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For normality, minimum two graphs. Note: If using R, for Levene's test, install the R package "car". Does the response variable need any transformation? Why? e) Compare vitamin D levels for country A and country B at a significance level of 5% using a t- test, one-way ANOVA, and regression. Compare the results of all three techniques. For one-way ANOVA use t-test (LSD. test). Plot t-test and regression. Note: use the "Question_1_Country" dataset for this question. If you are using R, for the LSD. test function, install the package "agricolae". f) Write down the contrast and its related hypotheses to compare country A with country B for their vitamin D levels. Perform the contrast both by hand-calculation and using a statistical package and compare the answers. g) Change the variable Age from a numerical variable to a categorical variable with two levels. You need to select the criteria for this categorising. However, make sure you have enough observations in each group. Compare the variances of these two levels using Levene's test: You may need to change the criteria for Age group membership a few times, to get an appropriate spread of observations across groups. Before categorising, a summary of the variable "Age" might be useful: summary(Vitamin_DSAge) Min. 1st Qu. Median Mean 3rd Qu. 20.00 36.00 44.00 41.62 47.00 R code for solution: New Age

For normality, minimum two graphs. Note: If using R, for Levene's test, install the R package "car". Does the response variable need any transformation? Why? e) Compare vitamin D levels for country A and country B at a significance level of 5% using a t- test, one-way ANOVA, and regression. Compare the results of all three techniques. For one-way ANOVA use t-test (LSD. test). Plot t-test and regression. Note: use the "Question_1_Country" dataset for this question. If you are using R, for the LSD. test function, install the package "agricolae". f) Write down the contrast and its related hypotheses to compare country A with country B for their vitamin D levels. Perform the contrast both by hand-calculation and using a statistical package and compare the answers. g) Change the variable Age from a numerical variable to a categorical variable with two levels. You need to select the criteria for this categorising. However, make sure you have enough observations in each group. Compare the variances of these two levels using Levene's test: You may need to change the criteria for Age group membership a few times, to get an appropriate spread of observations across groups. Before categorising, a summary of the variable "Age" might be useful: summary(Vitamin_DSAge) Min. 1st Qu. Median Mean 3rd Qu. 20.00 36.00 44.00 41.62 47.00 R code for solution: New Age

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Country A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B Gender Male Male Male Male Male Female Female Female Female Female Other Other Other Other Other Male Male Male Male Male Female Female Female Female Female Other Other Other Other Other Male Male Male Male Male Female Female Female Female Female Other Other Other Other Other Male Male Male Male Male Female Female Female Female Female Other Other Other Other Other Male Male Male Male Male Female Female Female Female Female Other Other Other Other Other Male Male Male Male Male Female Female Female Female Female Other Other Other Other Other Sun_Exposure Low Low Low Low Low Low Low Low Low Low Low Low Low Low Low Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate High High High High High High High High High High High High High High High Low Low Low Low Low Low Low Low Low Low Low Low Low Low Low Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate High High High High High High High High High High ******* High High High High High Age 37 31 33 38 37 36 32 36 32 37 39 33 32 38 37 34 22 38 38 38 33 37 39 38 38 37 21 38 39 30 38 39 23 37 35 34 37 30 37 39 36 37 37 38 29 52 47 46 45 47 47 46 41 42 47 51 47 49 35 51 49 47 46 41 47 49 43 48 47 49 45 49 49 40 47 45 49 45 47 47 41 44 51 34 47 49 46 47 46 45 Vitamin_D_Level 45 40 39 42 38 38 39 37 44 38 43 36 41 44 34 48 57 38 45 37 60 40 42 42 44 39 38 39 45 47 55 59 46 55 51 49 51 62 55 53 53 66 53 51 57 53 47 57 47 51 49 53 55 45 48 51 48 46 51 45 45 58 48 55 52 44 48 48 48 62 ! 52 52 55 65 55 62 65 52 57 62 60 62 64 63 63 63 62 61 67 75
