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If there is some multiple of g units per block medications not to crush order 2.5 mg olanzapine visa, say 2g or 3g symptoms 9dp5dt purchase generic olanzapine from india, then we can randomly assign each treatment to two or three units in each block medications you can take during pregnancy order olanzapine online now. This design medicine technology purchase olanzapine 20mg otc, sometimes called a Generalized Randomized Complete Block treatment ind olanzapine 7.5 mg discount, still has a simple structure and analysis medications 230 buy olanzapine on line amex. The standard model has treatments fixed, blocks random, and the treatment by blocks interaction as the denominator for treatments. A third possibility is that units are expensive, but the block sizes are not a nice multiple of the number of treatments. For example, with three treatments (A, B, and C) and three blocks of size 5, we could use (A, B, C, A, B) in block 1, (A, B, C, A, C) in block 2, and (A, B, C, B, C) in block 3. So each block has one full complement of the treatments, plus two more according to an incomplete block design. The final possibility that we mention is that we can have blocks with dif- ferent numbers of units; that is, some blocks have more units than others. Standard designs assume that all blocks have the same number of units, so we must do something special. The most promising approach is probably op- timal design via special design software. Optimal design allocates treatments to units in such a way as to optimize some criterion; for example, we may wish to minimize the average variance of the estimated treatment effects. The algorithms that do the optimization are complicated, but software exists that will do what is needed (though most statistical analy- sis packages do not). An experiment was conducted comparing four treatments: sodium chloride, calcium chloride, a proprietary organic compound, and sand. Traf- fic level was used as a blocking factor and a randomized complete block ex- periment was conducted. One observation is missing, because the spreader in that district was not operating properly. A B C D Block 1 32 27 36 Block 2 38 40 43 33 Block 3 40 63 14 27 Our interest is in the following comparisons: chemical versus physical (A,B,C versus D), inorganic versus organic (A,B versus C), and sodium ver- sus calcium (A versus B). A factorial experiment was conducted to determine which factors affect graininess. The factors were drying temperature (three levels), acidity (pH) of pulp (two levels), and sugar content (two levels). The exper- iment has two replications, with each replication using a different batch of pulp. D 44 B 26 C 67 A 77 B 51 D 62 A 71 C 49 C 39 A 45 D 71 B 74 C 63 A 74 D 67 B 47 B 52 D 49 A 81 C 88 A 74 C 75 B 60 D 58 A 73 C 58 B 76 D 100 D 82 B 79 C 74 A 68 Exercise 13. The six treatments are the factorial combinations of factor A at three levels and factor B at two levels. Give the sources and degrees of freedom for the Analysis of Variance of this design. A manufacturer compares four substrates: aluminum (A), nickel-plated aluminum (B), and two types of glass (C and D). It is felt that operator, machine, and day of production may have an effect on the drives, so these three effects were blocked. The design and responses (in microvolts ×10−2) are given in the following table (data from Nelson 1993, Greek letters indi- cate day): 13. Ruminant animals, such as sheep, may not be able to quickly utilize pro- Problem 13. Eventually the bacteria will die and the protein will be available for the ruminant, but we are interested in dietary changes that will help the protein get past the bacteria and to the intestine of the ruminant sooner. We can vary the cereal source (oats or hay) and the protein source (soy or fish meal) in the diets. There are twelve lambs available for the experiment, and we expect fairly large animal to animal differences. Each diet must be fed to a lamb for at least 1 week before the protein uptake measurement is made. The measurement technique is safe and benign, so we may use each lamb more than once. We do not expect any carryover (residual) effects from one diet to the next, but there may be effects due to the aging of the lambs. The nitrogen and depth fac- tors have two levels, and the date factor has three levels. You sell a lot of fries and keep four fry cutters and their operators going constantly. They decide to start small, using only one drug (a decongestant for which they have an analogous generic) and twenty patients at each of their five clinics. The patients at the different clinics are from rather differ- ent socioeconomic backgrounds, so some clinic to clinic variation is expected. We are interested in the time it takes nesting red-shouldered hawks to re- spond to invading calls, and want to know if that time varies accord- ing to the type of intruder. At each nest, we play two pre- recorded calls over a loudspeaker (several days apart). One call is a red-shouldered hawk call; the other call is a great horned owl call. The response we measure is the time until the nesting hawks leave the nest to drive off the intruder. There are twenty subjects—ten randomly selected males and ten randomly selected females—from a large food science class. At the four sessions they receive two low-fiber muffins and two high-fiber muffins in random order. Part of the certification process for bank examiners involves a work basket of tasks that the exami- nee must complete in a satisfactory fashion in a fixed time period. New work baskets must be constructed for each round of examinations, and much effort is expended to make the workbaskets comparable (in terms of average score) from exam to exam. We have ten paid examinees (1 through 6 are certified bank ex- aminers, 7 through 9 are noncertified bank examiners nearing the end of their 13. We anticipate differences between the examinees and the graders; our interest is in the exams, which were randomized so that each examinee took each exam and each grader grades two of each exam. We want to know if either or both of the new exams are equivalent to the old exams. Student Grader 1 2 3 4 5 1 68 D 65 A 76 E 74 C 76 B 2 68 A 77 E 84 B 65 D 75 C 3 73 C 85 B 72 D 68 E 62 A 4 74 E 76 C 57 A 79 B 64 D 5 80 B 71 D 76 C 59 A 68 E 6 69 D 75 E 81 B 68 A 68 C 7 60 C 62 D 62 E 66 B 40 A 8 70 B 55 A 62 C 57 E 40 D 9 61 E 67 C 53 A 63 D 69 B 10 37 A 53 B 31 D 48 C 33 E An experiment was conducted to see how variety of soybean and crop Problem 13. These varieties are each used in four different 5- year rotation patterns with corn. The rotation patterns are (1) four years of corn and then soybeans (C-C-C-C-S), (2) three years of corn and then two years of soybeans (C-C-C-S-S), (3) soybean and corn alternation (S-C-S-C- S), and (4) five years of soybeans (S-S-S-S-S). The first group of eight plots at each location was randomly assigned to the variety- rotation treatments in 1983. The response of interest is the weight (g) of 100 random seeds from soy- bean plants (data from Whiting 1990). There were sixteen varieties of soybeans and three weed treatments: no herbicide, apply herbicide 2 weeks after planting the soybeans, and apply herbicide 4 weeks after planting the soybeans. Variety R StP R StP R StP Parker 750 1440 1630 890 3590 740 Lambert 870 550 3430 2520 6850 1620 M89-792 1090 130 2930 570 3710 3600 Sturdy 1110 400 1310 2060 2680 1510 Ozzie 1150 370 