Problems of recording and sampling in clinical investigations of caries

Arch.

Oral

Rid.,

Special Supplement, Vol. 6, pp. 58-69,

1961. Pergamon Press Ltd.

PROBLEMS OF RECORDING AND SAMPLING IN CLINICAL INVESTIGATIONS OF CARIES E. WELANDER Royal Dental School, Stockholm,

Sweden

Abstract-In the statistical analysis of the results of clinical caries investigations, the method of registration and the choice of observation unit cause a great many difficulties. In recent years attention has been paid to the method error which may be both random and systematical. It is obvious that statistical methods assume a central importance in the study of odontological problems, and applied to clinical investigations of caries the statistical analysis shows typical features. The natural observation unit in caries registration is the tooth or the surface, while the sampling unit usually is the individual (the whole dentition). The statistical analysis must, therefore, take into account the interdependence between the observation units (the teeth). This is most easily effected by calculating a caries index for each subject, expressed for example in DMF teeth or in the number of intact teeth. It should, however, be pointed out that the accuracy of different caries indices is more or less unreliable, since they are affected by such factors as previous dental care. In certain types of investigation the question of sampling may be even more complicated, e.g. in studies of the effect of caries inhibiting agents. In such investigations it is not unusual that the case material consists of children from different schools. The question then arises whether the child or the school should be considered as the observation unit. There is a possibility that children from one school present a caries status quite different from that shown by children from another school. If that is the case there would be a certain interdependence between children from the same school, a circumstance which must be taken into account when applying the analysis of statistical significance. Zusammenfassung-Bei der statistischen Analyse der Ergebnisse von klinischen Kariesuntersuchungen verursacht die Protokollierungsmethode und die Auswahl der Beobachtungsgruppe groRe Schwierigkeiten. In den letzten Jahren wurde dem methodischen Fehler, der sowohl zuf%llig wie such systematisch sein kann, Beachtung geschenkt. Es ist offensichtlich, daI3 statistische Methoden eine zentrale Bedeutung bei odontologischen Problemen haben. Auf die klinischen Untersuchungen angewandt, zeigt die statistische Analyse typische Grundziige. Die natiirliche Beobachtungseinheit bei der Kariesregistrierung ist der Zahn oder dessen Oberfl&he, wPhrend die Stichprobeneinheit im a!lgemainen der Patient ist (das ganze Gebifi). Die statistische Analyse muI deshalb die gegenseitige Abhlngigkeit der beiden Beobachtungswerte berticksichtigen. Das geschieht am einfachsten durch die Berechnung eines Kariesindex fiir jede Person, z.B. in Form des DMF-Wertes oder ausgedriickt durch die Zahl der gesunden Zlhne. Man sollte jedoch darauf hinweisen, da8 die Genauigkeit der einzelnen Kariesindices mehr oder weniger unzuverkissig ist, da sie durch Faktoren wit die Zahnpflege beeinflubt wird.

PROBLEMS

OF

RECORDING

AND

SAMPLING

IN

CLINICAL

INVESTIGATIONS

OF

CARIES

59

Bei gewissen Untersuchungsarten ist die Frage der Stichprobenauswahl sogar noch komplizierter, z.B. bei Untersuchungen tiber den Effekt von karieshemmenden Substanzen. Bei solchen Untersuchungen ist es nicht untiblich, dab das Material aus Kindern verschiedener Schulen besteht. Es erhebt sich dann die Frage, ob das Kind oder die Schule als Beobachtungseinheit betrachtet werden ~011.Es besteht die MSglichkeit, dab Kinder einer Schule einen anderen Kariesstatus zeigen wie Kinder einer anderen Schule. Wenn das zutrifft, gabe es eine gewisse Gemeinsamkeit der Kinder einer Schule, ein Umstand, der in Betracht gezogen werden mu& will man eine Analyse der statistischen Signifikanz durchftuhren. INTRODUCTION DURING the last decade there has been a vigorous intensification of work in all branches of caries research. In the field of caries statistics praiseworthy attempts have been made in some quarters to create some acceptable order in the technical terminology and to work out suitable statistical methods for scientific caries research. These attempts have not always brought us any nearer to the solution of the problems, and we have to face the fact that there still remains much to be done in this field. As regards the technical terminology appertaining to the clinical diagnosis of caries the sub-committee on standardization of caries recording methods, F.D.I., has presented us with an international programme. It is obviously a great advantage for future work to have obtained standard terms covering the various conceptions of caries. This is not sufficient, however, and does not mean that statistical investigations of caries from now on will give the desired results with any greater accuracy than hitherto. The real problems are in fact encountered when one actually launches out on scientific caries investigations.

