This study presented the&nbsp; evaluate of 20 types of cancer disease in Tikrit teaching hospital in Tikrit for the period from 1995 to 2005 . the data analyzed by RCBD (Randomized complete block design) to explain the significant difference between all kind of cancer disease and all age groups

AL Kutubi, Hadeel Salim

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   International Journal of Sciences: Basic and Applied Research (IJSBAR)  ISSN 2307-4531 (Print & Online)  http://gssrr.org/index.php?journal=JournalOfBasicAndApplied --------------------------------------------------------------------------------------------------------------------------- 032  On Randomized Complete Block Design Hadeel Salim AL Kutubi* Faculty of Computer Science and Mathematics, Kufa University, Najaf, 54001, Iraq Email: hadeel.alkutubi@uokufa.edu.iq   Abstract  This study presented the  evaluate of 20 types of cancer disease in Tikrit teaching hospital in Tikrit for the period from 1995 to 2005 . the data analyzed by RCBD (Randomized complete block design) to explain the significant difference between all kind of cancer disease and all age groups.  Keywords: Randomized; complete block design; cancer. 1. Introduction The randomized complete block design (RCBD) is a standard design for bio statistic experiments in which similar experimental units are grouped into blocks or replicates. It is used to control variation in an experiment by, for example, accounting for spatial effects in field or greenhouse. The defining feature of the RCBD is that each block sees each treatment exactly once.Randomized complete block designs differ from the completely randomized designs in that the experimental units are grouped into blocks according to known or suspected variation which is isolated by the blocks. Variation such as fertility, sand, and wind gradients, or age and litter of animals can be isolated by appropriate blocking. Therefore, within each block, the conditions are as homogeneous as possible, but between blocks, large differences may exist. There are many studies on this topic, including one [6]: He compared the effectiveness of split-plot design (SPD) over randomized complete block design (RCBD).  ------------------------------------------------------------------------ * Corresponding author.   International Journal of Sciences: Basic and Applied Research (IJSBAR) (2020) Volume 53, No  2, pp 230-243  032  The data used for comparison is a 2 1 x 5 2 split-plot experiment with three replicates,  Reference [10] reviews the problems associated with ignoring animal grouping during data analyses, and examples are provided for appropriate methods to use when animals are grouped in pens, Reference [9] provide a way to intuitively understand the error structure and resulting statistical analysis in split-plot designs through building on concepts found in simple designs, such as completely randomized and randomized complete block designs, and then provide a way for students to "see" the error structure graphically, Reference [11] study the consequences of more realistic assumptions about zi j. and verify that the usual F test, for testing treatment effects, can be used even if there is a constant covariance between responses from experimental units in the same block [12]. The goal of his research (1) to demonstrate the consequences of constructing an F-statistic based on a mean square error for testing the significance of treatment effects under the restricted randomization; (2) to describe an alternative method, based on split-plot analysis of variance, to analyze designed experiments that yield better power under the restricted randomization, Reference [5] derive asymptotic procedures as well as finite approximations, for the analysis of data arising from series of such experiments [8]. He is an attempt to build some new functions of Randomized Complete Block Design in R-software. Different computer programs are developed using Rsoftware. All these functions are run on real data set .The present work is an attempt to show the flexibility of R, Reference [7] consider two the most popular in practice designs for three – factorial experiments, split – split plot design and split – plot χ split – block (SPSB). 