Reference no: EM132400066
Medical Statistics Assignment -
Answer questions using SPSS and the data files related ("Heart_rate_HT19.xlsx" and "Blood_pressure_HT19.xlsx").
Question 1 - You want to estimate the mean resting heart rate in adults. The number of contractions of the heart per minute (bpm) is measured and recorded for 30 healthy individuals. The data is collected in the Excel file called "Heart_rate_HT19.xlsx".
a. Describe briefly (one or two sentences) your data set in words (no statistics is needed).
b. Show a histogram (for SPSS: use bins with a width of 8) with a normal curve and a Q-Q plot of the data.
c. Describe the purpose of generating these figures (graphs).
d. Based on the generated histogram and Q-Q plot, what conclusion can you draw about the distribution?
e. Use a statistic test to test if the data is normally distributed. Name the test that you used to test normal distribution and state the null hypothesis of the test.
f. Report the p-value obtained from the normality test. Based on the obtained p-value, should you reject or retain the null hypothesis?
g. What conclusion can you draw from this test and your previous graphs?
Question 2 - For this question, you should continue considering the data presented in "Heart_rate_HT19.xlsx" by summarizing the sample's central tendency and spread using appropriate measurements.
a. Which measures are appropriate to use to describe central tendency and spread of this sample?
b. Explain why these measures are appropriate to use based on the distribution of the data.
c. Use SPSS/R and compute both measures. Report your obtained values.
d. Explain how to calculate the median and the IQR manually.
Question 3 - You want to investigate if there is a difference in the concentrations of nitrogen oxides and hydrocarbons in a certain urban environment. You measure the concentrations of nitrogen oxides and hydrocarbons in microgram per cubic metre during ten days. The results of measurements are shown below:
Table 3.1. Nitrogen oxides concentrations (µg/m3)
|
Day
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
|
Nitrogen oxides
|
98
|
101
|
79
|
73
|
61
|
84
|
81
|
72
|
61
|
84
|
Table 3.2. Hydrocarbons concentrations (µg/m3)
|
Day
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
|
Hydrocarbons
|
108
|
118
|
89
|
91
|
76
|
93
|
88
|
96
|
86
|
87
|
a. Describe briefly your data set with words and the aim of the study (it is enough with one or two sentences).
b. Calculate mean and SD for both substance groups. Express your answers using one decimal place.
c. Generate a bar chart with error bars indicating the SD.
d. Illustrate the precision of your mean values by computing the standard error and the 95% confidence interval of the means for both substance groups. Express your answers using one decimal place.
e. Generate and report a 95% confidence interval of the difference in means between the two substances. Based in this interval, can you tell if there is a significant difference of the mean concentrations between the two substances? Draw a conclusion from this analysis. Express your answers using one decimal place.
Question 4 - You have collected data of age and diastolic blood pressure of 100 individuals. Your data is stored in the Excel file "Blood_pressure_HT19.xlsx".
a. Generate a histogram and a Q-Q plot for your variables. Show all four figures (graphs) in your report including figure numbering and descriptive figure legends.
b. Analyze the distribution of the two variables by inspecting the generated histograms and Q-Q plots. Which of the variables has a normal distribution and which has a uniform distribution?
c. Generate a new variable (recode into a different variable) where you group the individuals according to their age. Use the following grouping: 20-29 years, 30-39 years, 40-49 years, 50-60 years. Construct a table showing the frequency (number) and fraction (proportion) of individuals in each age group.
d. Based on the new variable that you have generated, construct a table that shows: number of individuals in each group, mean and SD of the blood pressure for each group. Tip: compute the values in SPSS/R and then construct the table in Word where you insert your computed values, as the example table below. Express your answers using one decimal place.
Table 5. Diastolic blood pressure (mmHg)
|
Age groups
|
N
|
Mean
|
SD
|
|
20-29
|
25
|
77.36
|
5.69
|
|
30-39
|
|
|
|
|
40-49
|
|
|
|
|
50-60
|
|
|
|
|
Total
|
100
|
|
|
e. Generate a bar chart for the age groups showing the mean and SE of the diastolic blood pressure.
f. Do you think that there is any difference in blood pressure between the age groups or is the difference you observe just due to chance? Discuss this.
Question 5 - Describe the 'hypothetico-deductive' model of how science is done, i.e., the process of hypothesis formulation and testing.
Question 6 - Most red-backed salamanders are red-striped whereas a few individuals are completely red. The ones being completely red are thought to be that in order to mimic another salamander species called Notophtalamus viridescens, which are poisonous for birds. You want to investigate if the red color variant is more successful in surviving than the red-striped variant. You set up an experiment in which 163 red-striped and 41 red individuals were exposed for predation from a natural bird population. After one week, 65 of the red-striped and 23 of the red salamanders were still alive. Does the red color variant have a higher survival rate than the red-striped? Construct a contingency table and test your hypothesis by an appropriate statistical test.
a. State a null and an alternative hypothesis.
b. Show your contingency table.
c. Which statistical test is appropriate to test your hypothesis and why?
d. Perform the statistical test and report the obtained p-value. Express your answer using two decimal places.
e. Should you retain or reject the null hypothesis? Draw a conclusion based on the obtained p-value.
