THE EXTENT AND NATURE OF CORPORATE LONGRANGE PLANNING IN THE UNITED KINGDOM — U BY B. W. DENNING AND M . E . LEHR INTRODUCTION

IN an earlier article a broad description with tabular results was given of some research into British corporate long-range planning practice. ^ A careful definition of long-range planning was given and a hypothesis about reasons for its introduction was advanced. This article examines the relationship between the incidence of long-range planning systems and certain key parameters of financial opportunity/risk and complexity. The Definition of Planning Companies

'Planning' companies were defined as those companies which answered yes to the question 'Does your company have a formal planning sequence ?' and who stated that this sequence covered a time period of at least tluee years. The remaining companies were classed as 'Other than Planning', including as a subset those companies that positively identified themselves as 'Non-Planning* by answering die first question in the negative. The Key Parameters

If the introduction of formal long-range planning is, in fact, a managerial response to critical strategic or co-ordinative needs, one would expect evidence to that effect in the observed pattern of incidence. Vital strategic needs exist in situations of high financial risk or opportunity', whereas co-ordinative needs increase with the complexity of organizations. The following key parameters were selected for the analysis: Financial risk/opportunity — Rate of technological change — Degree of capital intensity — Growth and variability of turnover/profits Complexity — Size — Type of organization structure — Degree of vertical integration The construction of satisfactory objective measures of these variables is difficult, but once done, analysis can proceed using standard statistical * Denning, B. W., and Lehr, M. £., 'The Extent and Nature of Corporate Long Range Planning in the \}YJ, Journal of Management Studies, Vol. 8, No. x, May 1971.

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techniques. In fact meaningful measures, described later, were constructed for all lite above variables except the degree of vertical integration. FINANCIAL RISK AND OPPORTUNITY

I. Rate of Technological Change

Although any assessment of the rate of tedinological change will be qualitative, judgements by independent experts have some degree of objectivity. Accordingly, six independent experts in universities, government departments and consultancy firms were asked to rate each company on a five-point scale, ranging from i (very slow) to j (very rapid). The mean of the six ratings for each company was used as the basic measure of rate of technological change. Appendix I gives the relevant comparisons and examination of the statistical implications. TABLE! COMPARISON OF COMPOSITE TECHNOLOGICAL CHANGE RATINGS BY CATEGORY OF COMPANY

Mean composite rating Standard deviation No. in sample

Planning ;-i4 0-45 76

Other than Nonplanning planning 2-63 2-71 0-32 224

0-30 42

Table I gives the mean composite ratings and standard deviation for the three basic categories from which it is apparent that the difference in means between 'planning' and 'other than planning' companies is high relative to the standard deviation. When tested against the normal distribution, the probability of the means differing by as much as 0-5 with sample sizes of 56 and 224 is less than i in 1000. These figures offer some evidence that 'planning' companies tend to have a higher rate of technological change than the remainder. The same conclusion emerges from a study of the individual ratings (Table II), although the degree of variation is higher. This is significant evidence tiiat there was an adequate degree of objectivity in the ratings used. These iigures demonstrate that the rate of technological change and tlie introduction of long-range planning are connected, a view strengthened by the more detailed breakdowns given in Table III and Fig. i, where a strong correlation between the rate of technological change and the existence of formal long-range planning is evident. Thus we may view rate of technological change as a progressive stimulus towards the introduction of formal long-range planning.

1972

CORPORATE LONG-RANGE PLANNING TABLE n MEAN TBCKNOLOGICAL CHANGE RATINGS BY EXPERT AND CATEGORT OP COUPANT

Other than planning

Ptarming ( Expert Mean I 2-24 2

3-36

5

3-01

3-18 4 3-21 5 3-87 6 No. in sample 76

Standard deviation Afean 0-65 2-01 0-70 X'83 113 z-44 l-IO 2-37 0-65 2-62 o-8j 3-50

Non-ptamting 1

Standard deviation 0-54 ^'^^ I-<3I 0-91 o-j8 0-86

114

Standard deviation 0-50 O-94 0-62

Mean 1-98 2-76 2-60 Z-67 2-71

0-7J 0-49

3-J7

I-OI 42

60

50 « 01

"% 40

d

20 10

200

E-SO

3 00

3 50

,100

Technological change rating Unshaded — total in class.

FIG. I Shaded — involTed in long-range planning.