2. Patients and Methods  2.1 Patients We taken 1555 case from Tikrit teaching hospital (1995-2005) in Tikrit . Data contain 20 types of cancer disease divided between age groups . So we will present the CRBD design to find the significant difference between the types of cancer and age groups.  2.2 The Randomized Complete Block Design RCBD The randomized complete block design (RCBD) is perhaps the most commonly encountered design that can be analyzed as a two – way ANOVA. In this design , a set of experimental unit is grouped (blocked) in a way that minimizes the variability among the units within groups (blocks). The objective is to keep the experimental error within each block as well as possible. Each block contains a complete set of treatments, therefore differences among blocks are not due to treatments, and this variability can be estimated as a separate source of variation. The removal of an appreciable amount of this source of variation reduces experimental error and improves the ability of the experiment to detect smaller treatment differences.  The greater the variability among blocks the more efficient the design becomes. In the absence of appreciable block differences the design is not as efficient as a completely randomized design (CRD) [1,2,3,4]. Sources of Variation: International Journal of Sciences: Basic and Applied Research (IJSBAR) (2020) Volume 53, No  2, pp 230-243  030       ,     , ∑    , ∑    ,    (   )    ,     ∑∑         ,                    ,      ∑         ,                       ,             ,     ∑                       (    )      ,            ,                ,                      ,           ,                               Table 1: ANOVA table for RCBD S.O.V df SS MS F  Block (reps.) r-1 SSB MSB F - Block Treatment  t-1 SSt MSt F- treatment  Error  (r-1)(t-1) SSE MSE  Total  rt-1 SST    3. Results and Discussion Table 2: Cancer types in 1995 distributed on age groups Types  1-20  T1 21-40  T2 41-60  T3 61-80  T4 81-100 T5 Leukemia 6 7 11 14 4 Lung 0 8 12 2 17 Bladder 0 0 2 7 6 Prostate  0 0 3 6 0 Bone 0 1 0 0 1 Brain 3 0 0 2 0 Stomach 0 0 0 0 0 Pancreas 0 0 2 0 4 Rectum 0 0 0 2 3 Kidney 1 1 0 3 2 Liver 0 0 0 0 0 Urinary 0 0 1 3 0 Larynx 0 0 2 4 8 Thyroid gland 0 0 1 0 3 Colon 0 3 0 0 1 Lymphoma 0 0 0 0 1 Small intestine 0 5 0 0 0 Skin 0 0 0 0 0 Uterus 0 2 4 5 9 Breast  6 9 5 7 8 International Journal of Sciences: Basic and Applied Research (IJSBAR) (2020) Volume 53, No  2, pp 230-243  033  Table 3: Significant different between all age groups (1995) by ANOVA S.O.V df SS MS F  Block (reps.) 19 193.79 10.199 1.05 Treatment  4 1712.11 428.02 44.125 Error  76 739.79 9.7  Total  99               , so there exist significant deference between the age groups because the             , but there is no significant deference between cancer's types . Table 4: Cancer types in 1996 distributed on age groups Types  1-20  T1 21-40  T2 41-60  T3 61-80  T4 81-100 T5 Leukemia 120 6 7 11 2 Lung 0 3 5 1 2 Bladder 0 0 1 3 1 Prostate  0 0 5 0 2 Bone 2 0 1 0 0 Brain 0 1 5 0 0 Stomach 0 2 1 2 0 Pancreas 0 0 3 0 4 Rectum 0 0 3 8 1 Kidney 2 2 0 3 7 Liver 0 0 0 0 4 Urinary 1 3 0 0 4 Larynx 1 0 0 2 1 Thyroid gland 0 0 0 0 1 Colon 0 2 0 3 1 Lymphoma 1 0 0 0 0 Small intestine 0 0 0 0 0 Skin 0 0 0 0 0 Uterus 0 2 2 8 6 Breast  0 2 2 6 1 Table 5: Significant different between all age groups (1996) by ANOVA S.O.V df SS MS F  Block (reps.) 19 184.78 9.725 1.103 Treatment  4 109.11 