Transcribed Image Text:Country A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B Gender Male Male Male Male Male Female Female Female Female Female Other Other Other Other Other Male Male Male Male Male Female Female Female Female Female Other Other Other Other Other Male Male Male Male Male Female Female Female Female Female Other Other Other Other Other Male Male Male Male Male Female Female Female Female Female Other Other Other Other Other Male Male Male Male Male Female Female Female Female Female Other Other Other Other Other Male Male Male Male Male Female Female Female Female Female Other Other Other Other Other Sun_Exposure Low Low Low Low Low Low Low Low Low Low Low Low Low Low Low Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate High High High High High High High High High High High High High High High Low Low Low Low Low Low Low Low Low Low Low Low Low Low Low Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate High High High High High High High High High High ******* High High High High High Age 37 31 33 38 37 36 32 36 32 37 39 33 32 38 37 34 22 38 38 38 33 37 39 38 38 37 21 38 39 30 38 39 23 37 35 34 37 30 37 39 36 37 37 38 29 52 47 46 45 47 47 46 41 42 47 51 47 49 35 51 49 47 46 41 47 49 43 48 47 49 45 49 49 40 47 45 49 45 47 47 41 44 51 34 47 49 46 47 46 45 Vitamin_D_Level 45 40 39 42 38 38 39 37 44 38 43 36 41 44 34 48 57 38 45 37 60 40 42 42 44 39 38 39 45 47 55 59 46 55 51 49 51 62 55 53 53 66 53 51 57 53 47 57 47 51 49 53 55 45 48 51 48 46 51 45 45 58 48 55 52 44 48 48 48 62 ! 52 52 55 65 55 62 65 52 57 62 60 62 64 63 63 63 62 61 67 75
Scientists claim that there is a possible relationship between the severity of Covid-19 and a low level of blood vitamin D. The normal level for vitamin D is around 30ng/ml. For this reason, the vitamin D blood level has been measured for 2 countries, A and B, and recorded in a Microsoft Excel file (Vitamin_D.xlsx). Enter this Excel file into the statistical package of your choice and answer all questions: (Please add the code and output to your answers.) a) Find the number of observations, mean, standard deviation of vitamin D level for the variables Country, Gender, and Sun_ Exposure using the statistical package of your choice: b) Write down the statistical hypotheses for three separate analyses comparing the means of the groups in the following variables: (1) Country, (2) Gender, and (3) Sun_ Exposure. Estimate the treatment effects for each of these three factors. Note: For the next questions, use a statistical software to randomly sample 30 observations for each Country, and save this subset of observations in a new dataset called "Question_1_Country". In SPSS: Data > Select Cases > Random sample of cases (you can save the random observations as a .sav or an excel file, if using SPSS). In R: you can use the following code to perform this random sampling. Learn this procedure as you may need to use it for other sections. Note: every time you run the following code, you will get a different dataset. Therefore, you will get different outputs (because of the random nature of random sampling). ### 30 Random observations for Country A ### Country A<subset (Vitamin D, subset= Country=="A") C.A - Country A[sample(nrow(Country_A), 30),] ### 30 Random observations for Country B ### Country B < subset (vitamin D, subset=Country--"B") C.B - Country_B[sample (nrow(Country_B), 30),] ### Combining them in a new dataset ### Question 1 Country <- rbind(C.A, C.B) View(Question_1_Country) c) Read the above code carefully and explain what each line is doing. d) To investigate the difference in vitamin D level between countries, write down the general assumptions of the appropriate statistical test, and check them using graphs and/or outputs from your statistical package of choice. Note: use the "Question_1_Country" dataset for this question. For normality, minimum two graphs. Note: If using R, for Levene's test, install the R package "car". Does the response variable need any transformation? Why? e) Compare vitamin D levels for country A and country B at a significance level of 5% using a t- test, one-way ANOVA, and regression. Compare the results of all three techniques. For one-way ANOVA use t-test (LSD. test). Plot t-test and regression. Note: use the "Question_1_Country" dataset for this question. If you are using R, for the LSD. test function, install the package "agricolae". f) Write down the contrast and its related hypotheses to compare country A with country B for their vitamin D levels. Perform the contrast both by hand-calculation and using a statistical package and compare the answers. g) Change the variable Age from a numerical variable to a categorical variable with two levels. You need to select the criteria for this categorising. However, make sure you have enough observations in each group. Compare the variances of these two levels using Levene's test: You may need to change the criteria for Age group membership a few times, to get an appropriate spread of observations across groups. Before categorising, a summary of the variable "Age" might be useful: summary(Vitamin_D$Age) Min. 1st Qu. Median Mean 3rd Qu. Max 20.00 36.00 44.00 41.62 47.00 65.00 R code for solution: New Age <- ffelse (Vitamin DSAge 40, 'Age_level_1', 'Age_level_2') ### Adding the new variable to our original dataset # Vitamin DSNew Age <- New Age #### Count the number of each level ###### table(vitamin DSNew Age) Now, check the equality of variances of vitamin D level between these two age groups using Levene's test: Note: use the standard residuals for the variance equality check. h) Perform a two-way ANOVA to investigate the effects of Sun_ Exposure (3 levels) and Country (2 levels) on vitamin D levels. Write all statistical hypotheses and the factorial models, produce the ANOVA table and Tukey's HSD test with graphs (if needed), and conclusions based on a 5% significance level. Note: Use a statistical package to randomly sample 5 observations for each combination of Sun_Exposure and Country, combine the datasets together and call it "Question_1_Factorial". In SPSS: Data > Select Cases > Random sample of cases (you can save the random