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TABLE III INCIDENCE OF LONG-RANGE PLANNING BY RATE OF TECHNOLOGICAL CHANGES

Composite rating 1-00-1-25 1-2J-1-50 I-5O--I-75 1-75-2-00 2-OO-2-25 2•25-2-50 2-50-2-75 2-75-3-OO 3-00-3-25 3-25-3-50 3-50-3-75 3-75-4-00 4-oo-4*2j 4-25-4-50 4 50-4-7J 4-75-j-oo Total

Total companies 0 2 10

Planning Planning companies companies at % 0/ rt/a/ 0 — 0 I

23 26

z

O'O

10-0

z6 6 I? 8

9 8 4 6 4 J

8.7 7-7 iJ-4 ^5* J 36-4 37-J 30-8 66-7 46-2 50-0 ioo-o

2 0

2 0

lOO-O —

«oo

76

2 10

6j 57 J)

J 20

24

2^'X

z. Degree of Capital Intensify

There are many possible measures of capital intensity. Since space docs not allow a full treatment of the arguments for any one measure, it will merely be noted that given the objectives of the research, the measure of capital intensity required needed to isolate the higher risk assets. This led us to choose as a measure of capital,fixedassets at cost less land and buildings since those indude the majority of single purpose assets, normally those of the highest risk. Accordingly, the measure of capital intensity is fixed assets at cost excluding land and buildings per employee.*

TABLE IV COMPARISON OF CAPITAL INTENSIES

Fixed assests at cost {less land and buildings) per employee Planning Aiean capital intensity 3023 Standard deviation 2554-9X10* No. in sample 76

Other tban planning Z367 ZJ5-OXI0* 214

Non-planning 2145 388-8x10* 42

' Capital intensities calculated in this fashion may still give rise to conaidenihle anomalies, e.g. because assets data may include overseas subsidiaries whilst the number of employees teUtes to the U.K. only. Such anomalies were corrected where possible by comparison with capital intensities, turnover per employee, etc., of other companies in the same industry.

CORPORATE LONG-RANGE PLANNING

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TABLE V &«CrDENCH OF LONG-RANGE PLANNING BY CAPITAL INTENSITY

Fixed assets at cost {less land and buildings) Number of Percentage per employee Number plamting of planning in companies companies Above Not above class in class ia class IO-O o J 30 70a 30 16-7 J k

1

700 851

lOJJ 1209 1J7J IJ85 1120 4130

8J2

lOJJ 1209

1)71 Ij8j 2120 4130 50000

Total

50 30 30 30 30 30 JO 30

6

2O*O

7 7

23-3 23-3 26-7 23-3 33 3 56-7 40-0

8

7 10 II IZ

76

]OO

TABLE VI COMPARISON OF GROWTH RATE AND VARIABILITY OF GROSS PROFITS BY CATEGORY OF COMPANY

Planning

Other than Nonplanning planning

8-66

Meangrowih rate (%) Standard deviation No. in sample

11-29 128-22 71

116-40 216

Mean variability (%) Standard deviation No in sample

13-79 III-JI

iJ-77 147-03 zi6

71

9-47 169-9: 41 1J-91 299-04 41

There is a clear tendency for planning companies to have a higher capital intensity than those without planning systems. However, the difference in means is not a significant measure in this case, for the distribution of capital intensity is highly skew — a few companies have very high capital intensities — nor is the standard deviation a meaningful statistic. Nevertheless, Table V and Fig. z suggest a relationship between capital intensity and long-range planning, although it is less impressive than with rate of technological change. In part this may result from the choice of measure, for as noted earlier, we cannot be certain that the fixed assets and employees figures refer to the same establishments, and the effect of inflation upon fixed asset valuation may be important. Nevertheless, the comparatively low incidence of planning among even highly capital intensive firms suggests that capital intensity is less critical than the rate of technological change.

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10 20 a

a. 30 50 Capital intensity

40

40

30

20

505

700 852 1055 "1209 1375 1585 2120 4130 30000 Fixed assets (less lond and buildings) per employee FIG.

2

3. Growth and Variability of TurnoverjPromts

Turnover figures over ten years were not suffidently broadly available to draw any conclusions relating to this variable. However, profit figures gross of depredation are available for most firms over ten years, and these were employed for the analysis of growth and variability. Profits net of depredation would have the disadvantage that their variability is critically dependent upon capital intensity, an undesirable characteristic if variables are to be as nearly independent as possible.

