Recipes for the Design of Experiments/Chapter 4: Completely Randomized Block Designs from the literature

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These data were originally analyzed by Lisa Ferrara and Anders Cohen in "A mechanical study on tennis racquets to investigate design factors that contribute to reduced stress and improved vibrational dampening". Based on these data, the results were reproducible. There were statistically significant differences in mean stiffness rate for the handle design. Further, material alone did not have an effect on stiffness, but handle design had an effect on stiffness rate.

The following recipe uses data taken from the “Influence of Variety and Harvest Maturity on Phytochemical Content in Corn Silk” by Sarepoua et al. The data was analyzed to determine if the variation in corn type and corn variation had an effect on the variation on the mean total phenolic content of corn silk. Multiple ANOVAs were performed, with hypotheses that the mean total phenolic content from all corn types and varieties were equal, to determine the significant difference. It was found that the variation of phenolic content can be attributed to both corn type and corn variety.

The analysis presented here is an example of a completely randomized block design taken from literature (Root distribution and growth of cotton as affected by drip irrigation with saline water by Wei Min, Huijuan Guo, Guangwei Zhou, Wen Zhang, Lijuan Ma, Jun Ye, Zhenan Hou: Department of Resources and Environmental Science, Shihezi University, Shihezi 832003, Xinjiang, People’s Republic of China). The paper investigates the effect of the 2 factors with 2 and 3 factor each on 3 response variables:root biomass, root length density, root surface area.For this analysis we focus only on one response variable: root biomass. Also, the paper repeats the analysis for 2 subsequent years therefore there are 2 blocking variables: year(2 years) and soil types (5 types). However, the statistical analysis presented here takes data for the year 2011 only. Multiple ANOVA is performed to test the effect of Water Salinity and Nitrogen Fertilizer rate on root biomass (in kg/ha) for 5 different soil depths. Each factor has a significant effect on the response variable separately but no interaction effect is found.

The following analysis was completed using data from Shihezi University's Department of Resources and Environmental Science. The title of the study was "Root Distribution and Growth of Cotton as Affected by Drip Irrigation with Saline Water." The study was based on a 3x2 factorial, completely randomized design. The response variables being analyzed were the total shoot biomass and the root-shoot ratio. The factors were water salinity (3 treatments levels) and N rate (2 treatment levels). It was found that for both response variables, both of the factors were significant - where the variation in the response variable could potentially be explained by something other than randomization. However, the interaction between the two factors were not found to be particularly significant.

The experiment below was replicated from a study from a research article titled: Root distribution and growth of cotton as affected by drip irrigation with saline water (see link below for reference). The study under question looked to examine the root length density and the effects N rate and Water Validity had on this response. A 3 x 2 (two factors, 1st with 3 levels, 2nd with 2 levels) factorial, completely randomized block design was utilized. The ANOVA model created suggested that N Rate and Water salinity together can explain the variation in root length density.

This experiment was to study the effect of irrigation water and n rate on Nitrogen uptake of cotton on stems. The data was collected from Shihezi University's Department of Resources and Environmental Science from the article "Root distribution and growth of cotton as affected by drip irrigation with saline water". This experiment was a 3x2 factorial design with completely randomized block. The three levels of irrigation water salinity were fresh water, brackish water, or saline water. The two rates of Nitrogen were 0 and 360 kg N/ha.There is a shortage of fresh water to some arid and semi-arid regions so there is an interest in using saline and brackish irrigation water to help increase crop yields however this can lead to a risk of soil salinization. The ANOVA model created suggested that the variation of Nitrogen uptake of cotton at the stem can be attributed to the Nrate.However when looking at water salinity, the variation in Nitrogen uptake of cotton can't be attributed to anything other than randomization.With the interaction, the total variation can’t be attributed to anything other than randomization so the effect of one factor is the same for all levels of the other factor when it comes to the Nitrogen uptake of Cotton at the stem.

This recipe replicates an analysis from a study titled "Yield traits of six clones of Miscanthus in the first 3 years following planting in Poland". In the study plant statistics were recorded for 6 different strains of a Miscanthus plant once each year for three years. The studies were blocked by year and the an analysis of variance was performed on the statistics (such as stem diameter and height) for the response variable of yield which was measured in weight of tuft.

This recipe for experimental design takes a look at a data set regarding the effects of treatment conditions, pepper type, and storage periods on the moisture content of peppers. This recipe focuses on demonstrating the proper usage of blocking in an experimental design to analyze the effects of specific factors while eliminating variation from other nuisance factors. The nuisance factor in this experiment will be referred to as 'treatment' and it describes the storage conditions of the experimental units (peppers) during experimentation.

