Statistical analysis of the factors which influence CEO pay.

1. 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.

2. 1
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.

3. 2
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

4. 3
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

5. 4
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

6. 5
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.

7. 6
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.

8. 7
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

9. 8
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
Lsalary
Lsalary (actual) vs Lsalary (modelled)
Lsalary

10. 9
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.

11. 10
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.

12. 11
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

13. 12
6. APPENDICES
Figure 6.1. Scatterplot of Lsalary vs number of directors

14. 13
Figure 6.2. Scatterplot of Lsalary vs number of executives on the board.

15. 14
Figure 6.3 Scatterplot of Lsalary vs assets

16. 15
Figure 6.4 Scatterplot of Lsalary vs proportion of executives on the board

17. 16
Figure 6.5 Scatterplot of Lsalary vs sales growth

18. 17
Figure 6.6 Scatterplot of Lsalary vs excess return proportion