Appendices Stats explanation
m anagers nec: Example 1: Individual data points plotted (20 male versus 12 female) for education the ANSZCO job category raw data 300,000 of education managers nec 250,000
base salary (p.a.)
They look fairly similar, except for one male (the green box above the $250,000 mark) that 200,000 However, there aren’t a appears to be an “extreme outlier” because of his abnormally high salary. lot of individuals in this group. There is no way to tell whether, if there were another ten or twenty 150,000 people, that outlier would in fact just be at the upper end of a continuous range that stretched from ~$75,000 to ~$275,000. 100,000 50,000 education m anagers nec: 0 m eans
Same data, shown as the means of 20 males and 12 females + standard deviation malebarsfemale 200,000 0.5
1
1. 5
2
2.5
base salary (p.a.)
The y-axis only goes to 200K instead of 300K because averaging the150,000 salaries of all the individuals within each sex “hides” the extreme outlier. However, because of that outlier, the standard deviation bar for the males is bigger than for the females, reflecting that there is more variability 100,000 in the males’ salaries. 50,000
0
male
female
education m anagers nec: m eans
base salary (p.a.)
A Student’s t-test compares male versus female wages within the single category, taking into consideration how much variability there is and how many individuals there are in each group. It 200,000 asks, how much difference is there in the male education managers nec salaries and the female p = 0.228 education managers nec salaries, and what are the odds that this150,000 difference (if any) is due to random chance – how likely is it that this is just the normal variation between two sexes in the same job, given the amount of variation within males and the amount of variation within females? 100,000 The Student’s t-test produces a p-value. A p-value of less than 0.05 (5%) is considered statistically significant. 50,000
0 In this case, the difference is not statistically significant. There is a 22.8% (22 in 100) chance it’s male female just random that the average male wage is 15% higher than the average female wage – mostly because of that one male outlier. program or project Example 2: Individual data points plotted (27 male versus 53 female) for the ANSZCO jobraw category adm inistrator: data 150,000 of programme or project administrator 125,000
181
base salary (p.a.)
The male and female data here look less similar to each other compared with the first example. 100,000 who are slight outliers There is one high male who is a bit of an “outlier”, and a couple of females 75,000 50,000 25,000 0