27.27 3.09 Error  76 669.77 8.812  Total  99    International Journal of Sciences: Basic and Applied Research (IJSBAR) (2020) Volume 53, No  2, pp 230-243  032             , so there exist significant deference between the age groups because the             , but there is no significant deference between cancer's types . Table 6: Cancer types in 1997 distributed on age groups Types  1-20  T1 21-40  T2 41-60  T3 61-80  T4 81-100 T5 Leukemia 1 1 2 5 0 Lung 0 2 0 0 4 Bladder 0 1 0 3 4 Prostate  0 0 0 0 6 Bone 0 0 0 1 0 Brain 3 0 2 1 0 Stomach 0 0 0 0 1 Pancreas 0 3 0 3 0 Rectum 0 0 0 0 3 Kidney 0 4 0 3 1 Liver 0 1 2 1 0 Urinary 0 0 0 0 4 Larynx 2 0 0 3 1 Thyroid gland 0 0 0 0 0 Colon 0 1 0 3 0 Lymphoma 0 1 0 2 0 Small intestine 0 0 0 3 0 Skin 2 0 2 0 0 Uterus 0 0 1 3 1 Breast  0 0 0 1 0 Table 7: Significant different between all age groups (1997) by ANOVA S.O.V df SS MS F  Block (reps.) 19 193.28 10.17 1.433 Treatment  4 1212.25 303.06 42.714 Error  76 539.22 7.095  Total  99               , so there exist significant deference between the age groups because the             , but there is no significant deference between cancer's types .   International Journal of Sciences: Basic and Applied Research (IJSBAR) (2020) Volume 53, No  2, pp 230-243  032  Table 8: Cancer types in 1998 distributed on age groups Types  1-20  T1 21-40  T2 41-60  T3 61-80  T4 81-100 T5 Leukemia 8 3 2 5 0 Lung 1 4 1 6 3 Bladder 0 0 4 3 1 Prostate  0 0 1 2 5 Bone 2 0 2 0 0 Brain 3 1 1 0 1 Stomach 0 0 2 0 2 Pancreas 0 2 0 3 0 Rectum 0 0 2 0 0 Kidney 2 0 0 1 3 Liver 0 0 0 0 0 Urinary 0 1 2 0 3 Larynx 0 0 1 0 0 Thyroid gland 0 1 0 0 0 Colon 0 0 1 0 2 Lymphoma 0 0 0 0 0 Small intestine 0 2 1 1 3 Skin 0 0 0 0 0 Uterus 0 0 2 2 2 Breast  0 0 5 5 0 Table 9: Significant different between all age groups (1998) by ANOVA S.O.V df SS MS F  Block (reps.) 19 201.78 10.62 1.17 Treatment  4 1681.13 420.28 46.337 Error  76 689.77 9.07  Total  99               , so there exist significant deference between the age groups because the             , but there is no significant deference between cancer's types .    International Journal of Sciences: Basic and Applied Research (IJSBAR) (2020) Volume 53, No  2, pp 230-243  032  Table 10: Cancer types in 1999 distributed on age groups Types  1-20  T1 21-40  T2 41-60  T3 61-80  T4 81-100 T5 Leukemia 4 0 6 2 2 Lung 1 3 5 2 1 Bladder 0 2 0 4 0 Prostate  0 0 2 0 3 Bone 3 0 0 1 0 Brain 2 1 0 0 1 Stomach 0 0 4 1 1 Pancreas 0 0 0 1 3 Rectum 0 0 0 0 1 Kidney 1 0 2 2 3 Liver 0 1 0 1 1 Urinary 0 2 0 2 2 Larynx 1 0 2 0 0 Thyroid gland 1 0 2 0 3 Colon 0 0 3 0 4 Lymphoma 0 0 2 0 2 Small intestine 1 0 6 0 6 Skin 4 0 0 0 2 Uterus 0 0 0 1 0 Breast  0 0 1 3 2 Table 11: Significant different between all age groups (1999) by ANOVA S.O.V df SS MS F  Block (reps.) 19 177.55 9.344 0.84 Treatment  4 1645.2 411.3 37.15 Error  76 841.74 11.07  Total  99               , so there exist significant deference between the age groups because the             , but there is no significant deference between cancer's types .    International Journal of Sciences: Basic and Applied Research (IJSBAR) (2020) Volume 53, No  2, pp 230-243  032  Table 12: Cancer types in 2000 distributed on age groups Types  1-20  T1 21-40  T2 41-60  T3 61-80  T4 81-100 T5 Leukemia 4 4 4 3 2 Lung 1 3 2 4 1 Bladder 0 2 6 1 2 Prostate  0 0 2 3 1 Bone 2 1 3 1 1 Brain 5 1 2 1 3 Stomach 0 0 2 3 1 Pancreas 0 1 2 1 2 Rectum 0 2 1 1 3 Kidney 2 1 2 4 3 Liver 0 0 1 3 1 Urinary 0 0 0 0 3 Larynx 2 2 2 3 1 Thyroid gland 0 2 1 1 3 Colon 0 0 1 1 2 Lymphoma 0 0 0 1 1 Small intestine 0 0 2 1 3 Skin 0 0 0 0 1 Uterus 0 0 3 0 0 Breast  0 0 1 3 1 Table 13: Significant different between all age groups (2000) by ANOVA S.O.V df SS MS F  Block (reps.) 19 144.51 7.60 0.824 Treatment  4 1682.4 420.6 45.61 Error  76 701.32 9.22  Total  99               , so there exist significant deference between the age groups because the             , but there is no significant deference between cancer's types .    