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f

Growth and variability are very closely related parameters. The degree of variability in profits is entirely dependent upon the secular trend about which these are assumed to vary. For tliis analysis an exponential curve was fitted to the profits data by least square methods and this was used to observe deviation of actual profits from this curve.^ A summary analysis of growth and variability of gross profits is given in Table VI, and in neither case is the difference in means significant with respect to the standard deviation.'* Thus, there is little to suggest that variability of growth and profits, as measured, help to explain the existence or non-existence of corporate planning. The detailed breakdowns of Tables VII and V i n (Figs. 3 and 4) confirm this. There is much variation in the incidence of planning from class to class but no discernible pattern to it. It should not be overlooked, however, that both of the measures have serious deficiencies. First, they do not distinguish internal expansion from growth by merger, and these two forms of growth have markedly different effects upon an organization. Secondly, merger growth completely violates the assumption of smooth exponential growth, producing an unduly high measured variability. There is no way out of this dilemma, for nearly all the three hundred companies are affected. But even if we eliminate those companies where merger effects predominate (Table IX), there is no improvement in the degree of explanation, confirming our view that growth and variability barely influence the incidence of corporate long-range planning. ' Thus, if we know profits {P) for years i-io, we can fit the curve:

to the data where Pt 7*0 p^* g

= = = =

actual profits in year / predicted profits in year o predicted profits in year / growth rate of profits

The growth rate Cg) fitted by this method is the geometric growth rate and the corresponding measure of variability is the mean percentage absolute deviation, which can be expressed mathematically as:

• There were thirteenfirmsfor which insufficient data was available to calculate accurate measures of the growth rate and variability of gross profits.

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TABLE VII

Growtb rate percentage

Number 1

Above -3J-0 -1-4

Not above -1-4 3-2 J-2

3-2 J-2

6-5

6-1

8-6

8-6 lo-o

IO-O IJ-O

12-O

14-9 21-6 70-0

14-9 21-6 Total

' "

class

Number of planning

Percentage planning

companies in class

class

32 27 28

4 7 7 6

31 31 29

10

8

J 6

25 27 31 26

10

8

287

71

in

12-J

25-9 15-0 19 4 52.3 27-6 20-0 22-2 32-3 30-8 24-7

TABLE VIII INCIDENCE OF PLANNING BY VARIABILITY OF GROSS PROFITS

Varit^ility Above

Not above

Number tn

Number of plan/ung

Percentage planning

companies in class

3>

10

in class IJ-2 40-0 20-7 2J-9 27-6 22-2 24-1 ai-4 21-4 31-3

287

71

24*7

class

0

4-4

33

5

4-4 5-5 7-6

5*5 7-6

«5

10

29

9-O

»7

10*6 12*1

39 27

14'9

29 28 28

6 7 8 6 7

9-O

fO'6 IX* I 14-9 18* 1 26-0 Total

i8*i 26*0 75-0

6

TABLE IX ADJUSTED GROWTH RATE AND VARIABIUTT OF Gposs PROFITS BT CATEGORY OP COMPANT

Mean growth rate {%) Standard deviation No. in sample Mean variability (%) Standard deviation

No. insane

Planning io-j2 ^ 3 J- 57 47 9*35 8 j - 26

47

Other than planning 8-72 103-62 176 II-j6 97-11 176

Nonplanning 8-30 155-37 M 13-36 201- 76 24

CORPORATE LONG-RANGE PLANNING

SSlUDdUJO) JO 'ON

IO

FEBRUARY

THE JOURNAL OP MANAGEMENT STUDIES COMPLEXITY

The size of a company is an elusive concept. Four possible measures were examined — fixed assets at cost, fixed assets at cost (excluding land and buildings), turnover, and number of employees. Comparative means and standard deviations for these four measures by category are given in Table X. Table X displays what one would intuitively expect, that larger companies are more likely to plan formally; but it cannot be said that any one dimension of size is clearly superior to the others. The separation between the means of the planning and other than planning categories is high whatever measure is chosen, and a highly skew distribution prevents the standard deviation from providing useful information. TABLE X COMPARISON OF MEASURE OF SIZE BY CATEGORY OF COMPANY

Other tban planning

Nonplanning

101364 33644X10" 76

4269 s 2495Xio"

4IJ45 2114X 10'

94743 21730X 10' 76

3J474 2157X l o '