In our attempts to solve caries problems the statistical method naturally assumes a central position. In planning investigations it is therefore necessary to study the special demands which have to be made, firstly on the planning of the investigation, and secondly on the analysis of the results. It must be quite clear what general conclusion are to be expected and what difficulties might arise in the interpretation of the results. It must also be clear what special demands are to be considered in the planning, depending on whether the investigation is to be descriptive or analytical, in the same way as in static or dynamic analysis. In the planning it is also important to know what methods of statistical analysis are available and to have a clear idea of how to carry out the statistical analysis of the material-this may be done by making up so-called blind Tables. Time does not permit a deeper penetration into detail, and I will confine myself to two main points: (1) The method error in caries recording and some aspects of its consequences in the planning of the research work; (2) The choice of units for recording and statistical analysis of significance.

60

E. WELANDER THE METHOD ERROR IN CARIES RECORDING AND SOME ASPECTS OF ITS CONSEQUENCES IN THE PLANNING OF RESEARCH WORK

In caries recording the method error is apparent in instances where two dentists have recorded the caries status of the same patient at about the same time. The error is shown up by different degrees of deviation between the recordings of the same tooth. Judging from the reported results of clinical investigations the method error has not been sufficiently considered, though it ought to be well known in these days (GYTHFELDT,1938; RADUSCH,1941; BERGGRENand WELANDER,1960b). There still seems to be an adherence to the misleading opinion that a levelling-out of the method error will take place if the case material is sufficiently large. This opinion would be justified if the method error in caries recording were only a chance happening. This does not, however, seem to be the case. In an investigation which will be described below, the method error was proved to be systematic. This means that some examiners always made too few recordings, others too many, in relation to the mean number, and the terms “over-recorder” and “under-recorder” therefore seem to be justified. The question of the method error was studied in great detail in an investigation carried out at school dental clinics in Stockholm. In connexion with the clinical investigation which is being carried out at ten schools in Stockholm for the purpose of establishing the effect of topical application of various fluoride compounds, a study of the recording error was also made in order to ascertain how the ten school dental officers participating in the investigation differed in their manner of recording carious lesions. In this study the ten dentists examined the same ten patients, all 10 years of age. The recording was done at the Department of Pedodontics at the Royal School of Dentistry in Stockholm, the examiners working under identical conditions. Their findings were noted on special charts by the nurses assisting them. As was expected there were considerable differences in the manner of detecting and recording caries. It should be pointed out that of the first five patients in Table 1, for special reasons only one half of the dentition was recorded. Table 1 shows the number of teeth with primary lesions recorded by the ten examiners. The figures in the bottom line show a range from 11 to 26. If the surface was used as the observation unit instead of the tooth, a still wider dispersion was found, as seen in Table 2. In a clinical investigation with probe and mirror it is often difficult to detect incipient caries or very small lesions on surfaces not easily accessible owing to adjacent teeth. It is equally difficult to decide whether a fissure is carious or not. In order to make a closer study of the recording of fissure caries only this type of caries was entered in Table 3. This Table shows that there were also large discrepancies between the figures given by the different examiners in the case of fissure caries only (lowest 1, highest 8 cavities).