International Journal of Sciences: Basic and Applied Research (IJSBAR) (2020) Volume 53, No  2, pp 230-243  032  Table 14: Cancer types in 2001 distributed on age groups Types  1-20  T1 21-40  T2 41-60  T3 61-80  T4 81-100 T5 Leukemia 6 2 6 2 4 Lung 0 2 1 1 5 Bladder 0 0 1 1 3 Prostate  0 2 1 1 0 Bone 1 0 3 1 2 Brain 4 2 2 1 4 Stomach 0 0 2 1 3 Pancreas 0 0 0 1 2 Rectum 0 0 1 2 3 Kidney 1 0 0 2 5 Liver 0 3 1 2 0 Urinary 0 0 0 2 1 Larynx 1 0 2 1 1 Thyroid gland 0 0 1 2 1 Colon 0 1 3 0 2 Lymphoma 0 0 1 3 1 Small intestine 0 2 3 2 0 Skin 1 0 0 1 1 Uterus 0 0 2 0 0 Breast  0 0 0 1 0 Table 15: Significant different between all age groups (2001) by ANOVA S.O.V df SS MS F  Block (reps.) 19 244.32 12.85 1.317 Treatment  4 1810.12 452.53 46.413 Error  76 741.25 9.75  Total  99               , so there exist significant deference between the age groups because the             , but there is no significant deference between cancer's types .    International Journal of Sciences: Basic and Applied Research (IJSBAR) (2020) Volume 53, No  2, pp 230-243  032  Table 16: Cancer types in 2002 distributed on age groups Types  1-20  T1 21-40  T2 41-60  T3 61-80  T4 81-100 T5 Leukemia 12 3 9 12 5 Lung 0 0 2 3 1 Bladder 0 0 5 1 3 Prostate  0 0 0 0 1 Bone 2 0 0 1 0 Brain 3 1 1 0 1 Stomach 0 0 0 4 1 Pancreas 1 0 0 0 0 Rectum 0 0 3 0 1 Kidney 3 0 0 5 0 Liver 1 0 0 0 0 Urinary 0 0 0 0 0 Larynx 1 3 2 0 2 Thyroid gland 0 0 0 0 0 Colon 0 0 1 0 0 Lymphoma 2 0 0 0 0 Small intestine 0 3 0 1 2 Skin 0 0 0 0 0 Uterus 0 0 3 0 0 Breast  0 0 1 3 1 Table 17: Significant different between all age groups (2002) by ANOVA S.O.V df SS MS F  Block (reps.) 19 187.10 9.847 1.045 Treatment  4 1654.41 413.60 43.89 Error  76 716.12 9.422  Total  99               , so there exist significant deference between the age groups because the             , but there is no significant deference between cancer's types .    International Journal of Sciences: Basic and Applied Research (IJSBAR) (2020) Volume 53, No  2, pp 230-243  022  Table 18: Cancer types in 2003 distributed on age groups Types  1-20  T1 21-40  T2 41-60  T3 61-80  T4 81-100 T5 Leukemia 8 1 2 15 15 Lung 0 2 1 0 1 Bladder 0 0 5 1 4 Prostate  0 0 0 4 2 Bone 1 0 2 2 0 Brain 6 0 0 2 0 Stomach 0 0 0 2 3 Pancreas 0 0 0 1 0 Rectum 0 0 0 0 1 Kidney 2 0 0 3 1 Liver 6 2 0 5 2 Urinary 0 0 0 0 0 Larynx 1 0 3 1 0 Thyroid gland 0 0 0 2 1 Colon 0 1 3 0 5 Lymphoma 0 0 0 0 2 Small intestine 0 0 2 0 3 Skin 0 0 0 0 0 Uterus 0 3 0 4 0 Breast  0 0 3 0 1 Table 19: Significant different between all age groups (2003) by ANOVA S.O.V df SS MS F  Block (reps.) 19 174.64 9.19 1.531 Treatment  4 1423.17 355.79 59.29 Error  76 456.47 6.00  Total  99               , so there exist significant deference between the age groups because the             , but there is no significant deference between cancer's types .    International Journal of Sciences: Basic and Applied Research (IJSBAR) (2020) Volume 53, No  2, pp 230-243  022  Table 20: Cancer types in 2004 distributed on age groups Types  1-20  T1 21-40  T2 41-60  T3 61-80  T4 81-100 T5 Leukemia 8 5 2 5 4 Lung 2 0 3 6 1 Bladder 0 0 2 7 3 Prostate  0 0 2 0 6 Bone 2 0 2 0 1 Brain 3 3 7 2 2 Stomach 0 0 0 2 0 Pancreas 0 0 0 0 2 Rectum 0 0 0 0 0 Kidney 3 0 5 2 4 Liver 0 2 0 0 0 Urinary 0 9 1 1 2 Larynx 1 0 0 0 0 Thyroid gland 0 0 0 3 0 Colon 0 2 5 2 0 Lymphoma 0 0 0 0 0 Small intestine 0 0 0 2 2 Skin 0 0 0 0 0 Uterus 0 0 3 0 1 Breast  0 0 2 0 3 Table 21: Significant different between all age groups (2004) by ANOVA S.O.V df SS MS F  Block (reps.) 19 178.44 9.39 0.89 Treatment  4 1765.52 441.38 41.91 Error  76 800.85 10.53  Total  99               , so there exist significant deference between the age groups because the             , but there is no significant deference between cancer's types .    