# Statistics and Difference

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• Published : November 28, 2012

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BIO 2003 SUMMATIVE ASSIGNMENT 2
Introduction:
The report analyses the result of a study on workers from brick and tile industries conducted by the Health and Safety Laboratory (HSL). HSL put down few criteria’s to the workers which being that neither of the workers from the tiles and brick industries should have worked in both the industries and that they did not smoke. The criteria’s put across was an assurance to attain reliable results. The essence of the study lies in detecting any difference in the health of the workers in these industries (as identified by cell damage) if any and also to determine if any relationship exists between the length of service and the recorded health effect. The Null Hypothesis (Ho) states that no difference in the median between the percentage-damaged cells of the workers from the brick and tile industries is observed. Null Hypothesis for the correlation study also states that there is no correlation between the health effects of the workers and the time period they have worked in the industries. Nonetheless the Alternative Hypothesis (H1) states that the median percentage of damaged cell of the workers in the brick industry is different when compared to the median percentage of damaged cells of workers of both the operations. H1 for the correlation study states that correlation exists between the time period the workers have worked in the industry and their health effects. Analysis will be carried out with the help of the following 5 samples: * Worker ID

* Age
* Department
* Length of service
* Percentage of cell damage

The above samples are independent within and also between each other. To obtain an accurate analysis of the data, the normality, box plot and straight-line relationship and independence of the statistical analysis will be checked. The Null or Alternative Hypothesis will be accepted or rejected on the basis of a statistical analysis, which will be used to analyse the median percentage of damaged cells got from the brick and tile operations.

Table 1: Descriptive Statistics of brick and tile operation workers percentage damaged cells Variable| N| N*| Mean| SE Mean | St: Dev.| Minimum| Q1| Median| Q3| Maximum| % Damaged cells of Tile operation| 27| 0| 1.337 | 0.210 | 1.090 | 0.200 | 0.600 | 1.100| 1.500 | 4.700| % Damaged cells of Brick operation | 38| 0| 1.532 | 0.179 | 1.106 | 0.200 | 0.536 | 1.370| 2.189 | 4.562|

Table 1 gives a descriptive data of the workers of the respective industries.As seen in the table above the % of damaged cells of the workers in the brick industry is higher when compared with the tile operation workers.The median percentage of brick industry workers is 1.370 which is higher as compared to the brick operation workers which is 1.100.The inter-quartile range which being the difference between Q3 and Q1 is higher for the brick operation compared to that of the tile.

Figure 1:Box plot displaying %damage of cell in workers from both tile and brick industries.
The figure above shows that the percentage-damaged cell for tile operators is lower when compared with the brick operators indicating a difference in the mean and median. Figure 1 shows a difference in the health hazard of the tile and brick workers. There is evidence of skewness in the distribution of brick operators whereas the tile distribution is symmetric, as the median line for the brick operators has shifted away from the centre. The % cell damage in workers of the tile operation is closely grouped apart from the 2 extreme outliers when compared to the % cell damage of the brick workers, which is quite wide. For the above box plot the need for a further analysis is to be carried out as the hypothesis cannot either be accepted neither rejected since the box plot only denotes statistical measures (mean, median, Q1, Q3, max & min values) which are not ample to prove the difference...