did not necessarily apply to the other ethnic or racial group or sub group.

Rajasthan is the largest state in India and Mewar & Marwar are the two major areas of

it. With the increasing number of children of Rajasthan seeking professional

treatment for malocclusion, it has become apparent that there is need to determine

what constitutes a pleasing or normal face for the chidlren of Rajasthan. A

comprehensive and accurate diagnostic assessment of any orthodontic patient involve

the comparison of the patients cephalometric findings with the norms of his or her

ethnic groups or racial groups or sub groups. Treatment plan and clinical procedure

should not be freely switched without considerations of the racial group involved and

without thorough understanding of the differences between races and their ranges of

normal.

The aim of this study was to

(a) To compare the dentofacial pattern of Mewari children (males & females)

with Marwari children (males & females) using Steiners analysis.


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(b) To compare values obtained for Mewari children using Steiners analysis with

the values/ norms given by Steiner for Caucasian population.

MATERIALS AND METHOD

This cephalometric radiographic study was carried out in the Department of

Pedodontics and Preventive Dentistry, Darshan Dental College and Hospital, Udaipur

in association with Jodhpur Dental College and Hospital, Jodhpur.

Source of data

A total of 200 children, 100 from Mewar and 100 from Marwar region of

Rajasthan with equal male and female ratio, between the age group of 11-13 years

were taken for the study from various schools of respective regions. Lateral

cephalogram of all the subjects were taken with an Ortho Ralix 9200, Gendex OPG

machine with a Cephalostat (Dentsply Italia, Italy).

Each cephalogram was placed on an illuminated tracing table, with the profile facing

to the right side. The landmarks and point to be used in the analysis were marked with

lateral cephalogram on acetate tracing paper using sharp 3H pencil. Each landmark

and point was re-checked and then the McNamara & Steiner analysis were done.

STATISTICAL ANALYSIS

The collected data was analyzed statistically using SPSS software, version 10

(SPSS Inc. Chicago, IL).

The mean value and standard deviation of each measurement in both Mewari

and Marwari children were calculated using following formulae:


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Mean, .

Standard Deviation, SD = () Independent sample t-test was used to compare measurements of combined

(males & females) Mewari & Marwari children.

Independent sample t-test, || - Mean of group one - Mean of group two SEdStandard error of difference

Student t-test was used to compare measurements of Mewari children with

measurements given by Steiner.

Student t-test,

- Mean of first sample - Mean of unknown population. SE - Standard Error.


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Comparison of measurements between Mewari & Marwari children using

Steiners analysis

Parameters 't' value 'p' value

SNA angle 4.36 0.05

SNB angle 3.28 0.05

ANB angle 1.03 NS

Occlusal angle -3.67 .05

Mandibular plane angle 2.59 NS

Maxillary Incisor (angular) 2.46 NS

Maxillary Incisor (mm) 0.31 NS

Mandibular Incisor (angular) 0.82 NS

Mandibular Incisor (mm) 0.97 NS

Inter Incisal angle -1.02 NS

Lower Incisor to Chin (mm) -2.35 NS

Independentt-test (P value 0.05, Significant, Non Significant)

SNA angle-

A significant difference was observed between values of combined (males & females)

Mewari & Marwari children at 4.368 t-value, indicating maxillary protrusion in

Marwari children as compared to Mewari children.

SNB angle

a significant difference between values of combined (males & females) Mewari &

Marwari children at 3.283 t-value, indicating mandibular protrusion in Marwari

children as compared to Mewari children.


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Occlusal angle

there was a significant difference between values of combined (males & females)

Mewari & Marwari children at -3.673 t-value (Table 13), indicating more anteriorly

placed occlusal plane in Mewari children as compared to Marwari children.

Comparison of measurements between Mewari children and measurements given

by Steiners

Parameters 't' value 'p' value

SNA angle -3.20 0.01

SNB angle -4.37 0.01

ANB angle 7.60 0.01

Occlusal angle 37.69 .01

Mandibular plane angle -10.31 .01

Maxillary Incisor (angular) 3.81 .01

Mandibular Incisor (mm) 4.66 0.01

Mandibular Incisor (angular) 8.03 0.01

Mandibular Incisor (mm) 6.49 0.01

Inter Incisal angle -8.85 0.01

Lower Incisor to Chin (mm) -16.54 0.01

Studentt-test (P value 0.01, Significant, Non Significant)

SNA angle -

The mean value of SNA angle in the present study was slightly less in Mewari

children i.e. (81.062.93) (Table 1) than those presented by Steiner (822),


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indicating retrusion relative to cranial base for Mewari children as compare to those

given by Steiner.

SNB angle

The mean value of SNB angle in the present study was significantly less in Mewarichildren (77.152.52) than those presented by Steiner (802) , indicating

mandibular retrusion relative to cranial base.

ANB angle

ANB angle represents the relative positions of jaw to each other, the mean value of

ANB angles Mewari (3.051.38) children was slightly more than those presented by

Steiner (2), indicating greater convexity.