1730 2420 4870 1700 M89-1743 1210 430 6070 2790 4480 5070 M89-794 1330 190 1700 1370 3740 610 M90-1682 1630 200 2000 880 3330 3030 M89-1946 1660 230 2290 2210 3180 2640 Archer 2210 1110 3070 2120 6980 2210 M89-642 2290 220 1530 390 3750 2590 M90-317 2320 330 1760 680 2320 2700 M90-610 2480 350 1360 1680 5240 1510 M88-250 2480 350 1810 1020 6230 2420 M89-1006 2430 280 2420 2350 5990 1590 M89-1926 3120 260 1360 1840 5980 1560 Analyze these data for the effects of herbicide and variety. An experi- ment was performed to study how the orientation of the embryo during expo- sure to cytokinin and the type of growth medium after exposure to cytokinin affect the rate of vitrification. There are six treatments, which are the fac- torial combinations of orientation (standard and experimental) and medium (three kinds). On a given day, the experimenters extract embryos from white pine seeds and randomize them to the six treatments. The embryos are ex- posed using the selected orientation for 1 week, and then go onto the selected medium. The response is the fraction of shoots that are normal (data from David Zle- sak): Medium 1 Medium 2 Medium 3 Exp. The over- all objective of this phase of the program was to determine how these vari- 352 Complete Block Designs ables affect azimuth error (that is, side to side as opposed to distance) in the rocket impacts. Twenty-seven rockets are grouped into nine sets of three, which are then assigned to the nine factor-level com- binations in random order. The three rockets in a group are fired all at once in a single volley, and the azimuth error recorded. Treatments 2 through 5 contain alfalfa meal type 22; treatments 6 through 9 contain alfalfa meal type 27. Treatments are separately randomized to pens grouped 1–9, 10–18, 19–27, and so on. The response is average daily weight gain per bird for birds aged 7 to 14 days in g/day (data from Turgay Ergul): 13. We choose eight substrate loca- tions and measure the length of the substrates at those eight locations on the seven substrates. Laminate Location 1 2 3 4 5 6 7 1 28 20 23 29 44 45 43 2 11 20 27 31 33 38 36 3 26 26 14 17 41 36 36 4 23 26 18 21 36 36 39 5 20 21 30 28 45 31 33 6 16 19 24 23 33 32 39 7 37 43 49 33 53 49 32 8 04 09 13 17 39 29 32 Analyze these data to determine the effect of location. In this experiment, four trees (Dipterocarpus kerrii) will be tapped seven times each. Each of the tappings will be treated with a dif- ferent strength of sulfuric acid (0, 2. Each location was divided into four plots, and trees were planted at densities of 185, 90, 70, and 0 trees per hectare. Data are the yields of coffee (kg of fresh berries per hectare) for the 1994-95 cropping season (data from Amoah, Osei-Bonsu, and Oppong 1997): Location 185 90 70 0 1 3107 2092 2329 2017 2 1531 2101 1519 1766 3 2167 2428 2160 1967 Analyze these data to determine the effect of tree density on coffee produc- tion. Twenty-four judges will rate both types of chips; twelve judges will rate the chips in the order regular fat, then reduced fat; and the other twelve will have the order reduced fat, then regular fat. We anticipate judge to judge differences and possible differences between the first and second chips tasted. The response is a liking scale, with higher scores indicating greater liking (data from Monica Coulter): 1 2 3 4 5 6 7 8 9 10 11 12 A first 8 5 7 8 7 7 4 9 8 7 7 7 B second 6 6 8 8 4 7 8 9 9 7 5 3 13 14 15 16 17 18 19 20 21 22 23 24 B first 4 6 6 7 6 4 8 6 7 6 8 7 A second 7 8 7 8 4 8 7 7 7 8 8 8 Analyze these data to determine if there is a difference in liking between the two kinds of potato chips. Give a heuristic argument, based on randomization, suggesting why your relationship is true. The inspector general is coming, and an officer wishes to arrange some Question 13. The officer is trying to arrange 36 soldiers for inspection in a six by six square with one soldier from each state-rank-gender combination. Furthermore, the idea is to arrange the soldiers so that no matter which rank or file (row or column) is inspected by the general, the general will see someone from each of the six states, one woman of each rank, and one man of each rank. Incomplete block appear in an designs also group units into blocks, but the blocks do not have enough units incomplete block to accommodate all the treatments. Incomplete block designs share with complete block designs the advan- tage of variance reduction due to blocking. The drawback of incomplete block designs is that they do not provide as much information per experi- Incomplete blocks mental unit as a complete block design with the same error variance. Thus less efficient than complete blocks are preferred over incomplete blocks when both can be con- complete blocks structed with the same error variance. If each subject can only be used during one treatment period, then we must use one brand of drop in the left eye and another brand in the right eye. We are forced into incomplete blocks of size two, because our subjects have only two eyes. Suppose that we have three subjects that receive brands (A and B), (A and C), and (B and C) respectively. How can we estimate the expected difference in responses between two treatments, say A and B? We can get some infor- mation from subject 1 by taking the difference of the A and B responses; the 358 Incomplete Block Designs subject effect will cancel in this difference. We can also get an estimate of A-B by subtracting the B-C difference in subject three from the A-C difference in subject two. Thus the incomplete block design has more variance in its estimates of treatment differences than does the complete block design with the same variance and number of units. Several of the incomplete block designs given in this chapter have balanced in their name. It is important to realize that these designs are not balanced in the sense that all block and factor-level combinations occur equally often. Rather they are balanced using somewhat looser criteria that will be described later. Two general classes of incomplete block designs are resolvable designs Resolvable and connected designs. A resolvable design is one in which the blocks can be arranged into replications r groups, with each group representing a complete set of treatments. Resolv- able designs can make management of experiments simpler, because each replication can be run at a different time or a different location, or entire replications can be dropped if the need arises. A design is disconnected if you can separate the treatments into two Connected groups, with no treatment from the first group ever appearing in the same designs can block with a treatment from the second group. You cannot estimate all treatment differences in a disconnected differences design; in particular, you cannot estimate differences between treatments in different groups. Session 1 2 3 4 5 6 7 8 9 10 11 12 A 19 D 6 G 21 A 20 B 17 C 15 A 20 B 16 C 13 A 20 B 17 C 14 B 17 E 26 H 19 D 7 E 26 F 23 E 26 F 23 D 7 F 24 D 6 E 24 C 11 F 23 J 28 G 20 H 19 J 31 J 31 G 21 H 20 H 19 J 29 G 21 difference of treatment effects αbi − αbj is the same for all pairs of treatments i, j. There are N = 6 total units, and each pair of treatments occurs together in one block. For example, suppose that we have three factors each with two levels for a total of g = 8 treatments. The three operators wash at the same speed during each test, and the response is the number of plates washed when the foam disappears.

