1. INTRODUCTION

Chief executive compensation is a highly debated subject amongst investors, politicians and

the average workers. The link between chief executive officer (CEO) compensation and

performance is important for investors, as it serves as a motivation to generate sustained

market related returns (Deysel & Kruger, 2015). The decisions of the board, are influenced

by the proportion of executives on the board and it is believed that this is the case for

compensation as well. Moreover, if the CEO is the chairperson of the board he/she may even

have more influence over the determination of their compensation package.

It is believed that a significant difference exist between the compensations of CEOs who

chair the board and those who do not, and this strongly prompts for in depth statistical

analyses of the assumed contributing variables. A strong correlation between compensation

and sales growth, and/or excess return is accepted as an indicator that compensation is

determined by performance. If a strong correlation exists between compensation and the

proportion of executives on the board, then it can be concluded that chief executives have

influence over the determination of their compensation. Other independent variables analyzed

are size of the board size and book value of the firm.

The aim of this research was to undertake statistical analyses, to determine the factors that

influence CEO compensation. The research work also aims to establish the extent to which

these variables can be used to predict CEO salaries.

2. METHODOLOGY

Data was collected from a sample of 300 medium and large UK businesses. The data

categories and definitions are;

Salary: CEO remuneration (salary, bonuses, etc.) £'s.

Dir: Number of directors on the board.

Exec: Number of executive directors on the board.

Assets: Book value of firms assets, £m. Measure of firm size.

Exec1: Proportion of executive directors on the board.

Dummy: 1 if the CEO and chairman of the board is the same person, 0 otherwise.

Sgrow: Sales growth, proportionate growth.

Exret: Excess return, proportion. Calculated as the return on companies’ shares on and above

the industry average (company return minus industry average). It is a measure of shareholder

wealth.

Lassets: Natural logarithm of firm assets figures.

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Lsalary: Natural logarithm of CEO remuneration figures.

All the data is annual. The natural logarithms of salary and assets have been included in order

to reduce the impact of outliers.

The analyses were performed in three phases. The first phase involved simple descriptive

statistics, in order to summarize and understand the sample. Descriptive univariate analyses

done were: mean, measure of dispersion (standard deviation) and measure of normality.

Skewness and kurtosis (peakdness) were used as a primary measure of normality in the

distributions, the variables with skewness and kurtosis greater than the modulus of the

doubled standard error, were considered to be asymmetrically distributed, and thus the

distributions are not normal (Tabachnick & Fidell, 2013). The variables that failed the

primary normality tests, were subjected to the Kolmogorov–Smirnov and the Shapiro–Wilk

tests for normality. A P value less than or equal to 0.05 was used to indicate 95% confidence

in the acceptance of normality.

The second phase involved bivariate analyses, to test if there is significant difference between

the salaries of the two groups (CEO is chairperson and CEO is not chairperson). The

independent variables were split and analyzed for normality. The Mann–Whitney U test was

used for non-parametric data and the Student's t-test for parametric data. The relationship

between salaries and all the other continuous independent variables (Dir, Exec, Assets, Exec

1, Sgrow, Exret, Lassets and Lsalary) was then tested in order to determine which ones

contribute in determining CEO salary. Scatterplots were formulated for depiction of

relationship and correlation tests for the establishment of the type (positive or negative) and

strength of relationship.

In the third phase, multiple linear regression was performed, for the sake of establishing

which of the variables can be used to extrapolate and predict CEO salaries. The variables that

did not show significant correlation were dropped, and the remaining ones were compared for

statistical differences after categorizing them in two groups namely, CEO is chairperson and

CEO is not chairperson. Multivariate analysis of variants (MANOVA) was performed to test

the differences between the means. This primarily tested if there is a difference in the

performance of companies, whose board is chaired by the CEO and those not, thus if a

difference exists in compensation of the two groups, it can be attributed to performance.

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3. RESULTS AND DISCUSSIONS

Phase 1: Univariate tests

The results in table 3.1 show that, only the number of directors, sales growth and excess

return follows the normal distribution according to the standard error rule. The dependent

variable, salary is significantly skewed to the right (+0.831), indicating that the sample

salaries are not normally distributed around the mean (£422 579.71), due to the fact that a

significant amount of CEOs from our sample, earn salaries that are far larger than the sample

mean.

The number of executives on the board as well as the proportion are also positively skewed,

+0.352 and +0.592 respectively. This means that some companies in our sample have too

many executives on the board than the normal. The average board in our sample consist of 15

directors, of which 4 are executives. This is also affirmed by the mean of the proportion of

executives on the board (~29%). The kurtosis values for number of executives on the board (-

0.664) and assets (-0.638) are lower than the minimum acceptance value in the normal range,

meaning that the distributions are too flat. This is also affirmed by the large standard

deviations relative to the mean. The natural logarithms of salaries and assets are also not

normal as the transformation of assets results into a highly peaked distribution (kurtosis =

15.912), meaning too many assets are now distributed in the centre, which is really just the

opposite of the untransformed data set. The natural log also transforms salaries into a

negatively skewed distribution (-0.318), which results in an opposing transformation of the

distribution. Although not exactly, it is nonetheless outside the acceptance range.