Transcribed Image Text:Scientists claim that there is a possible relationship between the severity of Covid-19 and a low level of blood vitamin D. The normal level for vitamin D is around 30ng/ml. For this reason, the vitamin D blood level has been measured for 2 countries, A and B, and recorded in a Microsoft Excel file (Vitamin_D.xlsx). Enter this Excel file into the statistical package of your choice and answer all questions: (Please add the code and output to your answers.) a) Find the number of observations, mean, standard deviation of vitamin D level for the variables Country, Gender, and Sun_ Exposure using the statistical package of your choice: b) Write down the statistical hypotheses for three separate analyses comparing the means of the groups in the following variables: (1) Country, (2) Gender, and (3) Sun_ Exposure. Estimate the treatment effects for each of these three factors. Note: For the next questions, use a statistical software to randomly sample 30 observations for each Country, and save this subset of observations in a new dataset called "Question_1_Country". In SPSS: Data > Select Cases > Random sample of cases (you can save the random observations as a .sav or an excel file, if using SPSS). In R: you can use the following code to perform this random sampling. Learn this procedure as you may need to use it for other sections. Note: every time you run the following code, you will get a different dataset. Therefore, you will get different outputs (because of the random nature of random sampling). ### 30 Random observations for Country A ### Country A<subset (Vitamin D, subset= Country=="A") C.A - Country A[sample(nrow(Country_A), 30),] ### 30 Random observations for Country B ### Country B < subset (vitamin D, subset=Country--"B") C.B - Country_B[sample (nrow(Country_B), 30),] ### Combining them in a new dataset ### Question 1 Country <- rbind(C.A, C.B) View(Question_1_Country) c) Read the above code carefully and explain what each line is doing. d) To investigate the difference in vitamin D level between countries, write down the general assumptions of the appropriate statistical test, and check them using graphs and/or outputs from your statistical package of choice. Note: use the "Question_1_Country" dataset for this question. For normality, minimum two graphs. Note: If using R, for Levene's test, install the R package "car". Does the response variable need any transformation? Why? e) Compare vitamin D levels for country A and country B at a significance level of 5% using a t- test, one-way ANOVA, and regression. Compare the results of all three techniques. For one-way ANOVA use t-test (LSD. test). Plot t-test and regression. Note: use the "Question_1_Country" dataset for this question. If you are using R, for the LSD. test function, install the package "agricolae". f) Write down the contrast and its related hypotheses to compare country A with country B for their vitamin D levels. Perform the contrast both by hand-calculation and using a statistical package and compare the answers. g) Change the variable Age from a numerical variable to a categorical variable with two levels. You need to select the criteria for this categorising. However, make sure you have enough observations in each group. Compare the variances of these two levels using Levene's test: You may need to change the criteria for Age group membership a few times, to get an appropriate spread of observations across groups. Before categorising, a summary of the variable "Age" might be useful: summary(Vitamin_D$Age) Min. 1st Qu. Median Mean 3rd Qu. Max 20.00 36.00 44.00 41.62 47.00 65.00 R code for solution: New Age <- ffelse (Vitamin DSAge 40, 'Age_level_1', 'Age_level_2') ### Adding the new variable to our original dataset # Vitamin DSNew Age <- New Age #### Count the number of each level ###### table(vitamin DSNew Age) Now, check the equality of variances of vitamin D level between these two age groups using Levene's test: Note: use the standard residuals for the variance equality check. h) Perform a two-way ANOVA to investigate the effects of Sun_ Exposure (3 levels) and Country (2 levels) on vitamin D levels. Write all statistical hypotheses and the factorial models, produce the ANOVA table and Tukey's HSD test with graphs (if needed), and conclusions based on a 5% significance level. Note: Use a statistical package to randomly sample 5 observations for each combination of Sun_Exposure and Country, combine the datasets together and call it "Question_1_Factorial". In SPSS: Data > Select Cases > Random sample of cases (you can save the random
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