178J8J 82554X 10' 76

74990

339JJ 1984X 10* 76

IJ7S5 284X 10*

Planning Fixed assets {at cost) Mean Standard deviation No. in sample Fixed assets {at cost) excluding land and buildings Mean Standard deviation No. in sample Turnover N[ean Standard deviation No. in sample No. of employees Mean Standard deviation No. in sample

42

224

224

1119X 224

224

31269 2100X 10' 42

10'

101092 24200X10* 42

i9*JJ 496x10' 42

The breakdown for each variable shows (Fig. 5) that fixed assets exduding land and buildings is the best single explanatory variable and Table X and Fig. 6 demonstrate that size is an extremely important parameter, the inddence of planning in the largest companies being as high as 67 per cent. 5. Organisation Structure

Organization structure is a different type of parameter susceptible to classification rather than measurement with a spectrum of organization structures that makes it difficult, for example, to distinguish functional from

1972

CORPORATE LONG-RANGE PLANNING

small

Employees

II

large

Fixed ossets (less land ond buildings)

«mall

Fixed assets

large

F I G . 5. COMPARISON OF DIPFERENT MEASURES OF SIZE IN EXPLAINING INCIDENCE OF CORPORATB LONG-RANGE PLANNING

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10 20

50

40 SIZ*

40

R 30

20

10

4-8

6'9 8-6 11-2 !4-6 i9-2 23-5 34-0 75-2 I74O'O Fixed ossets (iess iand and buiidings) FIG.

6

divisional structures. However, great subtlety of classification seemed inappropriate and the companies were allocated to one of seven categories as follows: 1. Single-plant functional. 2. Multi-plant functional. 3. Multi-plant divisional (not more than one foreign manufacturing subsidiary). 4. Muld-plant divisional (2-5 foreign manufacturing subsidiaries). J. Multi-national (more than 5 foreign manufacturing subsidiaries). 6. Subsidiary of foreign multi-national. 7. Conglomerate.

CORPORATE LONG-RANGE PLANNING

I)

TABLE X I INCIDENCE OF PLANNING BT FIXED ASSETS AT COST (LESS LAND AND BUILDINGS)

Fixed asset! at cost (Jess land and buildir^s) £m r • ' * ^ Above Not above o-o 4-8 6-9 8-6 14-6 19-2 2JJ

54-o 75-2 Total

?v umber in class

4-8 6.9

JO JO

8-6

30 JO JO 30 JO JO 30 JO

11-2

14-6 19-2 23-J 34-O 7J-2 1740-0

300

Number of planning Percentage tompaniii planning class in class in class I 3-3 I 3'3 J 16-'7 J 16- 7 23-•3 7 8 26-•7 10 33-3 10 33-3

9 20

jo-o 66-7

76

Categories 1-5 are in ascending order of complexity, but the last two are somewhat different, with no necessary increase in complexity between j and 6. The conglomerate companies were classified into a separate group since they have co-ordinative needs of a distinctive type. Organization structure appears to play a considerable part in determining the strength of the pressure towards the introduction of formal long-range planning (Table XII and Fig. 7). The average length of time that longrange planning had been in existence at the date of the questionnaire is also given in Table XII. It strikingly confirms the conclusions drawn from pattern of incidence data. Not only is corporate planning more frequently found in the more complex organizations, but it will have been introduced at a much earlier date. ^ Furthermore the pioneering role of overseas-owned companies is clearly displayed, well over half of those in our sample being engaged in corporate long-range planning. Another interesting conclusion is that the co-ordinative needs peculiar to conglomerate companies do not result in a greater tendency towards the introduction of long-range planning. 6. Vertical Integration

Differences in vertical integration are not susceptible to the analytical approach so far used. We discovered no simple method which would enable us to assign values to this parameter; nor did we feel ourselves able to make even rough groupings. Given sufficient data on input and output a scale ' The single planning company in group 2, something of an anomaly, is a pit>duct of government influence. It is therefore a special case.

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2

FEBURARY

3 4 5 6 Class of organizotion FIG. 7

TABI£ x n L^CTOENCE AND AVBRAGE LENGTH OF LONG-RANGE PLANNING BY ORGANIJWTION AND TYPE

Type of All Planning 9rgiak(ation companies companies I 2

3 4 5 6 7 Total

9 87 78 8? 17

^4 300

Planning as % of total

I 9

11*1 1O-5

19 30 II 6 76

04-4 3J-5 64-7

Average length of .Standard existence [years) deviation

o 4-4 3*7 7-O

12-6 3-3

II* I 2-6 58-1 29* I 1-2

2J.3

might be constructed and this could be a further research step. However, we are left only with an unsupported view, arguable from first principles, that there is greater complexity where successive operations must be closely integrated internally than when all materials and components can be obtained externally and all sales are to outside customers.