The values in red font are out of acceptance range.

Table 3.1

Descriptive Statistics

Variable

Mean

Std.

Deviation Skewness Kurtosis

Statistic Statistic Statistic

Std.

Error

Normal

range

(+/-) Statistic

Std.

Error

Normal

range

(+/-)

Salary 422579.71 218947.346 .831 .141 .281 .372 .281 0.561

Dir 14.63 2.793 .134 .141 .281 -.246 .281 0.561

Exec 4.06 2.237 .352 .141 .281 -.664 .281 0.561

Assets 7298.12 3840.009 .250 .141 .281 -.638 .281 0.561

Exec1 .2885 .17082 .595 .141 .281 -.219 .281 0.561

Sgrow .3548 .24625 .027 .141 .281 -.437 .281 0.561

Exret .2275 .11135 .032 .141 .281 .116 .281 0.561

Lassets 8.6628 .90543 -3.138 .141 .281 15.912 .281 0.561

Lsalary 12.8141 .54819 -.318 .141 .281 -.382 .281 0.561

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The Kolmogorov-Smirnov and Shapiro-Wilk test results in Table 3.2 confirms at 95%

confidence that most of the variables that failed the kurtosis and skewness normality tests are

not normal (P values less than 0.05). The natural log of salaries however, can be accepted as

normal as the P values (0.2 and 0.08) for both tests are larger than 0.05.

Table 3.2

Further tests of normality

Variable Kolmogorov-Smirnov Shapiro-Wilk

P P

Salary .000 .000

Exec .000 .000

Assets .004 .001

Exec1 .000 .000

Lassets .000 .000

Lsalary .200 .008

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Phase 2: Bivariate tests

Phase 2 tests focussed on identifying if a significant difference exist between salaries of CEO

who serve as the chairperson of the board and those who do not. The normality tests results

between groups in Table 3.3, shows that the natural log of salaries, sales growth and excess

return are normally distributed.

Table 3.3

Tests of normality group wise

Dummy

Kolmogorov-Smirnov Shapiro-Wilk

P P

Salary 0 .002 .000

1 .000 .000

Exec 0 .000 .000

1 .000 .000

Assets 0 .186 .032

1 .093 .022

Exec1 0 .000 .000

1 .000 .000

Lassets 0 .000 .000

1 .000 .000

Lsalary 0 .200 .802

1 .200 .005

Sgrow 0 .200 .509

1 .200 .340

Dir 0 .024 .076

1 .000 .008

Exret 0 .200 .436

1 .200 .387

Table 3.4 shows that the mean salaries of CEOs who do not serve as chairpersons is £

281 149.70 and those who do earn a mean salary of £ 481 286.51. Out of the total sample, 88

companies have a different person as chairperson of the board, while the remaining 212

companies have the CEO as the chairperson of the board.

Table 3.4

Group Statistics

Dummy N Mean

Salary 0 88 281149.70

1 212 481286.51

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Comparison of means

In order to compare the salaries of the two groups, the Student's t-test for parametric data was

used to compare the natural log of salaries, as this distribution is normal. The Mann–Whitney

U test for non-parametric data was used for salaries, as the distribution is asymmetric and

unknown. The reason for doing the non-parametric test was to eliminate any doubt due to

logarithmic transformation.

The independent sample t-test results are shown in Table 3.4. The sub test, Lavene’s test for

equality of variances, shows that the variances of the two groups are equal (P larger than

0.05). This means that the dispersion of the natural logarithm of salaries are equal for the

groups. The P value for the t-test is less than 0.05, this implies that with 95% confidence,

there is a significant difference between the mean scores of salaries for CEOs who are

chairman, and those who are not.

Table 3.4

Independent samples t-test

Levene's

Test for

Equality of

Variances

t-test for Equality of Means

P t P (2-tailed)

Lsalary .803 -8.662 .000

In order to test if this difference is not by chance, the population effect size is calculated

(Cohen, 1992). This statistic uses the t value to calculate the difference between the two

groups. Eta squared is commonly used to calculate effect size. The equation is given as

(Pallant 2013, pp. 251-6);

Eta squared = t2

t2+(N1+N2−2)

Where N1 and N2 are the sample sizes of the two respective groups. In this case we have 212

companies with CEO as chairperson and 88 where the chairperson is not the CEO, thus the

Eta squared value is 0.201. This implies that 20% of the variance in Lsalary is explained by

the fact that the CEO is the chairperson of the board. A value larger than 14% is considered a

large effect (Pallant, 2013).

