case 3

This committee reviewed the presented results of the new prostate cancer treatment research and found that , based on our evaluation of the study 's statistical significance , the researchers succeeded to prove that the new treatment may be effective . A significant statistical difference was shown between the existing average outcome of the disease and the outcome of the disease after the experimental treatment Therefore , our recommendation is to grant additional funds to this research

We used the Measures of Central Tendency as well as Measures of Variability to evaluate the study results

and their statistical significance . The results data set consists of 12 outcome values (weeks that the patient lived after the confirmed diagnosis : 3 , 5 , 6 , 6 , 8 , 8 9 , 9 , 9 , 10 , 11 , 45 . Since the data set does not contain a large number of high or low data points , the mean (average ) is the best indicator of the data set middle . Therefore , comparing the sample mean of 10 .75 to a known value of 9 .6 (average number of weeks that a prostate cancer patient lives after receiving a confirmed diagnosis , we can see the difference that can be statistically significant

However , we have to point out that the results distribution is noticeably skewed , with a substantial difference between the mean of 10 .75 and median of 8 .5 . Also , the range of data set (the difference between the highest and the lowest value , 45 - 3 42 , as well as interquartile range (the difference between the upper and the lower quartile , 18 .25 - 5 .25 13 , are very high in comparison to the mean and median of the data set . This dispersion range results in increased standard deviation value (11 .04 in comparison to standard deviation of 3 .2 for the known average , which indicates that the results are not uniform . Additional research is needed in to achieve more uniform results that will increase the confidence level of the new treatment effectiveness

Mostly , the dispersion of results and the large positive skew was caused by one outlay value of 45 weeks . Due to the sample size , we do not recommend to eliminate this outlay result , but we do recommended to conduct additional analysis on the outlay subject , to determine what , if any , additional factors may have caused this large deviation

To further evaluate the statistical significance of the results inferential statistics methods such as t-test analysis should be used to compare the null hypothesis (that there is no such difference ) with the alternative hypothesis (that the treatment had a statistically significant result , using alpha and p-values methods

While the results presented to this committee show possible benefits of the new treatment , we conclude that more research is needed to confirm the statistical significance of these benefits . Our recommendations for further research are to increase the sample size , to conduct a two-sample study (potentially double-blind study ) and to use the probability sampling methods to achieve more representative results that can be projected to the stage 4 of prostate cancer

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