PROBLEMS

61

AND SAMPLING IN CLINICAL iNVESTIGATIONS OF CARlES

OF RECORDING

TABLE 1. NUMBER OF TEETH WITH PRIMARY LESIONS RECORDED BY TEN EXAMINERS Examiner

Patient

1

_

II

III

v

IV

1

2

2

2

0

2. J. N.

0

1

1

1

0

1

1

3. 0.

s.

0

1

1

1

0

1

0

4. M.

J.

1. M.

T.

I

0

0

0

0

0

0

0

5. L. J. J.

2

3

5

2

2

2

2

6. L.

3

1

4

1

0

2

2

7. I. s.

5

3

8

10

3

6

3

8. E. ii.

3

2

3

3

4

3

2

9. E. K.

1

1

2

4

2

1

0

0

2

0

3 4~

10. s.

B.

s.

No. of teeth with primary lesions ~~

~-Ih-[

,,

L-26

I;;1

25

1 11 ~

2

;?_;;;19;1_-24

TABLE 2. NUMBER OF SURFACES WITH PRIMARY LESIONS RECORDED

0 I_

12

BY TEN EXAMINERS

Examiner

Patient

I

1 Vl

v

1

1. M. T.

0’

2. J. N.

3

1

3. 0.

s.

1

4. M.

J.

0

5. L. J. J.

3

6. L. B.

2

7. 1. s.

11

8. E. ii.

3

9. E. K.

6

10. s.

11

s.

2

TABLE 3. NUMBER OF CARIOUS FISSURES RECORDED BY TEN EXAMINERS Examiner

Patient

1

j

11

V

VI

VII

VIII

1X

, 1. M.

T.

1

0

2

1

2. J. N.

0

0

0

0

3. 0.

s.

0

0

0

0

4. M.

J.

0

0

0

0

5. L. J. J.

0

0

0

0

6. L. B.

1

0

2

1

1

7. 1. s.

2

2’

0

1

2

8. E. ij.

1

1

1

1

1

9. E.

0 Ye

:~

10. s.

K. s.

No. of teeth fissure caries

0 with 5

0 01

4~

;I

;

62

E. WELANDER

Five of the ten examiners recorded five fissure cavities each which might have indicated close agreement had it not been for the fact that the cavities were recorded in different teeth (Table 4). TABLE4. DISTRIBUTION OF FISSURE CARIESACCORDING TO TOOTH Examiner

Patient

I

1. M. T.

0

0 0 0 0

s.

4. M. J. 5. L. J. J.

6. L. B.

0 0 0 05t 6t

05t 5+

I. I. s.

-4

III -6

-6

2. J. N. 3. 0.

I

II

IV

_

1 v

VI

0

0 0 0 0

0 0 0 0

0 0 0 0

05+

0

to5

0

5t

5+ 4+

5+ -4

63

6+

6t

6+

6+

9. E. K.

0

0

0

;$

0

0

0

0

0

0

I-

VII

I.-05

-6

8. E. 6.

10. s. s.

I

-6

-6

0 0 0 0

to5

VIII

1 IX

1 x

-6

/ -6

-6

0

0

0

0

0

0

0

0

05+

to5

0 0 0 0 05+

05t

05+

0

0

5-t

6+

6+

6t

6+

0

0

0

0

$5 5t

0

6+ -6 0

6t

$5

+5

5-t

051 -4

5+ -4

In order to improve the clinical examination with probe and mirror the use of X-ray examination has been proposed. Earlier investigations (LUNDBERG and MARKEN, 1958) have shown, however that also in X-ray examinations there is an observation error. To ascertain how the ten school dental officers differed in their interpretation of the X-ray pictures, a special study was made. Full mouth roentgenograms of five of the patients were studied by the examiners with regard to carious lesions. The results are shown in Table 5 which makes clear that the dentists differed greatly in their interpretations. The range is from 2 to 19. TABLE 5. NUMBEROF CARIOUSLESIONS RECORDED BY TEN EXAMINERS ROENTGENOGRAMS

FROMFULL MOUTH

OF FIVE PATIENTS

.___~

Examiner

Patient

L. B.

1

1

E. K.

1

1

1

0

6 2 3

0 0 2

4 0 13 j

2

/ 19 1 11

I. s.

1

1

s. s.

