Formal Inference: The Median Female Agreeableness

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Statistics AS91582 - Formal Inference

Personalities

Problem, Plan & Data:
I wonder whether there is a difference between the median female agreeableness and the median male agreeableness, according to the Big5 personality test http://personality-testing.info/tests/BIG5.php. Agreeableness is measured on a scale of 1-5 (with 1 being the least agreeable, 5 being the most agreeable. This investigation may be beneficial to those whose looking to hire employees that are going to be more valuable to their business. Pg 306.

Studies carried out by psychologists Paul R. Sackett and Philip T. Walmsley of the University of Minnesota, indicate that agreeableness was the second most prized personality trait of those looking to employ. Agreeableness
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In saying this, there is a lot of overlap - the female median (4.1) is the same as the upper quartile of the males agreeableness (so also 4.1). The middle 50% of female agreeableness is slightly higher when compared to the male middle 50%, as the middle 50% for females is between 3.6 and 4.5 (IQR = 0.9) whereas the middle 50% of male agreeableness lies between 3.2 and 4.1 (IQR = 0.9). The lower quartile for females (3.6) is just below the median of males (3.7), thus indicating the strong overlap as over half of the male 50% (between the median and upper 75%) is within the middle 50% of females. The overall visual spread is 1.3 (female UQ-male LQ = 4.5-3.2 =1.3). The median for female agreeableness is 4.1, while the median for males is 3.7, meaning the median for female agreeableness is larger by 0.4 (difference/median shift). This difference between medians of 0.4 is 0.31 or 31% of the overall visual spread ((4.1-3.7)/(4.5-3.2)=0.31), is significant considering the sample size of 491. Thus, implying that the median for males to match/equal the median females, the male inter quartile range (IQR) should move 31% of the overall visual spread. From this we can make the decision that back in the population of females and males, based on this sample size, females are more agreeable than males. The standard deviation …show more content…
We can thereby conclude that female agreeableness is higher than male agreeableness. This may explain why there is a correlation between agreeableness becoming a more sought after trait among employees and a rise in female employment, and explain why women (in a lot of cases) are more likely to be hired than men, even with the same qualifications.

Statistical

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