A truncated precursor form of prostate-specific antigen is a more specific serum marker of prostate cancer medications ending in pam buy cheap olanzapine line. A precursor form of prostate-specific antigen is more highly elevated in prostate cancer compared with benign transition zone prostate tissue medications and breastfeeding generic olanzapine 10mg visa. Tumor-associated forms of prostate specific antigen improve the discrimination of prostate cancer from benign disease medications lexapro discount olanzapine 2.5mg without a prescription. Lower urinary tract symptoms suggestive of benign prostatic hyperplasia: latest update on alpha-adrenoceptor antagonists symptoms xanax overdose olanzapine 7.5 mg fast delivery. Update on the use of dutasteride in the management of benign prostatic hypertrophy medications you can give your cat olanzapine 7.5 mg overnight delivery. Nephron-sparing surgery for renal cell carcinoma-is tumor size a suitable parameter for indication medications venlafaxine er 75mg buy generic olanzapine 20 mg online. Cooled thermotherapy for the treatment of benign prostatic hyperplasia: durability of results obtained with the Targis System. Atorvastatin treatment for men with lower urinary tract symptoms and benign prostatic enlargement. Studies of the pathophysiology of idiopathic detrusor instability: the physiological properties of the detrusor smooth muscle and its pattern of innervation. Transition zone volume measurement-is it useful before surgery for benign prostatic hyperplasia. Prostate-specific antigen and transition zone index - powerful predictors for acute urinary retention in men with benign prostatic hyperplasia. The importance of prostatic measuring by transrectal ultrasound in surgical management of patients with clinically benign prostatic hyperplasia. Prediction of alpha- blocker response in men with benign prostatic hyperplasia by magnetic resonance imaging. Clinical characteristics of alpha-blocker responders in men with benign prostatic hyperplasia. Urinary bladder involvement in patients with systemic lupus erythematosus: with review of the literature. Production of serum-free and total prostate-specific antigen due to prostatic intraepithelial neoplasia. Diagnostic accuracy of percent free prostate-specific antigen in prostatic pathology and its usefulness in monitoring prostatic cancer patients. Transurethral resection versus minimally invasive treatments of benign prostatic hyperplasia: results of treatments. Pressure- flow studies in men with benign prostatic hypertrophy before and after treatment with transurethral needle ablation. Our experience in left internal vein ligature for symptomatic varicocele and in circumcision. Adenoid cystic carcinoma of the prostate: a case report with immunohistochemical and in situ hybridization staining for prostate-specific antigen. Treatment of lower urinary tract symptoms in benign prostatic hyperplasia and its impact on sexual function. Benign prostatic hyperplasia cell line viability and modulation of jm-27 by doxazosin and Ibuprofen. Correlation between detrusor collagen content and urinary symptoms in patients with prostatic obstruction. Expression of cystatins, high molecular weight cytokeratin, and proliferation markers in prostatic adenocarcinoma and hyperplasia. Does intraprostatic inflammation have a role in the pathogenesis and progression of benign prostatic hyperplasia. To what extent do real life practice studies differ from randomized controlled trials in lower urinary tract symptoms/benign prostatic hyperplasia. Preservation of glomerular filtration rate on dialysis when adjusted for patient dropout. Efficacy of tolterodine in preventing urge incontinence immediately after prostatectomy. Serum neutrophil gelatinase-associated lipocalin as a marker of renal function in children with chronic kidney disease. Vesicourethral function in diabetic patients: association of abnormal nerve conduction velocity with vesicourethral dysfunction. Persistent detrusor overactivity after transurethral resection of the prostate is associated with reduced perfusion of the urinary bladder. A clinicopathological study of bladder cancer associated with upper urinary tract cancer. Serum level of cathepsin B and its density in men with prostate cancer as novel markers of disease progression. Ultrasonic measurement of bladder weight as a possible predictor of acute urinary retention in men with lower urinary tract symptoms suggestive of benign prostatic hyperplasia. Serum insulin-like growth factor binding protein-3/prostate- specific antigen ratio is a useful predictive marker in patients with advanced prostate cancer. Expression of thymidylate synthase, dihydropyrimidine dehydrogenase, thymidine phosphorylase, and orotate phosphoribosyl transferase in prostate cancer. Prognostic role of prostate-specific antigen and prostate volume for the risk of invasive therapy in patients with benign prostatic hyperplasia initially managed with alpha1-blockers and watchful waiting. Prostate-specific antigen as an estimator of prostate volume in the management of patients with symptomatic benign prostatic hyperplasia. Post-void residual urine volume is not a good predictor of the need for invasive therapy among patients with benign prostatic hyperplasia. Polymorphisms in the alpha1A-adrenoceptor gene do not modify the short- and long-term efficacy of alpha1-adrenoceptor antagonists in the treatment of benign prostatic hyperplasia. The effect of labeling on perceived ability to recover from acute illnesses and injuries. Diagnostic utility of a p63/alpha-methyl-CoA-racemase (p504s) cocktail in atypical foci in the prostate. High prevalence of patients with a high risk for obstructive sleep apnoea syndrome after kidney transplantation-association with declining renal function. Crossover comparison study on the therapeutic effects of tamsulosin hydrochloride and naftopidil in lower urinary tract symptoms associated with benign prostatic hyperplasia. Finasteride 5 mg and sexual side effects: how many of these are related to a nocebo phenomenon. Urinary transforming growth factor-beta1 levels correlate with bladder outlet obstruction. Urodynamic predictors of outcomes with photoselective laser vaporization prostatectomy in patients with benign prostatic hyperplasia and preoperative retention. Urodynamic predictors of outcomes with photoselective laser vaporization prostatectomy