What assumptions should be satisfied in order to perform the analysis of variance for a randomized block design?
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What assumptions should be satisfied in order to perform the analysis of variance for a randomized block design?
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- what does MS stand for in analysis of variance?A pharmaceutical company conducted a study to test the effect of a new high blood medication. The company selected 15 subjects from a population. Each subject was randomly assigned to one of three treatment groups equally (i.e. each group consists of five subjects): Group 1 (10mg/day), Group 2 (50mg/day) and Group 3 (100mg/day). After 30 days, doctors measured the blood pressure of each subject. Summary of Analysis of Variance table is shown in Table 3. Table 3 Sum of Degree of Freedom Mean Source F Square Squares (i) Treatments (iv) 320 3.98 (ii) (iii) (v) (vi) Error (vii) Total (a) Calculate the value for (i)-(vii) from the above table. (b) Conduct a hypothesis test to test whether all treatment groups have the same mean using a 5% level of significance.Last school year, the student body of a local university consisted of 35% freshmen, 25% sophomores, 24% juniors, and 16% seniors. A sample of 300 students taken from this year's student body was taken to determine if there had been a significant change in % of students for each classification for this year as compared to last year. This analysis is an example of a Regression O Goodness of Fit Analysis of Variance Test of Independence
- Suppose a dataset has 3 variables, X₁, X₂ and X3. Each variable is standardized and a principal component analysis is then carried out using the standardized data. (a) Write down the total variance that would result. Justify your answer. (b) Suppose that Kaiser's criterion indicates 2 components should be retained. Write down variances for each of the 3 components that would be compatible with this observation. (c) Sketch a scree plot that indicates only one of the 3 components should be retained. (Note the corresponding variances for the components need not match those you give in part (b).)can ridge regression be applied if sample size is smaller than the number of predictors?Aggregate data were collected for a recent year in 44 Denver neighborhoods on various demographic measures, including the crime rate (# of crimes per 1000 population). A multiple linear regression was used to build a predictive model predicting crime rate from four of these neighborhood characteristics: population size, % of children in the population, % of participation in free school lunch, and % change in household income over recent years. A portion of the ANOVA table from this model is below. Analysis of Variance Sum of DF Squares Mean Source Square F Value Pr>F Model 299771 74943 <.0001 Error Corrected Total 43 473806 Provide the 5 values that have been omitted from this table. Specifically, provide: df(model), df(error), SS(error), MS(error), and the F statistic. Include intermediate calculations wherever used.
- Suppose that different amounts of fertilizer had been used in different fields that were involved in trials of different types of wheat seeds. (a) Explain how the use of different amounts of fertilizer confounds the experimental analysis in the absence of randomization. (b) Considering the regression models with explanatory variables, if the amount of fertilizer were known, how could an analyst adjust for this confounding effect? (a) Choose the correct answer below. O A. Seed variety is highly correlated with fertilizer use. O B. Yield is uncorrelated with fertilizer use. O C. Differences in yield could be due to fertilizer rather than seed variety. O D. Fertilizer use is not uniform for each type of seed. (b) Choose the correct answer below. O A. Add a quantitative explanatory variable for the amount of fertilizer used. O B. Add a categorical explanatory variable for whether fertilizer was used. OC. Add a quantitative explanatory variable for whether fertilizer was used. O D. Add a…To improve driver safety, Federal government is always encouraging states to lower the variance of stopping distances of automobiles on wet roads. LDOTD engineers claim that the variance of stopping distances of automobiles on wet roads in Louisiana is really smaller than the variance of stopping distances of automobiles on dry roads because of the materials used to build the roads. To test the claim for allocation of highway funds, Federal Department of Transportation tested 16 automobiles traveling at the same speed for stopping distances on wet roads and then on the dry roads in Louisiana. On the wet roads the standard deviation of the stopping distances was 32 feet while on dry roads it was 16 feet. Test the claim at 5% level of significance.A study compared physical activity among 4 different professions. A total sample size of 32 people was studied (8 people from each program) using a one-way analysis of variance. The Error Sum of Squares is SS Error = 40. What is the Mean Square Error (MS Error)?
- Identifying individuals with a high risk of Alzheimer’s disease usually involves a long series of cognitive tests. However, researchers have developed a 7-Minute Screen, which is a quick and easy way to accomplish the same goal. To assess if the 7-Minute Screen is as effective as the complete series of tests, a researcher administered both tests to a group of ten patients and got a correlation coefficient of 0.84. What percent of the variance of the cognitive scores is predicted from the 7-Minute Screen scores in the example above?Students in one class are asked to complete the same questionnaire 3 times throughout the semester: at the beginning, at the midterm, and at the end. The purpose of the questionnaire is to track students' perception of their progress at different points in the semester. Scores at Time 1 (beginning of the semester), Time 2 (midterm), and Time 3 (end of semester) are compared against one another. What type of analysis of variance would be appropriate for examining the results from this dataset?A study involving 20 college students aimed to investigate the impact of a novel study technique on their exam performance. The researchers recorded the exam scores of each student both before and after the implementation of the new study technique. On average, there was an observed increase of 7 points in exam scores after the new technique was utilized. The variance of the score differences across the entire sample was determined to be 36. To assess whether there is a statistically significant difference in exam scores before and after implementing the technique, a two-tailed test with a significance level of 0.05 (alpha = 0.05) was employed. Is there a significant difference?