CORPORATE LONG-RANGE PLANNING

XJ

THE PROBLEM OF INDEPENDENCE

The type of analysis so far carried out assumes the independence of the variables in two quite different ways; first, it assumes that the variables themselves are independent of one another, and second, that their effects upon the incidence of long-range planning are independent. There is no a priori reason to think that either of these is true. First, the variables we have employed cannot reasonably be considered independent. For example, there is clearly some relationsliip between size and organization structure. Even where there is no causal relationship, however, it may happen that variables are linked because of the industry structure of this particular sample. High technological change and capital intensity, for example, are both characteristics of the petro-chemical industry. Although in our sample this is balanced by the much less capital intensive electronics sector which also has a high rate of technological change, relationships of this kind may well lead to erroneous conclusions, if the effects of variables are evaluated independently. Similarly, the second assumption cannot be sustained. We would not expect a high rate of technological change alone to prompt the introduction of sophisticated procedures in comparatively small one-product companies. Different environmental factors dearly act together in prompting a company to introduce formal long-range planning. The nature of the relationship may be very complex — the effects of some combinations of variables may be additive, some may be independent, whilst others may exliibit a threshold effect. A MULTIVARIATE APPROACH

If the probability of a company being in the category 'planning' is constant over time, then the statistical teclinique of discriminant analysis may be employed. This seeks to establish that linear function of tiie independent variables that best explains the separation of the sample into two groups. The value of the function for any firm will then indicate the likelihood of that firm being found in the category 'planning'. For our sample the linear function that gave the best separation between the two categories was: Z = 2-49 TEC -h 0-56 CAP + 0-90 GRS - 0-07 DEV -|- 1-83 EMP -(- 1-17 FAC — O-86 SAL -{- 1-47 ORG where TEC is technological change rating CAP is capital intensity (at cost less land and buildings) GRS is squared deviation of growth rate of gross profits from mean growth rate of sample DEV is variability of profits

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EMP is number of employees FAC is fixed assets at cost, less land and buildings SAL is turnover ORG is organization structure. Since each variable has been divided by its standard deviation the coeffidents broadly indicate the relative importance of the different parameters. However, the negative coeffident of SAL indicates the presence of nonlinearities which qualify any conclusions: this coeffident becomes positive when other size variables are withdrawn from the model. Thus the three size variables must be considered together. If only one size variable is induded, number of employees gives the best separation, contrary to the condusions of the earlier unvariate analysis. The relative values of the coeffidents of the other variables are, however, comparatively stable and their values are significant. Only in the case of growth rates did a transformation increase the explanatory power of the variable. The mean values of Z for the two categories planning and other than plaoning, were 22-31 and 17-80 respectively. This means that if the value of Z for a particular company was more than halfway between 17-80 and 22-51 we would expect to find it in the category 'planning'. On this basis we can test the effidency of our discriminant function by examining how many companies it misclassifies. The figures are given in Table XIIL Clearly the predictive effidency of this approach is not great since only 78 per cent of non-planning companies and j8 per cent of planning companies are correctly dassified. TABLE X m

No. of companies classified in ff-oup r

No. of CPla.ttniftg companies -i. in group \^Noit-platming Totat

- . ..

,

^

Planning Non-panning 44 32

Total 76

49

175

224

93

i°7

300

This result, however, highlights one important characteristic of our problem: there is no presumption that companies will automatically be planning formally because they are in situations of high risk or complexity. They may react to such situations by introducing formal planning systems; but they may not. Furthermore, a static analysis can only deal with the situation at a point in time and cannot take into account the possibility that a company will introduce planning in the future.

