Assessment 3: Public Health Data Analysis
Section A: Understanding the context (8 marks)
The Council of Roberton is really concerned about the number of recent road accidents, and has called a community meeting. They have called for an enquiry named the Roberton report. You are part of the team to help them make decisions for their community.
The aim of your assignment is to investigate injury prevention and road safety.
Let’s ask some preliminary questions about accidents.
Additional resources:
Stopping distances: speed and braking (graph)
Stopping distances on wet and dry roads (table)
What factors may influence road safety and contribute to the road toll?
List 2 direct factors and 2 upstream factors. (4 marks)
A person’s reaction time can be critical to their safety. Consider that you are driving a good car in dry conditions at 60 km/hr and a child unexpectedly steps out from behind a parked car which is only 45 meters in front of you. Will you have enough time to stop?
Using the graph provided, state the distance travelled in meters if the car is travelling at 60 km/hr on a dry road. (no units required) (1 mark)
Using the table provided, state the distance travelled in meters if the car is travelling at 100 km/hr on a dry road. (no units required) (1 mark)
Now that we know that driver reaction distance in meters and car braking distance play a role in stopping a car.
Describe your findings of whether the car stopped at 60 km/hr or 100 km/hr for the child 45 m away by completing these two sentences:
o At 60 km/hr, the car will … o At 100 km/hr, the car will … (2 marks)
Section B: Describing & Summarising Data (20.5 marks)
It is important to have an understanding of your data and variables in research.
Before we start our analysis, we need to understand our population and the sampling methods used. Then, before we do any statistical tests, we need to describe the data with descriptive statistics and graphs.
Resources: see the “Useful Assessment Resources” folder for a PDF of the questions in the quiz, as well as the “Formula Sheet & Tables” document.
5. The Roberton sample was obtained by stratified random sampling with the strata based proportionally on age groups. This type of sampling may be necessary for investigating the average reaction time.
What had to be known to achieve it? (Select 1 or more correct answers) [3 marks]
A sampling frame of the entire population, along with their age and the proportions of each sub-group in the population is needed to achieve this stratified sampling.
Age is not relevant to the condition investigated and therefore will have no effect on reaction time or cognition.
Stratified sampling allows for sequential order within the sample which ensures that the attribute studied is random.
Stratified sampling allows for the sampling to be random within each sub-group being investigated (in this case, each age group) – so the proportions of the different age groups are the same in the population and the sample.
Age is often referred to as “the universal confounder” – so reaction time might be affected by age.
A sampling frame which divides the population into a set of different coherent areas and randomly selects areas to assess.
Create a table of variables by matching the type of data to each variable listed below. [6 marks]
Variable Descriptors Type of Data
Age Years (recorded as the date of birth)
Gender Male (M) and Female (F)
Handedness Left Handed (LH) and Right Handed (RH)
Physical activity Hours per week
Reaction time Seconds
Reaction time: Slow and Quick Slow (>= 0.31 sec) & Quick (<0.31 sec)
A graph is a really useful way to see how the data is distributed.
Therefore your next step is to:
Draw a graph of reaction time.
Attach the graph as a file below.
In the text box, type the file name only. [5 marks]
Answers to FAQ for this question:
No other variables are required for this graph – only “reaction time”.
Part of the purpose of this question is for you to figure out what type of graph is appropriate & then graph it.
Time to identify the appropriate numerical summaries to describe the typical reaction time of individuals in Roberton.
What is the mean of the sample? (4 decimal places) [1 mark]
What is the median of the sample? (4 decimal places) [1 mark]
Indicate if this statement is True or False in regards to the graph and statistics obtained so far.
“The graph shows a fairly normal distribution, and the values of the mean & median are fairly similar.
Hence, the mean is an appropriate statistic to describe reaction time.” [0.5 mark]
Pick the 2 appropriate summary statistics you should report regarding the reaction time of the sample of the Roberton people who are aged 6 – 80 years? Select one or more: [2 marks]
Range
Mean
Inter-quartile range
Mode
Median
Standard deviation
We need some more information to continue.
What is the reaction time range of your sample? (4 decimal places) [1 mark]
What is the reaction time standard deviation (SD) of your sample? (4 decimal places) [1 mark]
Section C: Describing & Summarising Data using Graphs and % (11 marks)
Let’s have a closer look at some key variables: Gender and Reaction time: slow vs quick.
To answer this section, you’ll need to create a summary table that shows the frequency and percentages.
You’ll also need to create an appropriate graph & interpret your results.
Slow n (%) Quick n (%) Total n (%)
Male
Female
Total
What overall outcome percentage should be calculated for this table? [1 mark]
Questions 15 to 19 below are (1 decimal place, no units required) format.
What is the numerical value of the percentage identified above? [1 mark]
What is the percentage in the “females – slow” box of your table? [0.5 mark]
What is the percentage in the “females – quick” box of your table? [0.5 mark]
What is the percentage in the “males – slow” box of your table? [0.5 mark]
What is the percentage in the “males – quick” box of your table? [0.5 mark]
Graph the data from your table of Gender and Reaction time: slow and quick.
After creating your graph select the graph below which best represents your data. [1 mark]
The graphs in the previous question are a good way to look at the data but are not complete.
