Statistics and Difference

BIO 2003 SUMMATIVE appointment 2 Introduction The report analyses the result of a study on workers from brick and roofing roofing tile industries conducted by the Health and Safety Laboratory (HSL). HSL put chain reactor few criterias to the workers which macrocosm that neither of the workers from the tiles and brick industries should have worked in both(prenominal) the industries and that they did not smoke. The criterias put across was an assurance to attain secure results.The essence of the study lies in detecting each going away in the wellness of the workers in these industries (as identified by prison cadre alter) if any and as tumesce to determine if any relationship exists amid the space of service and the put down health effect. The Null shot (Ho) states that no exit in the median assess(a) grade between the role- shamed kiosks of the workers from the brick and tile industries is observed. Null Hypothesis for the correlation study excessively states that there is no correlation between the health effects of the workers and the clipping period they have worked in the industries.N geniustheless the Alternative Hypothesis (H1) states that the median region of modify cell of the workers in the brick industry is different when compared to the median per centum of disgraced cells of workers of both the functionings. H1 for the correlation study states that correlation exists between the magazine period the workers have worked in the industry and their health effects. Analysis tallyament be carried out with the help of the following 5 s healthys * Worker ID * years * Department * Length of service * Percentage of cell damage The high up samples are independent within and withal between each other.To chance an accurate analysis of the data, the normality, box plot of land and satisfying- disceptation relationship and independence of the statistical analysis bequeath be checked. The Null or Alternative Hypothesis will b e real or standed on the base of operations of a statistical analysis, which will be habituated to analyse the median percentage of alter cells got from the brick and tile operations. knock back 1 Descriptive Statistics of brick and tile operation workers percentage change cells Variable N N* nasty SE entertain St Dev. Minimum Q1 Median Q3 Maximum % Damaged cells of roofing tile operation 27 0 1. 337 0. 210 1. 090 0. 200 0. 600 1. 00 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 modify 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 discrepancy between Q3 and Q1 is higher for the brick operation compared to that of the tile. bod 1Box plot displaying %damage of cell in workers from both tile and brick industries. The figure of speech above shows that the percentage-damaged cell for tile operators is refuse when compared with the brick operators indicating a difference in the signify and median. Figure 1 shows a difference in the health hazard of the tile and brick workers. There is order of skewness in the scattering 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 primitive outliers when compared to the % cell damage of the brick workers, which is quite wide. For the above box plot the charter for a further analysis is to be carried out as the speculation give the axenot either be accepted neither rejected since the box plot only denotes statistical measu res (mean, median, Q1, Q3, max & min value) which are not ample to prove the difference between the deuce sites. Figure 2 Histogram of the tile and Brick operation data The % of damaged cells of the brick operation is higher when compared to the tile operation.This is reason from the histogram above which exhibits that the close off values which is the % damaged cells for brick operation is higher than the bar value of the tile operation. We have used a histogram, as it is one of the important tools for a data analysis. Figure 3The Test For competent Variance. The values of the estimated equal variances show no difference in the % cell damage of the workers from the brick and tile operations-value obtained from the Levenes Test is 0. 200 which is as well higher than 0. 05 implies that the hypothesis of difference cannot be rejected.The value of the F-Test is 0. 952 which being higher than 0. 05 shows besides shows no signs that the null hypothesis (H0) should be rejected and a lso that there is no difference between %cell damage of workers from brick and tile operations. The obtained values from the test for equal variance point out to an brachydactylic distribution of data stating the acceptance of the null hypothesis. Hence no suck up evidence of a difference in the median among the % damaged cells in the workers of both the operations. Figure 4Normal Distribution Graph For Brick And roofing tile Operation.Figure 4 illustrates a normal distribution graph for tile and brick operations. The figure above shows that the %damaged cells of brick and tile operations are not uniformly distributed, as the points are not scattered about a straight line. There is evidence that the residuals followed a skewed distribution and it can also be seen that the above graph does not follow any cut down or pattern. The is no persuade evidence to reject the null hypothesis (H0) as the P-Value is lower than 0. 05 in Fig4. From the above facts it whitethorn be reason out that the residuals do not follow a normal distribution.A MANN WHITNEY TEST will be used to statistically analyse the data as the %damaged cells of workers in the tile operation shows that the data is not normally distributed since the P-Value is lower than 0. 05 and also that the plots on the graph so no route any precise trend. MANN WHITNEY TEST Results & CI Of roofing tile & Brick Manufacturing Operations Table 2illuminates the number of samples used in the Mann Whitney test and the obtained median for data of brick and tile manufacturing operations Sample type Number of sample Median Tile 27 1. 