1972

CORPORATE LONG-RANGE PLANNING

17

A major characteristic required of our function is that most planning companies will show high values and that few low-valued companies will be planning. The discriminant function we have obtained does in fact exhibit this characteristic. Of the companies with the ioo lowest values only six are planning companies, whilst no fewer than thirty-six of the planning companies, almost half, are found within the sixty highest values, eighteen of them witliin the twenty highest values. Considering tlie limitations of both data and model, this must be considered significant evidence in support of the underlying hypothesis. A DYNAMIC MULTTVARIATE APPROACH

The probability function of a company becoming engaged in long-range planning does not remain constant over time. The situation is dynamic. There is a steady increase in this probability for all companies over time, as literature proliferates and knowledge spreads. This may or may not be desirable but it is an observed fact. Secondly, the process is dynamic in that we should be concerned with the change from the non-planning to the planning category, rather than the existence or non-existence of a planning system at a point in time." It has not proved possible to construct a model which is theoretically sound and for which the parameters can be estimated from our data. However, it is possible to demonstrate by the use of a regression model weighted by date of introduction that one could considerably improve upon the explanatory power of the discriminant function arrived at earlier. However, the purpose of this research is not predictive, in the sense that we are not attempting to establish threshold conditions under whidi corporate planning should be introduced. Rather we are examining sets of conditions and needs which may have led managers to introduce corporate planning before it became fashionable, and the differences in types of process as a response to the needs. Thus, the marginal improvements in ability to predict by a more sophisticated model, while of academic interest, have little relevance to the problems with which we are concerned. CONCLUSIONS

This artide has briefly explained the methods and presented the results obtained in the exploration of the hypothesis that the introduction of formal systematic corporate long-range planning is a managerial response to two separate sets of needs — strategic or co-ordinative. Examination of certain • There is, of course, the possibility that a company may in time abandon a planning system that has been introduced if it becomes inappropriate, but the presumption is that a system will tend to be retained once it has been established. ''

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critical dimensions of strategic need indicated a strong positive relationship between the introduction of long-range planning and a high rate of technological change, a positive and strong relationship with capital intensity, and a slight tendency for planning to exist where growth is either above or below average. Strong relationships also exist between the introduction of long-range planning and both the size of company and the complexity of its organization structure. The third element of complexity, degree of vertical integration, could not be explored. Multi-variate analysis strongly supported the tentative conclusions drawn from a variable by variable study. It had been anticipated that complexity would be an important element in the introduction of long-range planning, but its equal position with strategic factors was unexpected, and lends support to the view that the nature and design of the planning process may be critical in obtaining an effective response to management's needs. Secondly, the findings lend support to the view advanced in the earlier article, that if long-range planning is introduced to meet different managerial needs, it is appropriate that the organization of the process should be different in companies with different key parameters. We are currently examining aspects of the planning processes in the companies wliich responded positively to our questionnaire against the different variables and within this framework, hopes to provide some normative approaches to the organizing of corporate planning. APPENDIX I DISTRIBUTION OF TECHNOLOGICAL CHANGE RATING BY EXPERT

No. of companies given rating

Total •ompanies ^ i

1

3 4 147 2O J9 143 46 I O } 82 43 107 loi S "5 "7 I JJ 106 I

I 2

s

4 5 6

2

70

J 76 64 j6 32 57 IOO

7 14 13 17

3 58

300 JOO JOO JOO JOO JOO

Mean Standard rating deviation 2-07 2-96 2-J8 2-58 2-77 3-60

o-j8 0 87 I-10

1-08 0-66 0-88

Although considerable variation is seen both in the mean ratings and in the dispersion of individual ratings about the means, the comparative ratings accorded to different companies displayed a high degree of uniformity. Because of this consistency, the mean of the six individual ratings was used as a composite measure of the rate of technological change for each company. As had been hoped, the distribution of this variable was very close to the normal distribution, a quality looked for in a satisfactory measure of the rate of technological change. Standard statistical tests were, therefore, appropriate for the analysis of the data.

the extent and nature of corporate long- range planning ...

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May 1, 2002 - 1999a,b) have developed models that explain these .... ency to be satisfi ed with the 'model' or equation that gives ..... M. Diamond), pp. 81–120 ...

Consequences of Range Contractions and Range ...
neighboring demes, implying that these edges act as par- tially absorbing ... plus a 5-deme thick layer containing two refuge areas of size 5 В 5 demes. The four gray ..... Page 6 ... The comparison of range shift scenarios with isotropic and anisot

Identifying the Extent of Completeness of Query ... - Simon Razniewski
source feeds or operational failures of reporting systems may lead to the data warehouse having only partially .... about the completeness of the query result? Let us look at the example of the first selection operation in the .... The classical para

[PDF] Long Range Shooting Handbook Full Online
... are a teacher searching for educational material please visit PBS LearningMedia ... arts amp Literacy in History Social Studies Science and technical Subjects.