How could you improve the graph in the question above? (Select all that apply) [3 marks]
It needs a more detailed title
Label the y-axis
Requires a legend
Legend requires more detail
Label the x-axis
It needs a shorter title
Write a brief conclusion of Section C. [3 marks]
Section D: Conducting Statistical tests (25.5 marks)
Great news, the Council of Roberton has found your preliminary results very valuable.
Now let’s do some statistical tests to investigate the data in more detail.
The first thing we’ll be looking at is: Do males and females differ in their reaction times?
Over the next few questions you will need to create a summary table and conduct a test of significance (95% CI and p-value) between the males and females to answer if there is a difference between their reaction times. Follow all steps clearly and write a clear conclusion.
State the Null & Alternative hypotheses [2 marks]
For the following, match the assumption with how it is met in this test. [4 marks]
Distribution of data in each group:
Groups being compared are:
Patients within each group are:
Equality of group variance using Levenes (ratio) test:
What is the reaction time mean for females? (4 decimal places) [1 mark]
What is the reaction time standard deviation for females? (4 decimal places) [1 mark]
What is the reaction time mean for males? (4 decimal places) [1 mark]
What is the reaction time standard deviation for males? (4 decimal places) [1 mark]
Calculate the difference in means (Female – Male) (4 decimal places) [1 mark]
Calculate standard error (SE) (4 decimal places) [2 marks]
Calculate the degrees of freedom [1 mark]
What is the T-multiplier? (2 decimal places) [1 mark]
Congratulations. You’ve now got the necessary statistics to calculate the p-value and 95%CI
Calculate the T-statistic (2 decimal places). [1 mark]
What is the p-value? [1 mark]
Considering the p-value in the previous question, answer if the following statement regarding the pvalue is TRUE or FALSE? [0.5 mark]
“As the p-value is > 0.05, the p-value is not significant. Therefore, in this sample we can not justify rejecting the null hypothesis.”
What is the 95% Confidence Interval? (3 decimal places) [1 mark]
Hint: Write your answer as x.xxx to y.yyy, e.g. -0.123 to 1.234
The correct description and interpretation of your 95% Confidence Interval is: [3 marks]
Write a conclusion paragraph about your statistical conclusions for Section D. [4 points, 1 mark each = 4 marks]
Section E: Interpreting statistical test results (13 marks)
Now, let’s look at the relationship between handedness and reaction time: slow vs quick.
Hint: For this question, you’ll need your data summarised in the table below.
Slow Quick Total
Left
Right
Total
For the relationship between Handedness (left) and Reaction time (slow) calculate the Odds Ratio (2 decimal places). [1 mark]
For the relationship between Handedness (left) and Reaction time (slow): interpret the results of the odds ratio from the previous question [2 marks]
Next, you will calculate the SE and 95% CI of the Odds Ratio, and interpret the 95% CI.
You will need your odds ratio (handedness (left) and reaction time (slow)) from the earlier question to 6 decimal places.
Calculate the standard error of the odds ratio: (4 decimal places) [1 mark]
Calculate 95% CI of the Odds Ratio. (3 decimal places) [1 mark] Hint: Write your answer as x.xxx to y.yyy. e.g. 0.123 to 1.234.
Interpret your 95 % CI from the previous question, by filling in the gaps to the sentence below. [3 marks]
This interval <A> the value of <B>, so it <C> statistically significant
A: includes; excludes
B: 0; 1
C: is; is not
Calculate the Z-statistic (2 decimal places) [1 mark]
Calculate the p-value (3 decimal places) [1 mark]
Interpret the p-value from the previous question [3 marks]
As the p-value is <A> than 0.05, the null hypothesis is <B>.
The odds of having a slow reaction time is <C> left and right handed people.
A: greater than ; less than
B: not rejected ; rejected
C: the same among ; different between
(Section F follows on the next page…)
Section F: Using statistical packages (12 marks)
The Council of Roberton has contacted you and is really interested in the association between physical activity and how this impacts on your reaction time in the test.
Is there a correlation between the physical activity reported and their reaction times? You are going to need to justify your answer using appropriate graphs, interpreting correlation coefficients and appropriate summary conclusions.
Draw a graph for the variables: physical activity and reaction time.
Attach the graph as a file below.
In the text box, type the file name only. [5 marks]
What is your line of best fit? (All numbers to 4 decimal places) [1 mark]
What is the predicted reaction time for someone with 3 hours of physical activity per week? (3 decimal places) [1 mark]
State your r (correlation) value (4 decimal places) [1 mark]
State your R2 (coefficient of determination) value (4 decimal places) [1 mark]
Using your results from this section interpret your data by completing this sentence. [3 marks]
“Overall, there was a [X] correlation between reaction times and physical activity. [Y] in physical activity were correlated with [Z] reaction times of individuals.”
= strong negative; weak negative; weak positive; strong positive
= increases ; decreases
= increased; decreased
Section G: Putting it all together (10 marks)
Congratulations! This is the end of your investigation.
Now it is time to finalise those conclusions and submit your recommendations to the Council.
53. Describe your results and conclusions. Based on these, suggest recommendations in the form of a public health response that the Council of Roberton could implement to help improve this situation (max 300 words) [10 marks]