in patients with benign prostatic hyperplasia and preoperative retention. Assessment of live kidney donors by magnetic resonance angiography: reliability and impact on outcomes. Renal glomerular response to the inhibition of prostaglandin E2 synthesis and protein loading after the relief of unilateral ureteropelvic junction obstruction. Immunohistochemical expression of pi class glutathione S-transferase in the basal cell layer of benign prostate tissue following chronic treatment with finasteride. Review of phosphodiesterases in the urogenital system: new directions for therapeutic intervention. Holmium laser enucleation versus transurethral resection of the prostate: results from a 2-center, prospective, randomized trial in patients with obstructive benign prostatic hyperplasia. Holmium laser enucleation of the prostate with tissue morcellation: initial United States experience. Antidiuretic hormone in elderly male patients with severe nocturia: a circadian study. Incidence of erectile dysfunction in men 40 to 69 years old: results from a population-based cohort study in Brazil. Prevalence and correlates of erectile dysfunction in Salvador, northeastern Brazil: a population-based study. In vitro models: research in physiology and pharmacology of the lower urinary tract. Emerging pharmacologic approaches for the treatment of lower urinary tract disorders. Ionic dialysance and the assessment of Kt/V: the influence of different estimates of V on method agreement. Randomized, controlled trial of an interactive videodisc decision aid for patients with ischemic heart disease. Influence of high-grade prostatic intra-epithelial neoplasia on total and percentage free serum prostatic specific antigen. Prediction of prostate volume based on total and free serum prostate-specific antigen: is it reliable. Effect of inflammation and benign prostatic enlargement on total and percent free serum prostatic specific antigen. Intraindividual variations of total and percent free serum prostatic-specific antigen levels in patients with normal digital rectal examination. Vesicostomy revisited: the best treatment for the hostile bladder in myelodysplastic children. Prostatic tissual distribution of alfuzosin in patients with benign prostatic hyperplasia following repeated oral administration. Prostate-specific antigen-enhanced testing and risk stratification for chemoprevention trials. Endoscopic management of upper urinary tract disease using a 200-microm holmium laser fiber: initial experience in Japan. The relationship between angiogenesis and cyclooxygenase-2 expression in prostate cancer. Assessment of the impact of sildenafil citrate on lower urinary tract symptoms in men with erectile dysfunction. Urinary incontinence after radical retropubic prostatectomy is not related to patient body mass index. Growth factor, cytokine, and vitamin D receptor polymorphisms and risk of benign prostatic hyperplasia in a community-based cohort of men. Autoradiographic localisation and contractile properties of prostatic endothelin receptors in patients with bladder outlet obstruction. Peri-operative morbidity and changes in symptom scores after transurethral prostatectomy in Switzerland: results of an independent assessment of outcome. Systemic nitric oxide augmentation leads to a rapid decrease of the bladder outlet resistance in healthy men. Transurethral needle ablation of the prostate: an initial Japanese clinical trial. A concomitant tumour boost in bladder irradiation: patient suitability and the potential of intensity-modulated radiotherapy. The impact of targeted training, a dedicated protocol and on-site training material in reducing observer variability of prostate and transition zone dimensions measured by transrectal ultrasonography, in multicentre multinational clinical trials of men wi. Randomised controlled trial of an interactive multimedia decision aid on benign prostatic hypertrophy in primary care. Prostate cancer risk among users of finasteride and alpha-blockers - a population based case-control study. Conductive heat: hot water-induced thermotherapy for ablation of prostatic tissue. Transurethral water-induced thermotherapy for the treatment of benign prostatic hyperplasia: a prospective multicenter clinical trial. Transurethral ethanol injection for prostatic obstruction: an excellent treatment strategy for persistent urinary retention. Restoration of insulin-like growth factor binding protein-related protein 1 has a tumor-suppressive activity through induction of apoptosis in human prostate cancer. Analytical and clinical evaluation of a new urinary tumor marker: bladder tumor fibronectin in diagnosis and follow-up of bladder cancer. Safety and efficacy of transurethral resection of prostate glands up to 150 ml: a prospective comparative study with 1 year of followup. Trypsin stimulates the phosphorylation of p42,44 mitogen-activated protein kinases via the proteinase-activated receptor-2 and protein kinase C epsilon in human cultured prostate stromal cells. Epidemiology of bloodstream infection in nursing home residents: evaluation in a large cohort from multiple homes. Clinical comparison of selective and non-selective alpha 1A-adrenoceptor antagonists for bladder outlet obstruction associated with benign prostatic hyperplasia: studies on tamsulosin and terazosin in Chinese patients. Gatifloxacin 400 mg as a single shot or 200 mg once daily for 3 days is as effective as ciprofloxacin 250 mg twice daily for the treatment of patients with uncomplicated urinary tract infections. Gatifloxacin 200 mg or 400 mg once daily is as effective as ciprofloxacin 500 mg twice daily for the treatment of patients with acute pyelonephritis or complicated urinary tract infections. Primary squamous cell carcinoma of the prostate: a rare clinicopathological entity. Multiple bilateral cannon-ball lung metastases from carcinoma of the prostate: orchiedectomy induced remission. Aneuploidy of chromosome Y in prostate tumors and seminal vesicles: a possible sign of aging rather than an indicator of carcinogenesis. Comparison of real-time intraoperative ultrasound-based dosimetry with postoperative computed tomography-based dosimetry for prostate brachytherapy. Serum pro-gastrin-releasing peptide (31-98) in benign prostatic hyperplasia and prostatic carcinoma. Correlation between lower urinary tract symptoms and urethral function in benign prostatic hyperplasia.