100Brick 38 1. 370 Point estimate for ETA1-ETA2 is 0. 200 95. 0% CI for ETA1-ETA2 is (-0. 323, 0. 800) W = 1319. 0 Test of ETA1 = ETA2 vs. ETA1 not = ETA2 is significant at 0. 3905 The test is significant at 0. 3903 (adjusted for ties). The results shows a confidence interval of 95% between 0. 323 and 0. 800 in the %damaged cells of workers In the brick and tile operations. Contrariwise t he difference in the median is 0. 200(estimated), which means that 0. 200%(approximately) more % of damaged cells in workers of the brick operations than those of the tile operations.A 100% certain analysis cannot be proven as the confidence interval (CI) is only 95%, hence creating a need for more data in order to achieve a 100% certain analysis. An analyses of results obtained shows the P-value got from the Mann-Whitney test was 0. 3905. Since the P-value is higher than 0. 05 it indicated no evidence to reject the null hypothesis of no differences. Therefore it can be conclude that there is no convincing evidence of difference in the median between %damaged cells of workers in the 2 operations. endA use of various graphs and descriptive statistics were used and inferred to decide if there were any differences in the health of the workers of the 2 operations. The Mann Whitney U test was considered to find the difference in the %-damaged cells of the tile and brick operation worke rs. A destruction may be haggard from the these analyses that there is scarce evidence to suggest that there is noteworthy difference in the % damaged cells in workers of tile and brick operations. Question 2 Table 3 Paired T-test and 95% CI to determine if the data of % damaged cells and length of service of workers in two operations is paired. N Mean StDev SE Mean % Damaged cells 65 1. 451 1. 095 0. 136 length of service (years 65 8. 995 7. 349 0. 912 Difference 65 -7. 544 6. 964 0. 864 95% CI for mean difference (-9. 270, -5. 819) T-Test of mean difference = 0 (Vs. not = 0) T-Value = -8. 73 P-Value = 0. 000 The table shows the T-test and the P-value got is 0. 05 stating no convincing evidence to reject null hypothesis of no differences. It may be reason that the data is paired since the P-value is 0. 000. A scatter plot may also be used to test the relationship between the two samples.Figure5 A scatter plot showing the correlation between the % of cells damaged with a rev erse line and the length of service in years. The predicted value for Regression is 17. 4%, which states the 17. 4% of the variability in the data is delineate by the reversal model. This cannot be used to get future values as the predictive value itself is very low. Pearsons correlation demand to be conducted since the above scatter plot shows a minor prescribed association between the % damaged cells and the length of the service, but the damage of the cells in the future cannot be predicted.Pearsons Correlation results Difference 65 -7. 544 6. 964 0. 864 95% CI for mean difference (-9. 270, -5. 819) T-Test of mean difference = 0 (vs. not = 0) T-Value = -8. 73 P-Value = 0. 000 Pearson correlation of length of service (years) and % damaged cells = 0. 417 P-Value = 0. 001. The association between the length of service and %damaged cells of the tile and brick operations cannot be accepted since the values from Pearsons Correlation is 0. 417which is higher than 0. 400. Therefore a regression fitted line will be used to forecast the future data.The P-value is 0. 001 which being less than 0. 05 does not prove to be a convincing evidence to reject null hypothesis (H0) of no differences. Hence a conclusion may be drawn stating a difference in the length of services and the % damaged cells of workers from both the operations. Hence a regression fitted line plot will be used to predict future values. supercharge Analysis Figure6shows the data between the %damaged cells and the age of workers as well as the regression line. The scatter plot above shows that there is a moderate positive correlation between the age and the % damaged cells.Therefore a Pearsons correlation will be conducted. Pearson correlation of age (years) and % damaged cells = 0. 251 P-Value = 0. 044 The P value is 0. 044 which is less than 0. 05, this means that the null hypothesis must be rejected and the alternative hypothesis is accepted that there is not sufficient evidence available to say t hat there is a correlation. Conclusion The data was analysed using descriptive statistics, various graphs, Pearsons correlation and regression fitted line plot to find association between the % damaged cell and length of service in tile and brick operations.The results concluded that there is no association between the % of damaged cells and their length of service. However there was a positive correlation which was observed between the % of damaged cells and age of workers in both operations. This suggested that it is the age which is the cause of damage and not the dust. The first test carried out, concluded that there is no genuine difference between the health hazard of the worker at the tile and brick operation.The second test concluded that there is little relationship between the workers health and the length of their service. Since the R-sq value was only 17. 4%, the extent of damage cannot be predicted by the length of employment. Overall conclusion It can be concluded that there is unimportant difference in the percentage damaged cells in the workers of tile and brick operations. It can also be concluded that age of workers and not the length of characterisation to the dust in brick or tile operations increase % damaged cells of workers.