0

0 6

E. 0.

I

5

21 1’

1

1

1’1

3 0 6

0 9

2 0 9

19

1 13

I

.~ Total

I_s

9-j

l3 I

j

8

13

PROBLEMS

OF RECORDING

AND

SAMPLING

For a closer study of the differences of recording number

caries,

of decayed

between

of variance

surfaces per individual

6.

TABLE

an analysis

ANALYSIS

Examiner Patients

OF VARIANCE

63

IN CLINICAL INVESTIGATIONS OF CARIES

the ten examiners was carried

out (F-test).

and per examiner WITH

REGARD

as to their manner The diverse

was studied

TO DECAYED

(Table

6).

SURFACES

I I

Rest

The material differences

___~__ 99 1

Total ( _.- ~~ was derived

between

__~_~ 396.19

from Table

the findings

~__ I

-

2. The Pvalues

of the participating

-I--_

in Table

dentists

6 show that

were significant.

the This

implies that the differences were systematical and also that, in a comparison of the average figures, some dentists are “over-recorders” and others “under-recorders”. A similar result is obtained from the analysis of the data in Table 1 (Table 7.). TABLE

7. ANALYSIS

Source of

variance

Degrees of 1 freedom

Examiner Patients Rest Total In the next analysis however, differences

reach

OF VARIANCE

WITH

due to the limited

1

99

TEETH

Mean of squares

F

1

of variance

the findings

(fissure

Table

8) the F-value

of the examiners.

that

The low F-value

OF VARIANCE

Degrees of

[

Sum

WITH

REGARD

To FISSURE CARIES

_~__ -_____ of 1 Mean of 1

_l_

Total

1

81

]

24.84

99

1

54.96

j

0.30667

)

does not, were no

was most likely

F

variance -______ Examiner Patients Rest

there

of the material.

8. ANALYSIS 1

caries,

This does not mean

-.___ Source of

TO DECAYED

9 9 81

extent

TABLE

/

Sum of squares

the level of significance.

between

REGARD

-

E. WELANDER

64

The results presented in Table 5 were also subjected to an analysis of variance (Table 9). TABLE 9. ANALYSTS OF VARIANCE WITH REGARD TO THE RECORDING OF CARIES ON FULL MOUTH ROENTGENOGRAMS

Source of valiance __~

Degrees

of

~_

squares

9

48.1

Patients

4

236.6

36

113.8

Total

squares

F

~~

Examiner Rest

Mean of

Sum of

freedom

49

_I

-;98.5

’ 1

5.344 59.15 3,161

i

1.69 18.72***

-

-~

As may be seen in Table 9 the F-value does not reach the level of significance. This is surprising considering the very great deviation in the number of recorded lesions shown in Table 5. A closer study of Table 5 makes it evident, however, that the examiners with the highest total figures do not record top figures for all patients throughout. In other words, they are not systematical “over-recorders”. The purpose of the analysis of variance was to establish whether the difference in recording, as carried out by different examiners, was due to systematical error or not. The large error in caries recording may be attributed to a number of concurrent factors: In the first place it must be realized that there is no foolproof definition of the term clinical caries. The adequacy and efficacy of our technical aids are also of great importance. The human factor constitutes a highly irrational factor. The ability of different examiners to detect or evaluate a carious lesion has been dealt with earlier. Added to the individual difference in recording caries, the fatigue factor may also be of decisive importance. In appraising the consequences of the differences in recording by different examiners there is reason to make a distinction between two types of investigation:

(1) Descriptive studies, e.g. cross-section studies, the aim of which is to obtain a mean value for a population, for example the number of carious teeth or tooth surfaces per person; (2) Comparative studies such as comparisons of the development of caries in two different groups, one treated and the control group not treated, or comparison of the caries status in two different races or the two sexes. In such studies the point of interest is the difference between the mean values of the two groups. If only one examiner is employed in a descriptive study there is the risk that he may be a typical “over-recorded”, or the opposite, and the mean value will be quite misleading, systematically too low, The systematical error will obviously not be reduced by increasing the investigated material. An increase would be an advantage only in so far that sampling errors will be reduced.