International Journal of Sciences: Basic and Applied Research (IJSBAR) (2020) Volume 53, No  2, pp 230-243  020  Table 22: Cancer types in 2005 distributed on age groups Types  1-20  T1 21-40  T2 41-60  T3 61-80  T4 81-100 T5 Leukemia 10 2 8 1 3 Lung 0 2 3 3 6 Bladder 0 0 0 12 7 Prostate  0 0 0 6 7 Bone 12 1 7 9 5 Brain 4 2 0 0 7 Stomach 0 0 1 0 1 Pancreas 0 1 0 0 0 Rectum 0 0 5 3 1 Kidney 1 0 2 2 1 Liver 3 2 0 1 1 Urinary 0 0 0 1 0 Larynx 0 0 0 2 2 Thyroid gland 1 0 0 2 0 Colon 1 0 0 2 1 Lymphoma 0 0 3 2 6 Small intestine 0 1 0 0 1 Skin 0 1 0 0 4 Uterus 0 1 1 1 1 Breast  0 1 3 0 1 Table 23: Significant different between all age groups (2005) by ANOVA S.O.V df SS MS F  Block (reps.) 19 210.41 11.07 1.127 Treatment  4 1759.12 439.78 44.77 Error  76 746.54 9.822  Total  99               , so there exist significant deference between the age groups because the             , but there is no significant deference between cancer's types . 4. Conclusion 1. There exist significant deference between the age groups 2. There is no significant deference between cancer's types International Journal of Sciences: Basic and Applied Research (IJSBAR) (2020) Volume 53, No  2, pp 230-243  023  5. Recommendations It is possible to use the same data for cancer patients that were taken from a general hospital in the city of Tikrit in Iraq to be used again in new statistical methods such as designing a new experiment or a global trial to give us another type of results related to cancerous injuries in the city. Reference [1]. AlKutubi H. S. , Ibrahim N. and Yaseen N. K. 2009. On statistical analysis of cancer tumors in Tikrit hospital . European journal of scientific research , Vol.35, No. 1, 106-120. [2]. AlKutubi H. S. and Yaseen N. K. 2009. On completely random design of cancer in Tikrit teaching hospital. European journal of scientific research , Vol.35, No. 4, 633-640. [3]. AlKutubi H. S , 2009. Experimental design of HIV patients. European journal of scientific research , Vol.35, No. 1, 65-75.  [4]. Bland, Martin, 2000. An introduction to medical statistics, Third edition, Oxford    University Press ,Inc., New York. [5]. Bathke A. C, Harrar S. W, Wang H., Ke Zhang and Piepho H. Series of randomized complete block experiments with non – normal. Computational statistics and data analysis, Vol. 54, 2010: 1840 – 1857. [6]. David, I. J., Adehi, M. U. Effectiveness of Split-Plot Design over randomized Complete Block Design in Some Experiments. Biology Agriculture and healthcare, Vol. 4, No. 19, 2014.  [7]. Deregowska K. A., Mejza I. and Mejza S. On the relative efficiency of split – split – plot design to split – plot χ split – block design. Colloquium biometricum, Vol. 44, 2014: 69 – 78. [8]. Jeelani M. I, Nazir N, Sharma M. K, Bhat  A, Gul M. and Kumar B. R Codes for Randomized Complete Block Design. International Journal of Information Science and System, Vol. 6, No. 1, 2018: 1-8. [9]. Robinson T. J., Brenneman W. A. and Myery W. R. An intuitive Graphical approach to understanding the split- plot experiment. Journal of statistics education, Vol. 17, No. 1, 2009. [10]. St-Pierre N. R. Design and analysis of pen studies in the animal sciences. Journal of dairy science, Vol. 90, 2007. [11]. Peres C. A. Testing the effect of blocking in a randomized complete block design (RCBD). Journal communications in statistics – theory and methods, Vol. 10, issue 23, 1981. [12]. Pilla R. S, Kitska D. J, Loader C. Statistical analysis of modified complete randomized designs: applications to chemo – orientation studies. Journal of experimental biology, 2005, 208:1267-1276.   

On Randomized Complete Block Design

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On Randomized Complete Block Design

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