A P value less than 0.05 was obtained for the Mann Whitney U test, which also implies that

there is a significant difference between the salaries of the two groups.

The preceding tests show that salaries of the two groups differ significantly, and that CEOs

who serve as chairpersons of the board earn more than those who do not. Scatterplots where

developed to illustrate the relationships between the independent variables and salaries.

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This was done in order to see which variables play a vital role in determining CEO salaries.

The scatterplots in the appendix illustrate that a stronger linear relationship exist between

salaries and performance (sales growth and excess return), than all the other variables. This

relationship is also positive.

Correlation tests

To further test the relationships of the variables with CEO salaries, correlation tests were

done to obtain the correlation coefficients (strength) and directions. Since the natural

logarithm of salaries follows a normal distribution, Pearson’s correlation test was chosen.

Table 3.5 shows the significant correlation coefficients obtained for the two groups. The

absolute strength is ranked as (Pallant 2013, pp. 139):

0.1 – 0.29: small

0.30 – 0.49: medium

0.50 – 1.0: large

Table 3.5

Pearson's correlation coefficients for salaries and independent variables

CEO is not Chairperson CEO is Chairperson

Exret .917** .904**

Sgrow .549** .637**

Dir -.235*

Lassets .148*

Exec .136*

**. Correlation is significant at the 0.01 level (99% confidence).

*. Correlation is significant at the 0.05 level (95% confidence).

A strong positive relationship is exhibited between salaries and performance (excess return

and sales growth) for both groups. There is no significant relationship between salaries and

size of the company or the number of executives on the board, for companies whose CEO is

not the chairperson. However, a small negative relationship is exhibited between salaries and

the size of the board. For companies whose board is chaired by the CEO, there is a small

positive relationship of salaries with size, and number of executives on the board. The

correlation coefficient squared gives what is known as the coefficient of determination, thus

excess return explains more than 80% of the variance in salaries. This is a significantly huge

contribution.

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Phase 3 Multivariate analyses

Regression tests

Regressions tests the ability of the variables to predict the CEO salaries. Multiple linear

regression is sensitive to outliers and multicollinearity between independent variables

(Fabozzi et al, 2013). Bivariate Pearson’s correlation tests between independent showed that

the number of executives on the board and the proportion has a correlation coefficient of

0.929. A cut of level of 0.7 was used (Pallant 2013, pp.164), thus there exist an overlap

between the two mention variables. The number of executives on the board was dropped

from the regression tests. Three outliers were detected and removed using the Mahalonobis

distance measure (Todeschinia et al, 2013).

An R squared value of 0.8662 was obtained, meaning the model explains 86.62% of the

variance in CEO salary. The significance of the model is verified by the accompanied P value

which is less than 0.05 (the null hypothesis is that R squared is zero, hence rejected).

Table 3.6 summarizes the unique contribution of each variable to the model. P values for

number of directors, sales growth and excess return are less than 0.05. This implies that only

these three variables make significant unique contributions to the model. The order of

strength in unique contribution is indicated by the standardized beta coefficients. The order

is: excess return (0.830), sales growth (0.137), number of directors on the board (-0.062).

The part correlation values indicate that excess return uniquely contributes the most to the R

squared (0.622^2 = 44%), followed by sales growth (0.105^2 = 1.1%) and number of

directors (-0.059^2 = 0.35%). Tolerance values less than 0.1 and VIF values above 10,

indicates the presence of multicollinearity. In this case there is none.

Table 3.6

Model Parameters

Model Unstandardized

Coefficients

Standardized

Coefficients

P Correlations Collinearity

Statistics

B Beta Part Tolerance VIF

(Constant) 11.673 .000

Dir -.012 -.062 .007 -.059 .889 1.125

Exec1 .019 .006 .804 .005 .838 1.193

Sgrow .306 .137 .000 .105 .585 1.708

Exret 4.091 .830 .000 .622 .561 1.782

Lassets .032 .041 .065 .040 .939 1.065

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The unstandardized coefficients in Table 3.6 were used to model CEO salaries as follows:

L (salaries) = 11.673 - 0.012 (Dir) + Sgrow (0.306) + 4.091 (Exret)

Where L is the natural logarithm, not to be confused with Log base 10.

The model is compared to the actual data as illustrated in Figure 3.1.

Figure 3.1

The strength of the predictability of the model, is confirmed by the curves in Figure 3.1.

The model closely resembles the actual data.

Multiple analysis of variants (MANOVA) test.