PROBLEMS

OF

RECORDING

AND

SAMPLING

IN

CLINICAL

INVESTIGATIONS

OF

CARIES

65

In a comparative study the results will not be affected to the same extent if the same examiner is used in both groups. An “under-recorder” will of course obtain too low values in both groups but in comparing the values the systematic errors will mainly cancel each other. If more than one examiner is employed in investigations of the descriptive type the situation is more hopeful. To meet with two typical “over-” or “under-recorders” at the same time is fairly improbable, and there is also the possibility of comparing the mean values obtained by both examiners. A great difference between the mean values would be an indication that at least one of them must be an “over-recorder” or “under-recorder”. This argument holds good regardless of whether the examiners have made recordings of the same patient (duplicate recording) or each examiner has recorded every other patient, or made a random selection out of the whole case material. There is a certain advantage in employing several examiners in comparative studies as well as in descriptive studies, regardless of the method of recording. It is, however, definitely inadvisable to assign one whole group to each examiner, the treated group to one and the control group to the other. If this were done, the differences between the groups might be attributed to the systematic deviations between the two examiners and not be a definite expression of the effect of the treatment. In planning clinical investigations of caries there is usually a certain limit to the funds available and it is therefore necessary to consider which measures are the most expedient and possible to carry out. In a very simple pattern situation it is at least possible to decide on a criterion of successful planning. If the purpose of the investigation is limited to a comparison of the effect of two caries-inhibiting agents with the view only to find out which agent has the greater effect and not how much greater, then the investigation is simply planned for establishing the difference between the mean values for the treated group and the control group. The difference is then subjected to statistical analysis of significance. When the investigation has to be planned within certain financial limits it is of course to the greatest advantage to employ a method of analysis which will most decisively establish significance in preference to a method by which vague or no significance is obtained. The significant differences must be attributable, however, to the effect of treatment and not to the errors of recording. The following example may be given: The purpose of an investigation is to study the effect in children of two caries inhibiting agents. The recording may comprise the entire dentitions, and in order to keep the expenses within the given limits, the investigation must be limited to fifty children in each group. At the same cost one half of the dentition may be recorded in eighty children (partial recording) per group. The correlation between total and partial recording is very high, r = O-96 (WELANDER, 1959). This means that if there are any real differences between the caries inhibitors the possibility of securing significance is considerably greater when applying

66

E. WELANDER

partial recording, since the number of independent units for analysis is in the ratio of 80150. The efficacy of the planning may also depend on other factors. Those that may be considered as possible to vary are: (1) Number of patients. Increased case material should give a greater possibility of establishing an effect of the treatment; (2a) Number of examiners taking part; (2b) Number of examiners per patient (single or duplicate recording); (3) Number of recorded teeth or surfaces per patient (partial or total recording); (4) Technique of recording (examination with probe and mirror only or supplemented by X-ray and previous cleaning up of the dentition). When the costs of the investigation are fixed beforehand these four points will have to be balanced against one another. If each patient is to be recorded in duplicate the number of patients will have to be reduced. If the whole dentition is to be recorded, as apposed to partial recording, it is also necessary to cut down the number of patients. In order to make the most profitable balancing it is necessary to be fully informed of: (a) The cost of total recording of a patient carried out by one examiner, and the cost of duplicate recording by two examiners; (b) The cost of partial and total recording of one patient when supplementary X-ray is used; (c) Correlation between partial and total recording; (d) Systematic differences between examiners and between purely clinical and clinical-radiographical examination. Disparity between different examiners in recording the same patient groups; (e) The disparity between patients as regards the prevalent caries variate (so-called biological variation). These data are required for the calculation of significance. It would take too much time, however, to enter into details here of how these data are used. At present there are unfortunately only isolated reports obtainable of the costs and variations which I have mentioned. Experience from research in other fields shows that there is a great deal to be gained by devoting greater attention to the actual planning of investigations. In this connexion the question of record notes should also be touched upon. The sub-committee on standardization of caries recording methods have worked out their proposals in which they recommend that the records are made on a socalled tooth-diagram, and it is pointed out that anatomical diagrams would give the best results. The diagram being anatomically correct would enable the examiner to draw a picture of the actual extent of the cavity. As the examiner himself has to make this drawing and thus cannot rely on an assistant, much time is lost. It may