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For any other pair of factor-level Multiply and combinations symptoms definition buy cheap olanzapine 2.5mg on-line, multiply as usual but then reduce exponents modulo 2 symptoms 7 days post iui 2.5 mg olanzapine mastercard. Think of the zeroes and ones as exponents; for example medicine x stanford cheap 20mg olanzapine with mastercard, 1101 corresponds to a1b1c0d1 = abd symptoms ringworm olanzapine 2.5mg visa. Exponents 392 Factorials in Incomplete Blocks—Confounding add when we multiply medications used to treat bipolar disorder cheap olanzapine 10mg free shipping, so the corresponding operation is to add the zeroes and ones componentwise and then reduce them mod 2 medications known to cause tinnitus order cheap olanzapine on-line. If you multiply any two elements of the principal block together reducing exponents modulo two, Get alternate you get another element of the principal block. If you multiply all elements blocks from of the principal block by an element not in the principal block, you get an principal block alternate block. What this means is that you can find alternate blocks easily once you have the principal block. This is no big deal when there are only two blocks, but can be very useful when we have four, eight, or more blocks. Multiplying every element of the principal block by ac, we get the following (1) ⊙ ac = ac = ac a ⊙ ac = a2c = c bc ⊙ ac = abc2 = ab abc ⊙ ac = a2bc2 = b bd ⊙ ac = abcd = abcd abd ⊙ ac = a2bcd = bcd cd ⊙ ac = ac2d = ad acd ⊙ ac = a2c2d = d this is the alternate block, but in a different order than Table 15. The last subsection showed how to con- contrasts for 2q found into two blocks using one defining contrast. We can confound into blocks four blocks using two defining contrasts, and in general we can confound into 2q blocks using q defining contrasts. Start by choosing two defining contrasts for confounding a 24 design into Choose defining four blocks of size four. It turns out that choosing these defining contrasts is contrasts very important, and bad choices lead to poor designs. Alternatively, we compute L1 and L2 for the two defining contrasts, and take as blocks those combinations that are zero on both, one on both, zero on the first and one on the second, and zero on the second and one on the first. We have confounded into four blocks, so there are 3 degrees of freedom between blocks. We know that the two defining contrasts are confounded with block differences, but what is the third degree of freedom that is con- founded with block differences? This fact that we also confound the generalized interaction explains why Check we need to be careful when choosing defining contrasts. When choosing defining contrasts, we need to look at the full set of ef- fects that are confounded with blocks. We want first to find a set such that the lowest-order term confounded with blocks is as high an order as possi- ble. We prefer the second and lower order third sets to the first, because the first confounds a main effect, and the sec- interactions ond and third confound two-factor interactions. We prefer the second set to confounded as the third, because the second set confounds only one two-factor interaction, possible while the third set confounds two two-factor interactions. These defining contrasts must be independent of each other, in the sense that none of them is the gen- eralized interaction the other two. Divide the factor-level combinations into eight groups using the even/odd patterns of the three defining contrasts: (even, even, even), (even, even, odd), (even, odd, even), (even, odd, odd), (odd, even, even), (odd, even, odd), (odd, odd, even), and (odd, odd, odd). The three defining contrasts are confounded with blocks, as are their three two- way generalized interactions and their three-way generalized interaction, for a total of 7 degrees of freedom. We again note that once you have the principal block, you can find the other blocks by choosing an element not in the principal block and multiply- ing all the elements of the principal block by the new element and reducing exponents mod 2. This principal block was found by inspection, meaning work- ing through the factor-level combinations finding those that are even for all three defining contrasts. The remaining blocks can be found by multiplying the elements of the principal block by a factor-level combination not already accounted for. For example, a is not in the principal block, so we multiply and get a, abcd, ce, and bde for a second block. Next, b has not been listed, so we multiply by b and get b, cd, abce, and ade for the third block. These q defining contrasts must be independent; no defining contrast can be a generalized interaction of q defining two or more of the others. Form blocks by grouping the factor-level combina- contrasts for 2q q tions according to the 2 different even-odd combinations for the q defining blocks contrasts. There are 2q blocks, so there are 2q −1 degrees of freedom confounded with blocks. These are the q defining contrasts, their two-way, three-way, and up to q-way generalized interactions. Doing the actual blocking is rather tedious in large designs, so it is help- ful to have software that will do confounding. The usual even/odd or 0/1 methods are available if you must do the confounding by hand, but a little thinking first can save a lot of calculation. Combinations in the principal block always have an even number of letters from every defining contrast. This indicates that the principal block will contain (1) and combinations with four letters. We know that in the principal group we can multiply any two elements together, reduce the exponent mod 2, and get another element of the block. Thus we find that abcd ⊙ abef = cdef, abcd ⊙ bcfg = adfg, abef ⊙ bcfg = aceg, and abcd ⊙ abef ⊙ bcfg = bdeg are also in the principal block. Now that we have the principal block, we can find alternate blocks by finding a factor-level combination not already accounted for and multiplying the elements of the principal block by this new element. For example, a is not in the principal block, so we can find a second block as a = (1) ⊙ a, bcd = abcd ⊙ a, bef = abef ⊙ a, abcfg = bcfg ⊙ a, acdef = cdef ⊙ a, dfg = adfg ⊙ a, ceg = aceg ⊙ a, and abdeg = bdeg ⊙ a. Next, b is not in these first two blocks, so b = (1) ⊙ b, acd = abcd ⊙ b, aef = abef ⊙ b, cfg = bcfg ⊙ b, bcdef = cdef ⊙ b, abdfg = adfg ⊙ b, abceg = aceg ⊙ b, and deg = bdeg ⊙ b are the next block. The additional complication with confounding is that some of the treatment degrees of freedom are confounded with blocks. The approach we take is to compute the sum of squares or total effect for Use standard each main effect and interaction, remove from consideration those that are methods with confounded with blocks, and then analyze the remaining nonconfounded ef- nonblock effects fects with standard methods. The subject is supposed to click the mouse button when she sees an image on the screen. The experiment takes place in sixteen ten- minute sessions to prevent tiring; during each session we present 120 images. In fact, these are eight images repeated fifteen times each and presented in random order. We record as the response the fraction of times that the mouse is clicked for a given image type. We wish to study 128 different images, the factorial combinations of seven factors each at two levels: size of image, shape of image, color of im- age, orientation of image, duration of image, vertical