Occlusal plane angle

Occlusal plane angle shows the relation of occlusal plane to the cranium and face, in

the present study the mean of occlusal plane angle for Mewari (19.73 1.52)

children showed a significant difference than measurements given by Steiner (14).

This indicates more anteriorly placed occlusal plane as compared to those given by

Steiner.

Mandibular plane angle

Mandibular plane angle suggests growth patterns in individuals, the mean values of

this angle for both Mewari (30.361.59) children was slightly less than those

presented by Steiner indicating horizontal growth pattern in Mewari children.

Maxillary incisor position (angular & linear)

Maxillary incisor position represents the relative location and axial inclination of the

upper incisors. In the present study mean value of both angular & linear measurement

for maxillary incisor position of Mewari children were significantly higher than those

presented by Steiner indicating forwardly placed maxillary incisor teeth.

Mandibular incisor position (angular & linear)

Mandibular incisor position represents the relative anteroposterior location &

angulation of the lower incisor teeth. In the present study mean value of both angular

& linear measurement for mandibular incisor position of Mewari children were

significantly higher than those presented by Steiner indicating forwardly placed

mandibular incisor teeth.


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Inter incisal angle

Inter incisal angle relates the relative position of the upper incisor to that of the lower

incisors. The mean value of Interincisal angle in present study for Mewari

(123.637.19) children is significantly lower than those given by Steiner, indicating

proclined maxillary & mandibular teeth.

Lower incisor to chin

Lower incisor to chin indicates the prominence of chin when compared with lower

incisors. The mean value of lower incisor to chin in present study for Mewari

(1.71mm1.38mm) children is significantly lesser than those presented by Steiner

(4mm), indicating less prominence of chin to lower incisors for Mewari children as

compared to those given by Steiner.

P values

Definition of a P value

Consider an experiment where you've measured values in two samples, and the means

are different. How sure are you that the population means are different as well? There

are two possibilities:

The populations have different means. The populations have the same mean, and the difference you observed is a

coincidence of random sampling.

The P value is a probability, with a value ranging from zero to one. It is the answer to

this question: If the populations really have the same mean overall, what is the

probability that random sampling would lead to a difference between sample means as

large (or larger) than you observed?

How are P values calculated? There are many methods, and you'll need to read a

statistics text to learn about them. The choice of statistical tests depends on how youexpress the results of an experiment (measurement, survival time, proportion, etc.), on

whether the treatment groups are paired, and on whether you are willing to assume

that measured values follow a Gaussian bell-shaped distribution.

Common misinterpretation of a P value

Many people misunderstand what question a P value answers.

If the P value is 0.03, that means that there is a 3% chance of observing a difference

as large as you observed even if the two population means are identical. It is tempting


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to conclude, therefore, that there is a 97% chance that the difference you observed

reflects a real difference between populations and a 3% chance that the difference is

due to chance. Wrong. What you can say is that random sampling from identical

populations would lead to a difference smaller than you observed in 97% of

experiments and larger than you observed in 3% of experiments.

You have to choose. Would you rather believe in a 3% coincidence? Or that the

population means are really different?

"Extremely significant" results

Intuitively, you probably think that P=0.0001 is more statistically significant than

P=0.04. Using strict definitions, this is not correct. Once you have set a threshold P

value for statistical significance, every result is either statistically significant or is not

statistically significant. Some statisticians feel very strongly about this.

Many scientists are not so rigid, and refer to results as being "very significant" or"extremely significant" when the P value is tiny. Often, results are flagged with a

single asterisk when the P value is less than 0.05, with two asterisks when the P value

is less than 0.01, and three asterisks when the P value is less than 0.001. This is not a

firm convention, so you need to check the figure legends when you see asterisks to

find the definitions the author used.

One- vs. two-tail P values

When comparing two groups, you must distinguish between one- and two-tail P

values.

Start with the null hypothesis that the two populations really are the same and that the

observed discrepancy between sample means is due to chance.

The two-tail P value answers this question: Assuming the null hypothesis,what is the chance that randomly selected samples would have means as far

apart as observed in this experiment with either group having the larger mean?

To interpret a one-tail P value, you must predict which group will have thelarger mean before collecting any data. The one-tail P value answers this

question: Assuming the null hypothesis, what is the chance that randomly

selected samples would have means as far apart as observed in this experimentwith the specified group having the larger mean?

A one-tail P value is appropriate only when previous data, physical limitations or

common sense tell you that a difference, if any, can only go in one direction. The

issue is not whether you expect a difference to exist - that is what you are trying to

find out with the experiment. The issue is whether you should interpret increases and

decreases the same.

You should only choose a one-tail P value when you believe the following:


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Before collecting any data, you can predict which group will have the largermean (if the means are in fact different).

If the other group ends up with the larger mean, then you should be willing toattribute that difference to chance, no matter how large the difference.

It is usually best to use a two-tail P value for these reasons:

The relationship between P values and confidence intervals is more clear withtwo-tail P values.

