2012 Salary Survey
Contents
Summary
SalaryBot asked users to confirm their current salary as part of a survey focused on the gender pay gap in the UK. Using the data of 4,578 participants (2,571 male and 2,007 female), the survey found that with almost certainty (99.5%) males can expect to earn typically between £4,907 and £7,491 more than females. The analysis of the survey was completed by Dr David Fishwick, head of mathematics at Bradford Grammar School.
The first phase took a sample of survey data from August 2012, including both full time and part time workers. The result set was comprised of 3,376 records (1,859 male and 1,517 female), and only examined salaries under £100,000.
The second phase took a sample of survey data from July-September 2012, including just full time workers (employees working 35 hours or greater per week). The result set was comprised of 3,376 records (1,859 male and 1,517 female). The result set again only looked at salaries under £100,000, but also above £4,732 (the lowest possible wage for full time work above compulsory school age - at a rate of £2.60 per hour).
We are assuming that the sample variances are approximately equal to the population variances.
Analysis
From the box plot diagrams, the median male salary is £5,000 more than for women.
The interquartile range for men is £22,000, where as for women it is £15,000. This shows us that there is more variation in the types of salary that men receive.
The mean male salary is about £6,000 more than for women.
The standard deviation for men (£17,800) is about £4,000 more than for women (£13,800) confirming suggestion of more variation in male salaries.
Using confidence intervals, we can be 95% sure that the true (national) mean lies between £32,789-£34,169 for males, and £26,677-£27,883 for females.
Therefore, we can also be confident to a degree of 99.5% certainty that the difference between male and female wages is in the range of £4,907 and £7,491. We can further narrow this range to £5,283-£7,113 by reducing the amount of certainty to 95%.
Phase one
Bar chart
Plotting the results from a contingency table on a bar chart below demonstrates graphically how the wage distribution differs between genders.
Median values
The below table and box plot diagram maps the median values for the sample data.
| Male | Female | |
|---|---|---|
| Min value | £15 | £4 |
| Lower quartile | £20,000 | £17,000 |
| Median | £28,752 | £23,000 |
| Upper quartile | £41,900 | £31,700 |
| Max value | £98,200 | £97,000 |
Chi-squared test
The chi-squared contingency table calculation for the data sample confirmed the (obvious) fact very emphatically that there is strong association between gender and wages.
O values
| 0 - 10,000 | 10,001 - 20,000 | 20,001 - 30,000 | 30,001 - 40,000 | 40,001 - 50,000 | 50,001 - 60,000 | >60,000 | Total | |
|---|---|---|---|---|---|---|---|---|
| Male | 72 | 410 | 558 | 336 | 203 | 109 | 171 | 1859 |
| Female | 91 | 520 | 492 | 228 | 96 | 49 | 41 | 1517 |
| Total | 163 | 930 | 1050 | 564 | 299 | 158 | 212 | 3376 |
E values
| 0-10,000 | 10,001-20,000 | 20,001-30,000 | 30,001-40,000 | 40,001-50,000 | 50,001-60,000 | >60,000 | |
|---|---|---|---|---|---|---|---|
| Male | 89.76 | 512.11 | 578.18 | 310.57 | 164.64 | 87.00 | 116.74 |
| Female | 73.24 | 417.89 | 471.82 | 253.93 | 134.36 | 71.00 | 95.26 |
Chi-squared contingency table
| O | E | (O-E)²/E |
|---|---|---|
| 72 | 89.76 | 3.51 |
| 410 | 512.11 | 20.36 |
| 558 | 578.18 | 0.70 |
| 336 | 310.57 | 2.08 |
| 203 | 164.64 | 8.94 |
| 109 | 87.00 | 5.56 |
| 171 | 116.74 | 25.22 |
| 91 | 73.24 | 4.31 |
| 520 | 417.89 | 24.95 |
| 492 | 471.82 | 0.86 |
| 228 | 253.43 | 2.55 |
| 96 | 134.36 | 10.95 |
| 49 | 71.00 | 6.82 |
| 41 | 95.26 | 30.91 |
| 147.72 |
calc = 147.72- tab (5%) = 21.02
147.72 >> 21.02 so result is significant at 5% level of testing.
- calc = 147.72
- tab (0.05%) = 28.30
147.72 >> 28.30 so result is significant at 5% level of testing.
The chi-squared test reveals it is almost statistically certain that there is association, clearly in favour of men.
Phase two
Median values
The below table and box plot diagram maps the median values for the sample data.
| Male | Female | |
|---|---|---|
| Min value | £5,000 | £4,823 |
| Lower quartile | £20,000 | £18,000 |
| Median | £29,120 | £24,000 |
| Upper quartile | £42,000 | £33,000 |
| Max value | £98,200 | £97,000 |
Mean and standard deviation
| Mean | Sum of squares | Standard deviation | |
|---|---|---|---|
| Male | 33,478.9032 | 3699750599142 | 17,800 |
| Female | 27,280.1156 | 1875355777570 | 13,800 |
Skewness
It is evident from the bar chart and the box plots that the earnings for both male and female are positively skewed. However, the large amount of data collected allows us to justify the claim by applying the principle of central limit theorem.
Confidence intervals
We can be 95% confident that the true (national) mean lies within the interval:
- Men: £32,789 → £34,169
- Women: £26,677 → £27,883
Therefore, we can be confident that the difference between male and female wages is in the range of £4,907 and £7,491.
