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MATH1065: Quantitative Methods- Health Statistical Analysis Assignment
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Internal Code: MAS1173
Now that the data are “clean”, perform Exploratory Data Analysis to determine whether there are
significant gender differences in calcium levels:
(f) Using your "clean" data and MINITAB, obtain Descriptive Statistics for Age and Cammol. Compare the mean and standard deviation from the “messy” dataset with the mean and standard deviation from your “clean” dataset. Does cleaning the data make a difference? Explain briefly.
(g) Now construct boxplots of Cammol by Gender. Do you believe differences exist in Cammol levels with respect to Gender? Why or why not? Explain briefly.
(h) Now construct boxplots of Cammol by Lab. Do you believe differences exist in Cammol levels with respect to Lab? Why or why not? Explain briefly.
(i) One of the objectives of collecting this data was to propose a reference range of values that are to be considered “normal” for calcium. Looking at the results for Cammol for each of the labs, explain why a single reference range may be difficult to establish.
Question 3:
Are we getting enough sun? Vitamin D status has emerged as a significant public health issue in Australia and New Zealand. The most clearly established effects of vitamin D are to maintain calcium, and to optimise bone health and muscle function. An estimated 31% of adults in Australia have inadequate vitamin D status, increasing to more than 50% in people residing in southern states.1
The main source of vitamin D for people residing in Australia and New Zealand is exposure to sunlight as most adults obtain no more than 5%–10% of their vitamin D requirement from dietary sources. Population groups most at risk of vitamin D deficiency are the elderly and/or disabled, people with chronic illness, and others who regularly avoid sun exposure or work indoors.
Vitamin D status is checked by measuring serum 25-hydroxyvitamin D [25-OHD] concentration. In one
study2 it is reported that the serum 25-OHD levels in healthy adults are Normally distributed with mean of 68.3 nmol/L and a standard deviation of 29.5 nmol/L.
For the following questions, use MINITAB when requested and show your MINITAB output. Make sure you use correct statistical notation when expressing probabilities and round off each result with a comment.
(a) A serum 25-OHD level below 50 is indicative of inadequate vitamin D status. What percentage of otherwise healthy adults fall in that category? For full marks, provide a correct probability statement and include your MINITAB output.
(b) For optimal musculoskeletal health, a serum 25-OHD level between 60 and 70 nmol/L is required at the end of summer. What percentage of healthy adults fall in this range? For full marks, include a correct probability statement and appropriate MINITAB output.
(c) Suppose that for a randomly chosen adult, the 25-OHD level is 32 nmol/L. In which percentile does this vitamin D level fall? For full marks, provide a correct probability statement and include your MINITAB output.
(d) Suppose we plan to observe the mean serum 25-OHD levels of 4 randomly selected healthy adults. State the distribution of this mean (given reason). Ensure you include a justification as well as the values of the mean and standard deviation in your answer.
(e) If four healthy adults are randomly selected, find the probability that their mean 25- OHD level is adequate (above 50 nmol/L). Ensure you include an appropriate probability statement, your MINITAB output as well as any extra calculations.
(f) If we use the 1.5×IQR rule to identify outliers, how large would an observation need to be in order to be labelled an outlier? For full marks, provide an appropriate probability statement as well as show calculations and MINITAB output that support your answer.
Health Statistical Analysis Assignment:
Question 1: Are you getting enough sleep? Everyone needs to get enough sleep. Sleep helps keep your mind and body healthy. Most adults need 7 to 8 hours of good quality sleep on a regular schedule each night. Getting enough sleep is not only about total hours of sleep. It is also important to get good quality sleep on a regular schedule, and feel rested upon waking up. Self-reported amount of sleep per night by students in this course is stored in a MINITAB worksheet called Sleep.MTW, which you can download from the Data files folder on the course website. For full marks, ensure that appropriate axis labels and meaningful titles are included with all your graphical displays for this question. (a)Use MINITAB to produce histograms of the amount of sleep reported by male and by female students. For full marks, ensure appropriate axis labels and a meaningful title are included in each histogram. Additional MINITAB instructions: Once you have obtained the histograms, change the number of intervals to 10 as follows. Right-click bars of a histogram and select Edit Bars... In the dialogue box that opens switch to the tab called Binning, click the radio button next to ‘Number of intervals’ and type the number ‘10’ into the box. Click OK. (b)Use MINITAB to produce Descriptive Statistics for the amount of sleep per night, grouped by gender. (c)Use MINITAB to produce boxplots of the amount of sleep per night for the two genders, shown horizontally within the same graph. For full marks ensure that appropriate axis labels and a meaningful title are included with your graph. (d)Using your output from (a) to (c), comment on the shape of the distribution of the amount of sleep per night, broken down by gender. In particular, briefly describe: 1. The shape of the distribution (skewed or symmetric); 2. Whether there appear to be any outliers; 3. The appropriate measures of central tendency & dispersion. For full marks in this question, ensure you justify your choice of measures to describe & compare central tendency and dispersion, and interpret the corresponding values. (e)What are your conclusions regarding the amount of sleep students get? Explain briefly. Do not simply repeat your answers to previous parts of this question! Question 2: Are there problems with the data? Before performing any statistical analysis it is very important that the data have as