location of image, and horizontal location of image. Because we anticipate session to session vari- ability, we should design the experiment to account for that. There are fifteen factorial effects confounded with blocks, seven three- way interactions, seven four-way interactions, and the seven-way interaction. We could pool the five- and six-way interaction degrees of freedom for a 28-degree- of-freedom estimate of error, and then use this surrogate error in testing the lower-order terms that are not confounded with blocks. It would be best to make these plots using only the 112 nonconfounded terms, but it is usually tedious to remove the confounded terms. We begin the analysis by noting that the responses are binomial propor- tions ranging from. This plot has all 127 effects in standard order, including those confounded with blocks. All three are confounded with blocks, so we regard this as block rather than treatment effects. We conclude that of the treatments we chose, only factor E (duration) has an effect; images that are on the screen longer are easier to see. We must choose defining contrasts 400 Factorials in Incomplete Blocks—Confounding Complete versus for the confounding in each replication, and here we have an option. We can partial confound the same defining contrasts in all replications, or we can confound confounding different contrasts in each replication. Contrasts confounded in all replica- tions are called completely confounded, and contrasts confounded in some but not all replications are called partially confounded. Partial confounding generally seems like the better choice, because we will have at least some information on every effect. Suppose that we have four replications of a 23 factorial with two blocks of size four per replication, for a total of eight blocks. There are eight blocks, so there are 7 degrees of freedom between blocks, and the sum of squares for blocks is the sum of squares between the eight groups formed by the blocks. Second, the effects and sums of squares for A, B, and C can be computed in the usual way. In general, estimate where they are an effect and compute its sum of squares from those replication where the not confounded effect is not confounded. Compute sums of squares and estimated effects for any main effect adjusted for or interaction by using the standard formulae applied to those replications blocks in which the main effect or interaction is not confounded. This pattern works for complete or partial confounding, and when using statistical software for analysis is most easily expressed as treatments adjusted for blocks. The effective sample size for any effect is the number of replications in which the effect is not confounded. The fraction of information available for an partially effect is the effective sample size divided by the number of replications. Thus confounded in the example we have full or 100% information for the main effects and 3/4 effects information for the interactions. The goal is to get high flow at low capital and operating costs while still chilling the milk quickly enough to maintain sensory qualities. Basic chiller design is a set of refrigerated plates over which the hot milk is pumped. We are investigating the effect of the spacing between the plates (two levels), the temperature of the plates (two levels), and the flow rate of the milk (two levels) on the perceived quality of the resulting milk. There is a fresh batch of raw milk each day, and we expect batch to batch differences in quality. Because of the time involved in modifying the chiller, we can use at most four factor-level combinations in a day. The processed milk is judged daily by a trained expert who is blinded to the treatments used; the design and results are in Table 15. There is evidence for an effect of plate temperature, with lower temperatures giving better sensory results. By way of illustration, the sum of squares for the three-factor interaction in the second replicate is 10. Suppose that we have a confounding 2k treatment structure and that we have two sources of variation on which blocks on two to block; there are 2q levels of blocking on one source and 2k−q levels of sources of blocking on the other source. In double confounding, we choose q defining contrasts to generate row Products of blocking, and k − q defining contrasts to generate column blocking. To pro- principal blocks duce the design, we find the principal blocks for rows and columns and put these in the first row and column of the rectangular arrangement. The remain- der of the arrangement is filled by taking products and reducing exponents modulo 2. For example, in a 24 factorial we could block on two sources of variation with four levels each. The column principal block is (1), ab, bcd, and acd; the row principal block is (1), abc, cd, and abd; and the full design is 15. Each row of the treatment arrangement contains a block from the row-defining contrasts, and each col- umn of the arrangement contains a block from the column-defining contrasts. When we replicate a three-series design with con- complete founding, we can use complete or partial confounding, just as for the two- confounding series design. The levels of a factor in a three-series design are denoted 0, 1, or 2; for example, the factor-level combinations of a 32 design are 00, 10, 20, 01, 11, 21, 02, 12, and 22. Main effects in a three-series design have 2 degrees of freedom, two- factor interactions have 4 degrees of freedom, and q-factor interactions have 2q degrees of freedom. Each main effect contains one of these bundles, Partition each two-factor interaction contains two of these bundles, each three-factor three-series interaction contains four of these bundles, and so on. Each two-degree-of- effects into freedom bundle arises by, in effect, splitting the factor-level combinations two-degree-of- into three groups and assessing the variation in the 2 degrees of freedom be- freedom bundles tween these three groups. These two-degree-of-freedom splits provide the basis for confounding the three series, just as one-degree-of-freedom con- trasts are the basis for confounding the two series. The label for a two-degree-of-freedom split is the Label letters from the factors, each with an exponent of either 0, 1, or 2. By con- two-degree-of- vention, we drop the letters with exponent 0, and by further convention, the freedom splits first nonzero exponent is always a 1. Thus A1C2 and B1C1D2 are exam- with exponents ples of two-degree-of-freedom splits. The two-degree-of-freedom splits that make up an interaction are those splits that have nonzero exponents for the 404 Factorials in Incomplete Blocks—Confounding same set of factors as the interaction. We use these two-degree-of-freedom splits to generate confounding in the three-series in the same way that defining contrasts generate confounding in a two-series, so these splits are often called defining contrasts, even though they are not really contrasts (which have just 1 degree of freedom). Compute for each factor-level combination Sums of factor levels mod 3 L = xB + 2xC + xD mod 3. Principal block these L values will again be 0, 1, or 2, determining three groups. We need to compute the defining split L values, and then group the factor-level combinations into blocks, as shown here: xAxB xA + 2xB L 00 0 0 10 1 1 L = 0 L = 1 L = 2 20 2 2 00 10 20 01 2 2 11 21 01 11 3 0 22 02 12 21 4 1 02 4 1 12 5 2 22 6 0 this particular arrangement into blocks forms a Latin Square, as can be seen 15.