PROBLEMS

OF RECORDING

AND

SAMPLING

IN

CLINICAL

INVESTIGATIONS

67

OF CARIES

also be asked which caries problems are so simple that this method of recording is fully satisfactory? In a study of the development of untreated caries it is of course useful to have correct knowledge of the extent of each cavity, but the question is whether it is possible to obtain this knowledge from a drawing of the surface expanse of the cavity without any indication of its depth. Instead of anatomical diagrams the so-called Moulage system would seem to offer greater possibilities, the system being devised for a qualitative as well as a quantitative evalutation of each cavity. Experience has further proved that in large-scale statistical investigations of carries all modern technical recording aids such as machines for data recording on perforated cards ought to be used in order to save time and ensure accuracy. All record data are transferred to perforated cards, and the filing, tabulation, etc., are performed electrically. For a simple transfer of caries data a dental card should be used on which the records can be entered for each tooth and each surface, the card being in a suitable tabular form. The recording is carried out in the way shown in Fig. 1. 1 1 2

i

3

- I-~-~ /--Filling

)IM ’

Cf

m

d/

0

b

c

I

7-i.’ 61

1

/ I

-I _

I

I___

!

I

i

--

.___I

-.

_

~.

_

I

x

I

i

__I--1 i_;-.__~_.;_,-l _i ~_ i 1

__.~___~_,_,_,~_.~_._,_I ~

__‘.-,-_I-,-,

! i

1

__;_,__/__._;

~-

_.‘_I.__,_:_)d_.- I__ 1

x1 ’ I 1 I I_!-l_l__‘-_,_ _ - _ _I_\_ __!_I_’ _:._i_ ~---

I /

_.

FIG. 1. 5’

I

I- i__/_ _-

-.;_ ,_; 1-i-;_~~---

68

E. WELANDER THE

CHOICE

OF UNITS FOR RECORDING AND ANALYSIS OF SIGNIFICANCE

STATISTICAL

In using the mathematical-statistical equation complex which is used in the elucidation of intricate caries problems it is necessary to consider the premises for those equations. The method of statistical analysis of significance which is most commonly used is based on the presumption that the various units for analysis are independent of each other. This implies that the unit of recording (the tooth or the surface) is not identical with the unit of analysis (the individual person). One consequence of this is that the individual must be chosen as the unit of analysis. In other words, the extent of caries prevalence must be calculated for each individual. The natural recording unit in clinical studies of caries is the tooth or the surface. When the observations are recorded and put together a description may be made in different ways. We may, for instance, record the number of carious surfaces as a percentage of the total number of existing surfaces or state the quotient of the carious surfaces and the total number of surfaces in the examined group. When going a step further and calculating confidence intervals or carrying out analysis of significance, the problem arises of how many independent units are to be reckoned with. It is accepted as a general rule that the number of independent units does not exceed that of the primary sampling units, namely the number of individuals. This leads to certain practical consequences in the account of the results if confidence intervals are to be calculated, since the unit for analysis is always the individual and not the tooth. The method to follow then will be to record the number of intact teeth per patient or to use one of the accepted caries indices such as DMFT or DMFS. The index is recorded for each patient, whereafter mean values and disparity are calculated for the whole group. The recordings of 2800 teeth in 100 persons thus means that there are only 100 independent units of recording, not 2800, that is to say the same number of units of recording as if only one tooth had been examined in each person. It must be borne in mind that unfortunately the accuracy of the caries indices is not what it ought to be, since the indices are influenced by factors such as conditions of previous dental treatment. By way of illustration, let us take a set of identical twins who differ only in the way that dentistry has been applied. In one twin teeth with primary lesions have been extracted while in the other twin the cavities were filled immediately on appearance. If the number of caries-free teeth is recorded as an expression of the caries status of the patient, it may be assumed that the susceptibility of the other teeth will be lower for the twin whose teeth were extracted; in him the tendency for caries-free teeth will be greater than in the other twin whose carious lessions had been replaced by fillings. From this example it is apparent that the caries indices of either type do not eliminate the differences in dental treatment; the accuracy of the caries index is therefore fictive. Comparisons of the dietary practice in different population groups