This recipe replicates part of the analysis conducted in Rufino's study "Effect of substitution of soybean meal for inactive dry yeast on diet digestibility, lamb's growth and meat quality". A one factor, four level ANOVA is used to test the effect of Yeast Substitution Rate on the mean Nitrogen balance, the result shows that that the variation in mean nitrogen balance is not simply due to sample variation and the yeast substitution rate may help to explain the phenomenon. Wei Zou

This recipe presents an analysis on the effect of gender and education on fruit intake quantity. Using data from "Variety more than quantity of fruit and vegetable intake varies by socioeconomic status and financial hardship. Findings from older adults in the EPIC cohort" by UK researchers, an analysis was performed on the response variable of fruit quantity intake. After performing an ANOVA test, we rejected the null hypothesis that the variation of the two factors: gender and education, does not explain for the variation of the fruit intake quantity.

Following analysis is based on an article about how fertilization for planting influences seedling growth. The original experiment employed a randomized complete block design. This analysis includes two factors: plant species and different fertilizer; response variables are foliar nutient concentrations including nitrogen, phosphate and potassium; blocks include plant density numbers of plant population in each block and possible influence from plants nearby. ANOVA and follow-up Tukey's HSD test are conducted in order to analyse how different factors influence response variables. In this case, lurking variables could be humidity, temperature, locations and so on.

This recipe will conduct an experiment on a dataset representing the nitrogen uptake of cotton on leaves. The experiment will attempt to investigate the amount of nitrogen uptake of cotton and examine the analysis of variance between the N rate and Water Salinity on Cotton Uptake on Leaves in hopes of supporting or refuting the claim that the N Rate and Water Salinity on Cotton Uptake on Leaves do not have much variance. This shall be executed through a factorial, completely randomized block designed experiment. - Matthew Macchi

In this study, a two-factor, multi-level experiment is performed [using the research publication entitled "Effects of Plant Density on Yield and Canopy Micro Environment in Hybrid Cotton" (Yang et al., 2014)] to see if either plant density (in m^-2) or the number of bolls per unit of ground area (in m^-2) (or, both via interaction) has a statistically significant effect on the yield of seed cotton (in kg). In the dataset, the factor 'plants' refers to plant density and the factor 'bolls' refers to the number of bolls per unit of ground area. Additionally, this analysis' response variable is referred to in the dataset as 'seed.cotton.yield', which denotes the total yield of seed cotton in the analysis. In determining this level of significance, an ANOVA analysis is performed and Tukey Honest Significant Differences are computed.<br\>

The following analysis of a completely randomized experiment uses two-factor ANOVA to examine the feasibility of using rubber waste particles in cementitious composites. An analysis of variance is conducted to examine the effect of rubber waste volume content on two important mortar properties, using water/cement weight ratio as a blocking factor to increase precision.

2016 Projects

This project examines the pricing factors of diamonds by using a blocked design. The dataset contains both factors and continuous variables. ANOVA and ANCOVA are used in the analysis to determine whether a factor has a significant effect on the price of the diamond.

Kristen C. - This project looks at 452 observations from 1993 examining unemployment, the reasons for said unemployment, and information about those people. This analysis uses ANOVA, multiple models, and confidence intervals to understand whether race and reason have an effect of the duration of unemployment for these observations. By looking at the data and the patterns we can visually see it seems as though the data was collected randomly where there are not large amounts of “groupings” of duration.

(Benjamin B) The project examines the pricing of the diamonds. A block design is used to study the effects using ANOVA. The data contains a total of N=308 observations, with 3 variables. The response variable, also the continuous DV, is the pricing of the diamond, and the pair of categorical IVs are color and certification. Some topics that were studied include effect size, G*Power, multiple models, and confidence intervals. In the end, the results showed that there were differences in pricing of the diamond depending on color.

(Rajani D) This analysis looks at 2000 diamond prices in Singapore. The data set has 308 observations of diamonds and includes data on clarity, color, certification, carat, and price of the diamond. However, only the effect of clarity on price was analyzed while blocking on color. Methods include ANOVA, multiple models, and confidence intervals. Additionally, G*Power was used to determine the necessary sample size taking alpha and power levels into consideration.

(Trevor C.) For this recipe, a dataset of childrens’ health status in the U.S. in 1986 is analyzed. The health metric is a continuous Dependent Variable, which is dependent on factors including number of doctor visits, number of children per household, and access to healthcare. There were 485 observations. This data can be found under the Doctor section library in the Ecdat Package.

(Dede D.) This study contains tobacco information from 2724 Belgian households and 9 variables, taken from the Belgian household budget survey of 1995/1996. The data are supplied by the National Institute of Statistics, Belgium. This experiment will test whether or not occupation of the head of the household affects the Household Budgetshare of Tobacco, blocked on the region of the Belgian households.