Some tests compare three or more groups, which makes the concept of tailsinappropriate (more precisely, the P values have many tails). A two-tail P

value is more consistent with the P values reported by these tests.

Choosing a one-tail P value can pose a dilemma. What would you do if youchose a one-tail P value, but observed a large difference in the opposite

direction to the experimental hypothesis? To be rigorous, you should conclude

that the difference is due to chance, and that the difference is not statistically

significant. But most people would be tempted to switch to a two-tail P valueor to reverse the direction of the experimental hypothesis. You avoid this

situation by always using two-tail P values.

Statistical hypothesis testing

The P value is a fraction. In many situations, the best thing to do is report that number

to summarize the results of a comparison. If you do this, you can totally avoid the

term "statistically significant", which is often misinterpreted.

In other situations, you'll want to make a decision based on a single comparison. In

these situations, follow the steps of statistical hypothesis testing.

1. Set a threshold P value before you do the experiment. Ideally, you should setthis value based on the relative consequences of missing a true difference or

falsely finding a difference. In fact, the threshold value (called alpha) is

traditionally almost always set to 0.05.

2. Define the null hypothesis. If you are comparing two means, the nullhypothesis is that the two populations have the same mean.

3. Do the appropriate statistical test to compute the P value.4. Compare the P value to the preset threshold value. If the P value is less than

the threshold, state that you "reject the null hypothesis" and that the differenceis "statistically significant". If the P value is greater than the threshold, state

that you "do not reject the null hypothesis" and that the difference is "not

statistically significant".

Note that statisticians use the term hypothesis testingvery differently than scientists.

Statistical significance

The termsignificantis seductive, and it is easy to misinterpret it. A result is said to be

statistically significant when the result would be surprising if the populations were


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really identical. A result is said to be statistically significant when the P value is less

than a preset threshold value.

It is easy to read far too much into the word significantbecause the statistical use of

the word has a meaning entirely distinct from its usual meaning. Just because a

difference isstatistically significantdoes not mean that it is important or interesting.And a result that is notstatistically significant(in the first experiment) may turn out to

be very important.

If a result is statistically significant, there are two possible explanations:

The populations are identical, so there really is no difference. You happened torandomly obtain larger values in one group and smaller values in the other,

and the difference was large enough to generate a P value less than the

threshold you set. Finding a statistically significant result when the

populations are identical is called making a Type I error.

The populations really are different, so your conclusion is correct.There are also two explanations for a result that is not statistically significant:

The populations are identical, so there really is no difference. Any differenceyou observed in the experiment was a coincidence. Your conclusion of no

significant difference is correct.

The populations really are different, but you missed the difference due to somecombination of small sample size, high variability and bad luck. The

difference in your experiment was not large enough to be statistically

significant. Finding results that are not statistically significant when the

populations are different is called making a Type II error.

Confidence intervals Statistical calculations produce two kinds of results that help you make

inferences about the populations from the samples. You've already learned

about P values. The second kind of result is a confidence interval.

95% confidence interval of a mean Although the calculation is exact, the mean you calculate from a sample is

only an estimate of the population mean. How good is the estimate? It depends

on how large your sample is and how much the values differ from one another.

Statistical calculations combine sample size and variability to generate a

confidence interval for the population mean. You can calculate intervals forany desired degree of confidence, but 95% confidence intervals are used most

commonly. If you assume that your sample is randomly selected from some

population, you can be 95% sure that the confidence interval includes the

population mean. More precisely, if you generate many 95% CI from many

data sets, you expect the CI to include the true population mean in 95% of the

cases and not to include the true mean value in the other 5%. Since you don't

know the population mean, you'll never know for sure whether or not your

confidence interval contains the true mean.

Other situations When comparing groups, calculate the 95% confidence interval for the

difference between the population means. Again interpretation is


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straightforward. If you accept the assumptions, there is a 95% chance that the

interval you calculate includes the true difference between population means.

Methods exist to compute a 95% confidence interval for any calculatedstatistic, for example the relative risk or the best-fit value in nonlinear

regression. The interpretation is the same in all cases. If you accept the

assumptions of the test, you can be 95% sure that the interval contains the truepopulation value. Or more precisely, if you repeat the experiment many times,

you expect the 95% confidence interval will contain the true population value

in 95% of the experiments.

Why 95%? There is nothing special about 95%. It is just convention that confidence

intervals are usually calculated for 95% confidence. In theory, confidence

intervals can be computed for any degree of confidence. If you want more

confidence, the intervals will be wider. If you are willing to accept less

confidence, the intervals will be narrower.

Conclusion

In the view of the findings of the present study it is evident that, even with so called

well balanced faces, there are some fundamental variations in the craniofacial

structure of children of Mewar region of Rajasthan with Marwar region and also with

measurements given by Steiner . It is thus suggesting that, it may be required to use

separate norms for children of Mewar and Marwar region for orthodontic diagnosis

and treatment planning.

t Test. Abhishek

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