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With age, it was more and more likely that they would tell no one about their troubles. Reference: Olweus & Limber (2010) 51 There likely are numerous reasons why children and youth are reluctant to report being bullied. Particularly for older children and youth, they may fear being labeled tattlers or snitches by their peers. Many likely are concerned about possible retaliation by their aggressors if they report them. Additional Information: Boys may feel pressure to try to deal with bullying on their own so as not to appear weak or vulnerable. Research suggests that with age, students are less and less likely to perceive that adults are helpful in stopping bullying. As a result, it is critical that adults respond quickly, effectively, and sensitively when bullying is reported to them and that they are vigilant to possible bullying that is not reported, particularly among older youth and boys. Additional Information: In one study (Olweus & Limber, 2010), researchers found that 90% of 3rd‐5th graders said they felt sorry for students who are bullied. With age (in to middle and high school grades), fewer and fewer students expressed sympathy for bullied students, and girls were more likely than boys to say they felt sorry for bullied peers. References: Baldry (2004) Olweus & Limber (2010) Rigby & Slee (1993) 54 Unfortunately, this sympathy often does not result in positive action to help stop the bullying. In one study (Olweus & Limber, 2010), researchers found that even though the vast majority of elementary school children felt sorry for bullied students, fewer than half said they would try to help if they saw or knew that a student was being bullied (Olweus & Limber, 2010). Several researchers have found that younger children and girls are not only more likely to report bullying that they know about, but by self‐report, they also are more likely to respond—for example, by directly stepping in to help the bullied student or telling the aggressor to stop. When witnesses do try to help a bullied student, they are often effective in stopping the bullying in the moment. One study found that in the majority (57%) of these cases, the bullying stopped within 10 seconds (Hawkins, Pepler, & Craig, 2001). References: Hawkins, Pepler & Craig (2001) Olweus & Limber (2010) Trach, Hymel, Waterhouse, & Neale (2010) 55 A final finding to share is that there are a variety of state and federal laws in the United States related to bullying. Additional Information: School personnel are responsible for addressing bullying behavior that meets this threshold if they know about the behavior or if they reasonably should have known about the behavior. Reference: Ali (2010) 58 State and local lawmakers have taken action to prevent bullying and protect children. Through laws (in their state education codes and elsewhere) and model policies (that provide guidance to districts and schools), each state addresses bullying differently. Find out how your state refers to bullying in its laws and what they require on part of schools and districts. Bullying, cyberbullying, and related behaviors may be addressed in a single law or may be addressed in multiple laws. In some cases, bullying appears in the criminal code of a state that may apply to juveniles. Department of Education reviewed state laws and identified 11 key components common among many of those laws. Most (but not all) define bullying, but the definitions used by states vary a good deal. Additional Information: Most laws require or suggest that district policies address:. Responsibilities of school personnel for reporting and investigating incidents of bullying. Education for staff and students and/or bullying prevention efforts A minority of the laws address the need for mental health services for children involved in bullying. Because of the differences in these laws, it is important for educators, other professionals who work with schools, and parents to become familiar with their own state law and school district policy. Department of Education (2011) 60 With these key findings about bullying in mind, we will turn now to look at 10 principles or elements of best practices in the prevention of bullying. The research supporting these elements comes primarily from evaluations of school‐based programs and experiences in the field. There is growing evidence that communities that use a public health approach to prevention of issues such as bullying (that includes a focus on health promotion and risk reduction) see the best results. Additional Information It must become uncool to bully; children, youth, and adults must notice if children are being left out, made fun of or bullied in other ways; and cool to step in to be a friend or to help out in other ways if someone is bullied. It requires positive adult role models who focus on building strong positive relationships among children sand youth. References: Hargreaves, Earl, & Ryan (1996) Mulvey & Cauffman (2001) Nation, Crusto, Wandersman, Kumpfer, Syebolt, & Dafino (2003) Olweus (1993) 62 Olweus & Limber (2010) 62 Adults are not always very good at estimating the nature and prevalence of bullying. Teachers are often surprised by student reports on how often they are bullied or witness bullying, the forms it takes, and the hot spots where bullying occurs. There are various sources of information on the prevalence of bullying in schools and of youth violence in communities (see the Community Action Toolkit). However, local data can often be more useful in making decisions about community‐wide prevention strategies and programs. One of the most common is giving students an anonymous questionnaire about bullying. Findings can: ‐Help raise awareness and motivate adults to take action against bullying; ‐Help leaders monitor where bullying is occurring; ‐Help leaders to assess the need for training and tailor training and bullying prevention strategies to the particular needs of the organization; ‐Serve as a baseline so leaders can measure their progress in reducing bullying. It can be helpful to collect data – formally or informally –fromstaff and parents. This is because adults sometimes have different perceptions about bullying than youth 63 themselves. Programs should not be the responsibility of a single administrator, counselor, or case‐manager at a school, after‐school, or recreation center. Effective bullying prevention requires buy‐in from a majority of the staff and from parents and guardians. Enthusiasm and support for school‐based prevention efforts have been linked to program success. References: Payne, Gottfredson & Gottfredson (2006) Olweus & Limber (2010) 64 Of course, many schools (and other settings where children and youth gather) are working hard not only to address bullying, but also to address and prevent other social and emotional problems. This ensures that messages are consistent and that time, energy, and resources are being well spent. Bullying prevention efforts seem to work best when they are coordinated by a representative group of staff. Depending on the scope of the effort, this group should reflect the entire school or community group. For example, safety committees within schools might include an administrator, a teacher from each grade and other school staff, such as school psychologists, counselors, school nurses, librarians, and bus drivers, who can bring diverse perspectives on bullying. Additional Information A community coordinating team may include a