Question 7 - The most common eye color in the world is brown/hazel (63%) followed by blue/green (10%). The remaining colors include e.g., amber, black, grey (27%). You want to test if people in a certain town in Italy follows the same eye color distribution as what has been globally observed. You recruit 100 participants from this town and record following frequency in eye color:
|
Brown/hazel
|
57
|
|
Blue/green
|
17
|
|
Other colors
|
26
|
|
Total
|
100
|
a. Define your problem and state a null and an alternative hypothesis.
b. Construct and show a table of observed and expected frequency of each categorical variable.
c. Use the Chi-square goodness of fit test and test your hypothesis. Report the chi-square value, df and p-value.
d. Draw a conclusion from your results.
Question 8 - You do preclinical research on a new drug. The drug is supposed to reduce tumor size in the brain. You set up an experiment with 10 mice. You measure the tumor size before and after the treatment. You record the following results of your experiment:
|
Mouse #
|
Tumor size (mm) before treatment
|
Tumor size (mm) after treatment
|
|
1
|
0.6
|
0.3
|
|
2
|
0.4
|
0.2
|
|
3
|
0.6
|
0.6
|
|
4
|
0.5
|
0.4
|
|
5
|
0.3
|
0.2
|
|
6
|
0.8
|
0.5
|
|
7
|
0.4
|
0.5
|
|
8
|
0.5
|
0.3
|
|
9
|
0.6
|
0.4
|
|
10
|
0.4
|
0.4
|
a. Write a short description of the aim of the study.
b. State your null and alternative hypothesis.
c. State your significance level of the test.
d. Test your hypothesis by performing an appropriate statistical test. Report the obtained p-value and draw a conclusion.
e. Show an appropriate figure indicating if there is a significant difference between before and after. The bar chart should include error bars indicating the SDs for each group. Use appropriate text in your figure legend.
Question 9 - In this experiment you have the same aim as in "Question 3". However, you use a different experimental design. Instead of measuring before and after you randomly allocate 10 mice in a placebo group and 10 mice in the treatment group (the group which receives the drug).
|
Mouse # (in control group)
|
Tumor size (mm) after placebo treatment
|
Mouse # (in treatment group)
|
Tumor size (mm) after drug treatment
|
|
1
|
0.6
|
11
|
0.3
|
|
2
|
0.4
|
12
|
0.2
|
|
3
|
0.6
|
13
|
0.7
|
|
4
|
0.5
|
14
|
0.4
|
|
5
|
0.3
|
15
|
0.2
|
|
6
|
0.8
|
16
|
0.5
|
|
7
|
0.4
|
17
|
0.5
|
|
8
|
0.5
|
18
|
0.3
|
|
9
|
0.6
|
19
|
0.4
|
|
10
|
0.4
|
20
|
0.4
|
a) Write a short description of the aim of the study
b) State your null and alternative hypothesis
c) State your significance level of the test
d) Compute and report a 95% confidence interval of the difference. Express your answer using three decimal places.
e) Draw a conclusion based on the 95% CI for the difference.
f) Generate and show a bar chart indicating if there is a significant difference between the groups. The bar chart should include error bars indicating the SDs for each group. Use appropriate text in your figure legend.
Question 10 - You want to find out whether the weight of parsley plants is influenced by using a fertilizer. You select 30 plants and randomly divides them into three groups of 10 plants each. You apply a biological fertilizer to the first group, a chemical fertilizer to the second group and no fertilizer at all to the third group. After a month you weigh all plants. You get the following results:
|
Biological fertilizer (weight in gram)
|
Chemical fertilizer (weight in gram)
|
Control group (no fertilizer; weight in gram)
|
|
64
|
65
|
55
|
|
62
|
62
|
45
|
|
57
|
58
|
46
|
|
52
|
58
|
49
|
|
54
|
61
|
61
|
|
48
|
57
|
52
|
|
56
|
55
|
42
|
|
47
|
54
|
50
|
|
63
|
55
|
48
|
|
61
|
66
|
52
|
a. Write a short summary of the aim of this experiment.
b. State your null and alternative hypothesis.
c. State your significance level of the test.
d. Test your hypothesis by performing appropriate statistical tests. Report the obtained p-values and draw a conclusion.
e. Show an appropriate figure indicating significant difference between the groups. The figure should include error bars indicating the SDs for each group. Use appropriate text in your figure legend.
f. Based on the results, should any of the fertilizer be preferred in front of the other one considering weight gain?
Note - You must: 1. submit your reports in time, 2. complete all tasks including all information required for the report as stated in the assignment, 3. report correct results and conclusions with only minor mistakes for all questions, 4. use appropriate figures, tables and statistics for the questions requiring such information, and 5. if you show figures, they should have proper labels on the x- and y-axis, including units if possible.
Attachment:- Medical Statistics Assignment & Data Files.rar