The independent sample t-test and the Mann-Whitney U test both showed that the salaries

of CEOs in the two groups differ significantly. It has also showed that CEOs who are

chairperson of the board earn more than those who are not. The correlation and regression

tests also showed that salaries of CEOs are determined by performance and the number of

directors on the board, furthermore the relationship between salary and performance is

positive and large, while that between the number of directors is negative and small. This

must mean that the salaries of CEOs who are chairpersons are high because they

outperform CEOs who are not chairpersons. The MANOVA test was used to see if there

is a significant difference in performance as well as the number of directors of the two

groups.

0

2

4

6

8

10

12

14

16

Lsa

lary

Lsalary (actual) vs Lsalary (modelled)

Lsalary

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The MANNOVA results are summarized in Table 3.7. The Lavene’s test for equality of

variances tests the null hypothesis that the variances are not equal. MANOVA tests

requires for variances between group variables to be equal. From table it can be seen that

the respective P values for the variables are above 0.05, hence we reject the null

hypothesis and accept that the variances are equal. The Wilks’ Lambda tests the null

hypothesis that there is a significant difference between the two groups (CEO is

chairperson and CEO is not chairperson), with respect to performance and number of

directors. The respective P value is less than 0.05, hence we accept the null hypothesis.

The Test between subjects effects, tests if the difference established by the Wilks’ Lambda

is due to all the variables. The respective null hypothesis is that the difference is due all

the variables. This null hypothesis is rejected because the P value for number of directors

(0.225) is larger than 0.05, therefore the only significant difference between the two

groups is performance (sales growth and excess returns).

Table 3.7

MANOVA summary

Levene's

Test of

Equality

of Error

Variances

Wilks'

Lambda

Tests of

Between-

Subjects

Effects

Effect

size

P P P Partial

Eta

Squared

Dir .308 .000 .255 .004

Sgrow .776 .000 .047

Exret .766 .000 .154

The proportion of variance is indicated by the Effect size Partial eta squared values. The

proportion of variance which is due to sales growth and excess returns are 4.7% and

15.4% respectively.

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4. CONCLUSION

Chief executives who are chairpersons of the board earn more than those who are not. The

difference in compensation is not due to the influence of the CEO on the board, due to

performance. The evidence can be seen in the relatively strong and positive correlation

coefficients obtained when comparing the relationships of salaries with each of the

independent variables. Excess return and sales growth show strongest correlation with

salaries. The number of directors produces a weak and negative correlation.

A model for predicting salaries was successfully developed. The model explains up to 87% of

the variance in CEO salaries. Only three variables produce significant unique contributions to

the model. In order, these variables and their unique contributions are: excess return (44%),

sales growth (1.1%) and number of directors (0.35%). The equation produced by the model

was plotted against the actual salaries from the sample and it was clearly seen that the model

mimics the actual curve.

The Multiple analysis of variants test (MANOVA) showed that the only significant difference

between companies with CEO as the chairperson of the board and those not, is performance.

Therefore it can be concluded that CEOs with more influence in the company, yield better

performance. In this research, performance was measured as excess shareholder return, above

the market average and sales growth proportion. It should not be a concern for investors to

invest in companies where the CEO the chairperson, as CEO remuneration is related to the

performance of the firm.

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5. REFERENCES

Cohen, J. 1992. Statistical power analysis. Current directions in psychological science. 1(3):

98-101.

Deysel, B., Kruger, J. 2015. The relationship between South African CEO compensation and

company performance in the banking industry. Southern African Business Review. 19(1).

137-169.

Fabozzi, J., Focardi, M., Rachev, T. 2014.Basics of Financial Econometrics: Tools,

Concepts, and Asset Management Applications. Somerset, US: Wiley.

George, D., Mallery, M. 2010. SPSS for Windows Step by Step: A Simple Guide and

Reference. 10th edition), Boston: Pearson.

Tabachnick, B.G., Fidell, L.S. 2013. Using multivariate statistics, 6th edition, Boston:

Pearson Education.

Todeschinia, R., Ballabioa, D., Consonnia, V., Sahigaraa, F., Filzmoserb P. 2013. Eta squared

and partial eta squared as measures of effect size in educational research. Analytica Chimica

Acta. 787:1–9

Pallant, J. 2013. SPSS Survival Manual: A step by step guide to data analyisis using IBM

SPSS, 5th edition, McGraw-Hill

Xiaohong, H.C. 2012. Approaches to Quantitative Research, Cork, IE: Oak Tree Press

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6. APPENDICES

Figure 6.1. Scatterplot of Lsalary vs number of directors

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Figure 6.2. Scatterplot of Lsalary vs number of executives on the board.

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Figure 6.3 Scatterplot of Lsalary vs assets

15

Figure 6.4 Scatterplot of Lsalary vs proportion of executives on the board

16

Figure 6.5 Scatterplot of Lsalary vs sales growth

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Figure 6.6 Scatterplot of Lsalary vs excess return proportion