variety of partners across many disciplines and service sectors (e. These teams help to ensure that important voices are heard and that all members of the school community are engaged. Student/youth advisory groups can be formed in school to promote respect and inclusion, communicate about bullying prevention with their peers, and help develop rules and policies. Adults who teach or work with youth should be trained in bullying prevention and response. This training can help staff understand the nature of bullying, its effects, how to work with others to help prevent bullying, and what policies and rules are in place. Every adult who interacts with youth also needs to develop skills in how to stop bullying on‐the‐ spot and what to do if bullying is suspected. Additional Information Various educational tools can be used (staff meetings, one‐day training sessions, webcasts and teaching through modeling preferred behavior) to educate staff about bullying trends and best practices in bullying prevention (see the Community Action Toolkit). It is important to make clear that bullying behaviors are prohibited and explain what schools or youth organizations expect of all students to be good citizens and allies—not passive bystanders—if they are aware of bullying or students who appear troubled. Developing simple, clear rules about bullying that are posted throughout schools, agencies, and public places will remind youth not to bully and can help students who are bullied or who are at risk of being bullied. When children and youth do help out, this should be noticed by adults and reinforced. On the other hand, when children violate the rules and bully others, non‐hostile, developmentally appropriate consequences may be needed to help correct behavior. Additional Information Researchers, who have examined elements associated with effective school‐based bullying prevention programs, have found that having classroom rules and clear discipline for violations was related to reductions in bullying. References: Olweus (1993) Olweus & Limber (2010) Ttofi & Farrington (2009) 67 Bullying tends to thrive in locations where adults are not present or are not on the lookout for it. Once hot spots for bullying have been identified through local data collection efforts, all adults within the school or organization see it as their responsibility to be on the lookout for bullying. Additional Information Strategies for supervising young children will differ from those used for adolescents. Exchanges may be more instructive with younger children and subtle, yet firm, reminders to adolescents. Interviews are typically held separately with children who are bullied and with those who bully. Interviews with parents of children who are bullied and those who bully should also be held separately. In some situations, students may need to be referred to mental health professionals in or outside of school settings. The risks associated with aggressive, oppositional, and antisocial behaviors stem from many individual, familial, and societal factors. Just as some abusive behaviors are learned, children and adolescents can also be taught non‐hostile alternatives. With help, they can learn to act differently and not give into their impulses or desires to hurt or control others. Additional Information: 69 Emotionally vulnerable children, who have been chronically victimized or traumatized, may be silently coping with their fears and distress. They may avoid contact with peers and remain isolated as a way to protect themselves. And yet, their recovery is helped by a willingness to talk about the bullying and a look at feelings of self‐blame and worthlessness in a different way. Youth who are provocative victims or bully‐victims may require a combination of response strategies. Classrooms can be forums for sharing feelings and different viewpoints, and learning positive social behaviors. With support from administrators, teachers often see positive results from setting aside time each week or every other week to discuss bullying and peer relationships with students. During these meetings, youth can come to understand bullying and the harm it causes, gain skills in responding to bullying, and build understanding and empathy. Anti‐bullying themes and messages can be incorporated throughout the school curriculum. Bullying prevention should be ongoing in both schools and youth‐serving organizations. Research shows that the way schools and organizations implement their programs has a big impact on "quality" and "effectiveness. Additional Information: Good planning is critical but you can never plan for everything. If a redesign is necessary, the coordinating group can assist by evaluating prevention needs and outcomes, identifying gaps, and ensuring that the appropriate standards are met. Catherine Bradshaw, a national expert in research on bullying and bullying prevention, discusses some of these most common Misdirections in bullying prevention and response. This video will discuss five Misdirections, they are: Zero Tolerance Conflict Resolution & Peer Mediation Group Therapeutic Treatment Overstating or Simplifying the Relationship Between Bullying and Suicide Simple, Short‐Term Solutions 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 these are the main stakeholders you should consider including in your community event, but every community is different. Next, use the check marks to assign groups of individuals to smaller, breakout teams to discuss the immediate next steps needed to achieve the goals across the top of the page. Your event will provide a time to gather all of the stakeholders together to kick‐off your effort, identify areas of collaboration, understand the resources available in your community, and develop a call‐to‐action. A call‐to‐action that responds to bullying will include roles and responsibilities for stakeholders from across the community. Different stakeholders can also contribute unique resources and expertise to your community‐wide efforts. The Action Planning Matrix in the Community Action Toolkit will help your participants understand their roles in the effort. When developing your call‐to‐action, it is important to be aware of your timeline and resources. Completing the Landscape Assessment is a critical first step because it helps you understand efforts already underway and how your initiative can complement these activities. Having a full understanding of what already exists helps build trust with community members. This tool includes information on how to use data to understand bullying, determine community perceptions about bullying, assess existing bullying prevention strategies and capacities selecting community settings and use what you learned to inform next steps. Template Community Event Agenda the next item is a Template Agenda to guide the format of your event. Based on your learnings from the landscape assessment, this can be tailored to your community and event participants. It includes information on which community stakeholders should be invited to your event and tips for marketing the event. It also includes recommendations, such as building partnerships, using social media, and working with local newspapers and media outlets. Guide to Mobilizing Communities in Bullying Prevention this is a checklist of stakeholders to consider engaging in your initiative. There are blank spaces in the document where you can list additional groups that you may want to involve.

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