PROBLEMSOF RECQRDINGAND SAMPLINGIN CLINICALINVESTIGAIIONS OF CARIES

69

indicate that there is no standardized term for denoting dental treatment. Any effect of dietary factors on the dental status may thus be masked by dental treatment. The same applies when the caries status is expressed as the total number of caries-free teeth. In an analytical investigation the caries measure may be influenced by irrelevant factors. The question of units for analysis and sampling may become a crux in another connexion. Studies of the effect of caries inhibiting agents are commonly carried out on school-children, the material often comprising children from different schools. In the recent investigation of the effect of supervised tooth brushing with a sodium fluoride solution, the control material consisted of children of certain ages from ten schools, all situated in Stockholm, as were the test schools. A survey of the percentage of intact teeth showed fairly great variations, and the question presented itself whether these variations were merely chance phenomena or whether the school and school environment were responsible for the caries status of the children from each school. If there is a definite relation between the children of the same school we must use the school and not the child as the unit for statistical analysis, in accordance with our previous conclusions. The child may be used as the unit if the percentage of caries-free teeth in the ten control schools shows a standard mean deviation of a value compatible with the hypothesis that the children of the ten schools might constitute ten samples of the same population. The statistical analysis proved that the difference between the schools with regard to the relative rate of caries-free teeth was significant; the difference was actually so pronounced that it could not be considered a mere chance. There seemed to be a similarity between the children of the same school. Thus we had to use the school and not the child as the unit. In studies of this kind it is therefore to be recommended that groups to be compared with each other are selected from the same school. REFERENCES BERGGREN,H. and WELANDER,E. 1960a. Supervised tooth brushing with a sodium fluoride solution in 5,000 Swedish school children. Acta odont. stand. 18, 209. BERGGREN,H. and WELANDER,E. 1960b. The unreliability of caries recording methods. Acta odont. stand. 18, No. 4. GYTHFELDT, T. 1938. Die Grundlage

Cariesstatistische

Untersuchungen.

Norske Tundlae~efcren.

Tid. 48, 243. LUNDBERG,M. and MARK~N, K.-E. 1958. En jlmfijrelse mellan bissektrisinstlllning och bitewingteknik vidr ontgenologisk diagnos av cervico-proximal sekundarkaries. Svensk tandliik. Tidskr.

51, 482. RADUSCH, D. T. 1941. Variability

of diagnosis

of incidence

of dental caries, J. Amer. dent. Ass

28, 1959. WELANDER, E. 1955.

Wiksell,

Uppsala.

The Occurrence of Dental Curies

WELANDER, E. 1959. Partial recording

The Permanent Dentition. Almqvist and

of dental caries. Acta odont. stand. 18. 377.

YULE, G. U. and KENDALL, M. A. 1945.

London.

in

An Introduction to The Theory ofStatistics.

pp.368-369.