much integrity as possible. Data cleaning is a process including detection and then correction of problem values. Some common sources of problem values are: 1. missing data; 2. typing errors on data entry; 3. column shift (data for one variable column was entered under the adjacent column); 4. decimal point errors. Descriptive statistics and graphs can be used to identify problem values that are missing, appear erroneous, or are simply not possible. The data for this question are stored in a MINITAB worksheet called Messy Data.MTW and come from a clinical investigation of blood calcium levels for subjects aged 65 and older. The researchers wanted to know if significant gender differences existed between subjects. Testing was done at commercial laboratories and there are a number of problems with the data. The data consist of 58 subjects representing 24 males and 34 females. Blood samples taken from these subjects were analysed at 3 different locations. The categorical variables in this dataset are Gender (1 for male, 2 for female) and Lab (one of 3 labs where blood was analysed). The numerical variables in this dataset are Age (years) and Cammol (raw calcium, mmol/L). First you are going to check the validity of the data. Following the steps outlined below, determine if the dataset is “messy” with variable values that appear incorrect. For full marks, ensure that appropriate axis labels and meaningful titles are included with all your graphical displays for this question. (a) Use MINITAB to produce Descriptive Statistics and a boxplot for the variable Age. Is there any evidence of problem values for Age? How do you know? Explain briefly. (b) Use MINITAB to produce Descriptive Statistics and a boxplot for the variable Cammol. Is there any evidence of problem values for Cammol? How do you know? Explain briefly. (c) Use MINITAB to produce boxplots of Cammol by categorical variable Gender, shown horizontally within the same graph. Is there any evidence of problem values for Gender? How do you know? Explain briefly. (d) Use MINITAB to produce boxplots of Cammol by categorical variable Lab, shown horizontally within the same graph. Is there any evidence of problem values for Lab? Is there further evidence of problem values for Cammol? How do you know? Explain briefly. (e) Attempt to recover the correct values for the problem values identified in parts (a) to (d) by looking up the true values from the actual data records stored in a file called Patient record.pdf. Using a table like the one shown below, catalogue the problem values and the changes that were made to clean the dataset.
Now that the data are “clean”, perform Exploratory Data Analysis to determine whether there are
significant gender differences in calcium levels:
(f) Using your "clean" data and MINITAB, obtain Descriptive Statistics for Age and Cammol. Compare the mean and standard deviation from the “messy” dataset with the mean and standard deviation from your “clean” dataset. Does cleaning the data make a difference? Explain briefly.
(g) Now construct boxplots of Cammol by Gender. Do you believe differences exist in Cammol levels with respect to Gender? Why or why not? Explain briefly.
(h) Now construct boxplots of Cammol by Lab. Do you believe differences exist in Cammol levels with respect to Lab? Why or why not? Explain briefly.
(i) One of the objectives of collecting this data was to propose a reference range of values that are to be considered “normal” for calcium. Looking at the results for Cammol for each of the labs, explain why a single reference range may be difficult to establish.
Question 3:
Are we getting enough sun? Vitamin D status has emerged as a significant public health issue in Australia and New Zealand. The most clearly established effects of vitamin D are to maintain calcium, and to optimise bone health and muscle function. An estimated 31% of adults in Australia have inadequate vitamin D status, increasing to more than 50% in people residing in southern states.1
The main source of vitamin D for people residing in Australia and New Zealand is exposure to sunlight as most adults obtain no more than 5%–10% of their vitamin D requirement from dietary sources. Population groups most at risk of vitamin D deficiency are the elderly and/or disabled, people with chronic illness, and others who regularly avoid sun exposure or work indoors.
Vitamin D status is checked by measuring serum 25-hydroxyvitamin D [25-OHD] concentration. In one
study2 it is reported that the serum 25-OHD levels in healthy adults are Normally distributed with mean of 68.3 nmol/L and a standard deviation of 29.5 nmol/L.
For the following questions, use MINITAB when requested and show your MINITAB output. Make sure you use correct statistical notation when expressing probabilities and round off each result with a comment.
(a) A serum 25-OHD level below 50 is indicative of inadequate vitamin D status. What percentage of otherwise healthy adults fall in that category? For full marks, provide a correct probability statement and include your MINITAB output.
(b) For optimal musculoskeletal health, a serum 25-OHD level between 60 and 70 nmol/L is required at the end of summer. What percentage of healthy adults fall in this range? For full marks, include a correct probability statement and appropriate MINITAB output.
(c) Suppose that for a randomly chosen adult, the 25-OHD level is 32 nmol/L. In which percentile does this vitamin D level fall? For full marks, provide a correct probability statement and include your MINITAB output.
(d) Suppose we plan to observe the mean serum 25-OHD levels of 4 randomly selected healthy adults. State the distribution of this mean (given reason). Ensure you include a justification as well as the values of the mean and standard deviation in your answer.
(e) If four healthy adults are randomly selected, find the probability that their mean 25- OHD level is adequate (above 50 nmol/L). Ensure you include an appropriate probability statement, your MINITAB output as well as any extra calculations.
(f) If we use the 1.5×IQR rule to identify outliers, how large would an observation need to be in order to be labelled an outlier? For full marks, provide an appropriate probability statement as well as show calculations and MINITAB output that support your answer.